## The modular curve $X_{207d}$

Curve name $X_{207d}$
Index $96$
Level $16$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 7 & 0 \\ 0 & 3 \end{matrix}\right], \left[ \begin{matrix} 1 & 3 \\ 0 & 3 \end{matrix}\right], \left[ \begin{matrix} 7 & 7 \\ 0 & 5 \end{matrix}\right], \left[ \begin{matrix} 3 & 3 \\ 8 & 1 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $12$ $X_{27}$ $8$ $48$ $X_{92c}$
Meaning/Special name
Chosen covering $X_{207}$
Curves that $X_{207d}$ minimally covers
Curves that minimally cover $X_{207d}$
Curves that minimally cover $X_{207d}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -108t^{30} - 6480t^{29} - 74736t^{28} + 2830464t^{27} + 111428352t^{26} + 1831624704t^{25} + 17489184768t^{24} + 98262319104t^{23} + 227672211456t^{22} - 1027495231488t^{21} - 11106315730944t^{20} - 40916718452736t^{19} - 33829898158080t^{18} + 335189750317056t^{17} + 1579216105635840t^{16} + 2681518002536448t^{15} - 2165113482117120t^{14} - 20949359847800832t^{13} - 45491469233946624t^{12} - 33668963745398784t^{11} + 59682904199921664t^{10} + 206071019033591808t^{9} + 293419830516645888t^{8} + 245836506319552512t^{7} + 119645281921794048t^{6} + 24313500625010688t^{5} - 5135818813341696t^{4} - 3562417673994240t^{3} - 474989023199232t^{2}$ $B(t) = 432t^{45} + 38880t^{44} + 2524608t^{43} + 119035008t^{42} + 3749856768t^{41} + 79222800384t^{40} + 1133704581120t^{39} + 10574164942848t^{38} + 50047313412096t^{37} - 180547243868160t^{36} - 5547197342416896t^{35} - 51541099444961280t^{34} - 274005871363620864t^{33} - 699224096193380352t^{32} + 1539397909034827776t^{31} + 22876765719757848576t^{30} + 98016765829164564480t^{29} + 146610969832203485184t^{28} - 607190132200411496448t^{27} - 4235795678515314032640t^{26} - 10416869423878735134720t^{25} + 83334955391029881077760t^{23} + 271090923424980098088960t^{22} + 310881347686610686181376t^{21} - 600518532432705475313664t^{20} - 3211813382690064448880640t^{19} - 5997006872840201457106944t^{18} - 3228351403728207140093952t^{17} + 11731033694241119935660032t^{16} + 36776445513085454219476992t^{15} + 55341834128998112396574720t^{14} + 47650062340277363835666432t^{13} + 12407112124746939771125760t^{12} - 27513801517774654823989248t^{11} - 46505669234730873957384192t^{10} - 39888683820939501990051840t^{9} - 22299235893039349213691904t^{8} - 8443926771528766234558464t^{7} - 2144344070691376041295872t^{6} - 363834356737810341298176t^{5} - 44825588099114210426880t^{4} - 3984496719921263149056t^{3}$
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 + 35843892x + 3741877063568$, with conductor $141120$
Generic density of odd order reductions $139/1344$