Curve name | $X_{1}$ |

Index | $1$ |

Level | $1$ |

Genus | $0$ |

Does the subgroup contain $-I$? | Yes |

Generating matrices | |

Images in lower levels | |

Meaning/Special name | $X(1)$ |

Chosen covering | |

Curves that $X_{1}$ minimally covers | |

Curves that minimally cover $X_{1}$ | $X_{2}$, $X_{3}$, $X_{4}$, $X_{5}$, $X_{6}$, $X_{7}$ |

Curves that minimally cover $X_{1}$ and have infinitely many rational points. | $X_{2}$, $X_{3}$, $X_{4}$, $X_{5}$, $X_{6}$, $X_{7}$ |

Model | $\mathbb{P}^{1} \cong \mathbb{Q}(f_{1})$, where $f_{1} = j$ |

Info about rational points | None |

Comments on finding rational points | None |

Elliptic curve whose $2$-adic image is the subgroup | $y^2 + y = x^3 - x^2 - 10x - 20$, with conductor $11$ |

Generic density of odd order reductions | $11/21$ |