Show commands:
SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 49686.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
49686.b1 | 49686s1 | \([1, 1, 0, -30846897, -67586632875]\) | \(-2380771254001/69009408\) | \(-94091158492310036348928\) | \([]\) | \(10838016\) | \(3.1875\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 49686.b1 has rank \(0\).
Complex multiplication
The elliptic curves in class 49686.b do not have complex multiplication.Modular form 49686.2.a.b
sage: E.q_eigenform(10)