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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 13005c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13005.m1 | 13005c1 | \([1, -1, 0, 19020, -688249]\) | \(462866157/390625\) | \(-642165563671875\) | \([]\) | \(48384\) | \(1.5290\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 13005c1 has rank \(0\).
Complex multiplication
The elliptic curves in class 13005c do not have complex multiplication.Modular form 13005.2.a.c
sage: E.q_eigenform(10)