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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 75213c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
75213.c1 | 75213c1 | \([0, 0, 1, -219, 643]\) | \(1593413632/676917\) | \(493472493\) | \([]\) | \(71680\) | \(0.36475\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 75213c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 75213c do not have complex multiplication.Modular form 75213.2.a.c
sage: E.q_eigenform(10)