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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 3680.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3680.j1 | 3680c1 | \([0, -1, 0, -125, -523]\) | \(-53157376/2875\) | \(-11776000\) | \([]\) | \(576\) | \(0.11531\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 3680.j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 3680.j do not have complex multiplication.Modular form 3680.2.a.j
sage: E.q_eigenform(10)