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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 25215.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25215.d1 | 25215f1 | \([1, 0, 0, -691, 950]\) | \(21708480289/12301875\) | \(20679451875\) | \([]\) | \(18144\) | \(0.66931\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 25215.d1 has rank \(2\).
Complex multiplication
The elliptic curves in class 25215.d do not have complex multiplication.Modular form 25215.2.a.d
sage: E.q_eigenform(10)