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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 25050e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25050.a1 | 25050e1 | \([1, 1, 0, -7575, -1762875]\) | \(-24616775429/670674672\) | \(-1309911468750000\) | \([]\) | \(234240\) | \(1.5813\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 25050e1 has rank \(1\).
Complex multiplication
The elliptic curves in class 25050e do not have complex multiplication.Modular form 25050.2.a.e
sage: E.q_eigenform(10)