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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 25857a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25857.r1 | 25857a1 | \([0, 0, 1, -507, 4943]\) | \(-110592/17\) | \(-2215505331\) | \([]\) | \(16416\) | \(0.52225\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 25857a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 25857a do not have complex multiplication.Modular form 25857.2.a.a
sage: E.q_eigenform(10)