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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 42526.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
42526.a1 | 42526b1 | \([1, 0, 1, -78, 272]\) | \(-51520374361/3742288\) | \(-3742288\) | \([]\) | \(21120\) | \(0.010740\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 42526.a1 has rank \(3\).
Complex multiplication
The elliptic curves in class 42526.a do not have complex multiplication.Modular form 42526.2.a.a
sage: E.q_eigenform(10)