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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 40656.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
40656.r1 | 40656g1 | \([0, -1, 0, -19521, -876291]\) | \(123904/21\) | \(139439594654976\) | \([]\) | \(118272\) | \(1.4348\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 40656.r1 has rank \(0\).
Complex multiplication
The elliptic curves in class 40656.r do not have complex multiplication.Modular form 40656.2.a.r
sage: E.q_eigenform(10)