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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 51800.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
51800.r1 | 51800x1 | \([0, 1, 0, 772, 3773]\) | \(25408728832/17373979\) | \(-34747958000\) | \([]\) | \(44928\) | \(0.71125\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 51800.r1 has rank \(2\).
Complex multiplication
The elliptic curves in class 51800.r do not have complex multiplication.Modular form 51800.2.a.r
sage: E.q_eigenform(10)