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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 277350r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
277350.r1 | 277350r1 | \([1, 1, 0, -2575, -50375]\) | \(523181/12\) | \(43335937500\) | \([]\) | \(282240\) | \(0.82741\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 277350r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 277350r do not have complex multiplication.Modular form 277350.2.a.r
sage: E.q_eigenform(10)