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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 54390r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54390.u1 | 54390r1 | \([1, 0, 1, -9434, 354512]\) | \(-789145184521/6853140\) | \(-806265067860\) | \([]\) | \(138240\) | \(1.1093\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 54390r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 54390r do not have complex multiplication.Modular form 54390.2.a.r
sage: E.q_eigenform(10)