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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 66654.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
66654.r1 | 66654f1 | \([1, -1, 0, -2928114, -1934371148]\) | \(-25727239787761/101406816\) | \(-10943637306612960096\) | \([]\) | \(1520640\) | \(2.5108\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 66654.r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 66654.r do not have complex multiplication.Modular form 66654.2.a.r
sage: E.q_eigenform(10)