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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 84966.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
84966.r1 | 84966g1 | \([1, 1, 0, -3575947, -3610622147]\) | \(-301935091801/161243136\) | \(-2700628006834982117376\) | \([]\) | \(4725864\) | \(2.8163\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 84966.r1 has rank \(0\).
Complex multiplication
The elliptic curves in class 84966.r do not have complex multiplication.Modular form 84966.2.a.r
sage: E.q_eigenform(10)