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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 70602bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
70602.be1 | 70602bg1 | \([1, 0, 0, -494659, 314997185]\) | \(-194218207880195897/509703742291968\) | \(-35129291622504726528\) | \([]\) | \(2185920\) | \(2.4380\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 70602bg1 has rank \(1\).
Complex multiplication
The elliptic curves in class 70602bg do not have complex multiplication.Modular form 70602.2.a.bg
sage: E.q_eigenform(10)