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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 116688ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
116688.u1 | 116688ba1 | \([0, 1, 0, 18304, 678694068]\) | \(165568631260031/48580832601759744\) | \(-198987090336807911424\) | \([]\) | \(3075072\) | \(2.5739\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 116688ba1 has rank \(1\).
Complex multiplication
The elliptic curves in class 116688ba do not have complex multiplication.Modular form 116688.2.a.ba
sage: E.q_eigenform(10)