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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 80223.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
80223.b1 | 80223r1 | \([0, 1, 1, -1734, 90668]\) | \(-39404941312/222861483\) | \(-3262914972603\) | \([]\) | \(188928\) | \(1.0851\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 80223.b1 has rank \(1\).
Complex multiplication
The elliptic curves in class 80223.b do not have complex multiplication.Modular form 80223.2.a.b
sage: E.q_eigenform(10)