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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 209484z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
209484.bf1 | 209484z1 | \([0, 0, 0, -49197, 6704017]\) | \(-7626496/6831\) | \(-11795023552100976\) | \([]\) | \(1216512\) | \(1.7809\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 209484z1 has rank \(0\).
Complex multiplication
The elliptic curves in class 209484z do not have complex multiplication.Modular form 209484.2.a.z
sage: E.q_eigenform(10)