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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 412224i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
412224.i1 | 412224i1 | \([0, -1, 0, -218276289, -536405363775]\) | \(4387362075365553105987313/2064688435007280119808\) | \(541245685106548439726948352\) | \([]\) | \(156764160\) | \(3.8239\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 412224i1 has rank \(1\).
Complex multiplication
The elliptic curves in class 412224i do not have complex multiplication.Modular form 412224.2.a.i
sage: E.q_eigenform(10)