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SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 429429ct
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
429429.ct1 | 429429ct1 | \([1, 1, 0, -544183, 154661434]\) | \(-30515071121161/85766121\) | \(-50091178853284569\) | \([]\) | \(5318784\) | \(2.0767\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 429429ct1 has rank \(2\).
Complex multiplication
The elliptic curves in class 429429ct do not have complex multiplication.Modular form 429429.2.a.ct
sage: E.q_eigenform(10)