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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 409101p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
409101.p1 | 409101p1 | \([1, 0, 0, -219920, 39884109]\) | \(-925539769/5589\) | \(-7103249038654461\) | \([]\) | \(3104640\) | \(1.8811\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 409101p1 has rank \(0\).
Complex multiplication
The elliptic curves in class 409101p do not have complex multiplication.Modular form 409101.2.a.p
sage: E.q_eigenform(10)