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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 36414.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
36414.p1 | 36414bb1 | \([1, -1, 0, -236745, 44552389]\) | \(-288568081/1176\) | \(-5980344757199064\) | \([]\) | \(235008\) | \(1.8834\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 36414.p1 has rank \(1\).
Complex multiplication
The elliptic curves in class 36414.p do not have complex multiplication.Modular form 36414.2.a.p
sage: E.q_eigenform(10)