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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 104742p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
104742.c1 | 104742p1 | \([1, -1, 0, -858679776, 9646255952896]\) | \(648817971720191270353/3006677182316544\) | \(324475078493158364756312064\) | \([]\) | \(77045760\) | \(3.9374\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 104742p1 has rank \(1\).
Complex multiplication
The elliptic curves in class 104742p do not have complex multiplication.Modular form 104742.2.a.p
sage: E.q_eigenform(10)