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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 112710p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
112710.r1 | 112710p1 | \([1, 1, 0, -1045752, -489633984]\) | \(-62736640489/14976000\) | \(-30191524653124224000\) | \([]\) | \(3231360\) | \(2.4567\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 112710p1 has rank \(1\).
Complex multiplication
The elliptic curves in class 112710p do not have complex multiplication.Modular form 112710.2.a.p
sage: E.q_eigenform(10)