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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 206310.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
206310.p1 | 206310cg1 | \([1, 1, 0, 27233, -22503419]\) | \(15087533111/1488015360\) | \(-220279676663255040\) | \([]\) | \(2534400\) | \(2.0072\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 206310.p1 has rank \(1\).
Complex multiplication
The elliptic curves in class 206310.p do not have complex multiplication.Modular form 206310.2.a.p
sage: E.q_eigenform(10)