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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 50700p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
50700.c1 | 50700p1 | \([0, -1, 0, -10243653, -12829937823]\) | \(-769623354048512/15247889631\) | \(-2355156828861359328000\) | \([]\) | \(2822400\) | \(2.8938\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 50700p1 has rank \(1\).
Complex multiplication
The elliptic curves in class 50700p do not have complex multiplication.Modular form 50700.2.a.p
sage: E.q_eigenform(10)