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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 429429.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
429429.p1 | 429429p1 | \([0, 1, 1, -45812576, -111389515792]\) | \(5528367104/413343\) | \(795044746311592864460373\) | \([]\) | \(168030720\) | \(3.3315\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 429429.p1 has rank \(0\).
Complex multiplication
The elliptic curves in class 429429.p do not have complex multiplication.Modular form 429429.2.a.p
sage: E.q_eigenform(10)