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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 4002.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4002.p1 | 4002q1 | \([1, 0, 0, -1326, -88956]\) | \(-257854523348449/3260780423424\) | \(-3260780423424\) | \([]\) | \(5760\) | \(1.0828\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4002.p1 has rank \(1\).
Complex multiplication
The elliptic curves in class 4002.p do not have complex multiplication.Modular form 4002.2.a.p
sage: E.q_eigenform(10)