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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 4002.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4002.e1 | 4002d1 | \([1, 0, 1, -699, 14470]\) | \(-37693095294889/69371756544\) | \(-69371756544\) | \([]\) | \(3840\) | \(0.77025\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4002.e1 has rank \(0\).
Complex multiplication
The elliptic curves in class 4002.e do not have complex multiplication.Modular form 4002.2.a.e
sage: E.q_eigenform(10)