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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 254100e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
254100.e1 | 254100e1 | \([0, -1, 0, -486218, -130751883]\) | \(-17939139239680/66706983\) | \(-47270195804185200\) | \([]\) | \(2882880\) | \(2.0596\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 254100e1 has rank \(1\).
Complex multiplication
The elliptic curves in class 254100e do not have complex multiplication.Modular form 254100.2.a.e
sage: E.q_eigenform(10)