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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 257754.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
257754.e1 | 257754e1 | \([1, 1, 0, -884096, 319610256]\) | \(-4499807642857/279888\) | \(-4753495492419408\) | \([]\) | \(4727808\) | \(2.0675\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 257754.e1 has rank \(2\).
Complex multiplication
The elliptic curves in class 257754.e do not have complex multiplication.Modular form 257754.2.a.e
sage: E.q_eigenform(10)