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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 344800k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
344800.k1 | 344800k1 | \([0, 0, 0, -25, -1000]\) | \(-1728/431\) | \(-431000000\) | \([]\) | \(324864\) | \(0.33604\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 344800k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 344800k do not have complex multiplication.Modular form 344800.2.a.k
sage: E.q_eigenform(10)