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SageMath
E = EllipticCurve("fp1")
E.isogeny_class()
Elliptic curves in class 68400fp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
68400.z1 | 68400fp1 | \([0, 0, 0, -4800, -128500]\) | \(-4194304/19\) | \(-55404000000\) | \([]\) | \(80640\) | \(0.91309\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 68400fp1 has rank \(0\).
Complex multiplication
The elliptic curves in class 68400fp do not have complex multiplication.Modular form 68400.2.a.fp
sage: E.q_eigenform(10)