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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 54978.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54978.z1 | 54978s1 | \([1, 0, 1, -1888, -178510]\) | \(-6321363049/113144724\) | \(-13311363633876\) | \([]\) | \(122880\) | \(1.1994\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 54978.z1 has rank \(1\).
Complex multiplication
The elliptic curves in class 54978.z do not have complex multiplication.Modular form 54978.2.a.z
sage: E.q_eigenform(10)