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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 193600.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
193600.z1 | 193600t1 | \([0, 1, 0, -8680833, 9841230463]\) | \(233551483825/8192\) | \(2537553920000000000\) | \([]\) | \(7188480\) | \(2.6216\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 193600.z1 has rank \(1\).
Complex multiplication
The elliptic curves in class 193600.z do not have complex multiplication.Modular form 193600.2.a.z
sage: E.q_eigenform(10)