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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 250470z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
250470.z1 | 250470z1 | \([1, -1, 0, -20726415, 38026317181]\) | \(-6301258312598161/349801250000\) | \(-54662610296830511250000\) | \([]\) | \(31933440\) | \(3.1206\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 250470z1 has rank \(1\).
Complex multiplication
The elliptic curves in class 250470z do not have complex multiplication.Modular form 250470.2.a.z
sage: E.q_eigenform(10)