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SageMath
E = EllipticCurve("cm1")
E.isogeny_class()
Elliptic curves in class 139650.cm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
139650.cm1 | 139650fi1 | \([1, 0, 1, -593171, 1128294038]\) | \(-1569510182075597/36491419872936\) | \(-536647382078880933000\) | \([]\) | \(7354368\) | \(2.6584\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 139650.cm1 has rank \(1\).
Complex multiplication
The elliptic curves in class 139650.cm do not have complex multiplication.Modular form 139650.2.a.cm
sage: E.q_eigenform(10)