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SageMath
E = EllipticCurve("gp1")
E.isogeny_class()
Elliptic curves in class 139650.gp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
139650.gp1 | 139650di1 | \([1, 1, 1, -41503638, -102932591469]\) | \(-172041783999846385/1179967488\) | \(-54227341795200000000\) | \([]\) | \(12579840\) | \(2.9673\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 139650.gp1 has rank \(1\).
Complex multiplication
The elliptic curves in class 139650.gp do not have complex multiplication.Modular form 139650.2.a.gp
sage: E.q_eigenform(10)