Show commands:
SageMath
E = EllipticCurve("em1")
E.isogeny_class()
Elliptic curves in class 123840.em
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
123840.em1 | 123840cq1 | \([0, 0, 0, -167232, -26414944]\) | \(-43304636317696/176326875\) | \(-2106036910080000\) | \([]\) | \(786432\) | \(1.7965\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 123840.em1 has rank \(1\).
Complex multiplication
The elliptic curves in class 123840.em do not have complex multiplication.Modular form 123840.2.a.em
sage: E.q_eigenform(10)