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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 123840.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
123840.r1 | 123840bo1 | \([0, 0, 0, -25968, 10671392]\) | \(-162140591104/4025041875\) | \(-48074842552320000\) | \([]\) | \(786432\) | \(1.8816\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 123840.r1 has rank \(0\).
Complex multiplication
The elliptic curves in class 123840.r do not have complex multiplication.Modular form 123840.2.a.r
sage: E.q_eigenform(10)