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SageMath
E = EllipticCurve("cm1")
E.isogeny_class()
Elliptic curves in class 119952.cm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 119952.cm1 | 119952dm1 | \([0, 0, 0, -77763, -7060606]\) | \(7253758561/1193859\) | \(8559190137286656\) | \([]\) | \(552960\) | \(1.7787\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 119952.cm1 has rank \(1\).
Complex multiplication
The elliptic curves in class 119952.cm do not have complex multiplication.Modular form 119952.2.a.cm
sage: E.q_eigenform(10)