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SageMath
E = EllipticCurve("cm1")
E.isogeny_class()
Elliptic curves in class 221760.cm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 221760.cm1 | 221760et1 | \([0, 0, 0, -206688, 36177248]\) | \(-81756451446784/24958395\) | \(-298101472542720\) | \([]\) | \(1105920\) | \(1.7545\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 221760.cm1 has rank \(0\).
Complex multiplication
The elliptic curves in class 221760.cm do not have complex multiplication.Modular form 221760.2.a.cm
sage: E.q_eigenform(10)