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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 112710.co
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 112710.co1 | 112710cw1 | \([1, 0, 0, -50581, 4374641]\) | \(-171352638803089/14236560\) | \(-1189051727760\) | \([]\) | \(373248\) | \(1.3610\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 112710.co1 has rank \(1\).
Complex multiplication
The elliptic curves in class 112710.co do not have complex multiplication.Modular form 112710.2.a.co
sage: E.q_eigenform(10)