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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 189630.co
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 189630.co1 | 189630dc1 | \([1, -1, 0, -19854, 1986228]\) | \(-10091699281/13932000\) | \(-1194893597772000\) | \([]\) | \(1451520\) | \(1.5855\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 189630.co1 has rank \(0\).
Complex multiplication
The elliptic curves in class 189630.co do not have complex multiplication.Modular form 189630.2.a.co
sage: E.q_eigenform(10)