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SageMath
E = EllipticCurve("ko1")
E.isogeny_class()
Elliptic curves in class 487872.ko
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 487872.ko1 | 487872ko1 | \([0, 0, 0, 3541428, 9166234968]\) | \(137566156032/1096135733\) | \(-39139177573209681386496\) | \([]\) | \(30965760\) | \(3.0166\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 487872.ko1 has rank \(0\).
Complex multiplication
The elliptic curves in class 487872.ko do not have complex multiplication.Modular form 487872.2.a.ko
sage: E.q_eigenform(10)