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SageMath
E = EllipticCurve("gw1")
E.isogeny_class()
Elliptic curves in class 227136gw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 227136.ix1 | 227136gw1 | \([0, 1, 0, -1281089, -624949857]\) | \(-20994006260678308/3063651608241\) | \(-33931730733808287744\) | \([]\) | \(7372800\) | \(2.4779\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 227136gw1 has rank \(0\).
Complex multiplication
The elliptic curves in class 227136gw do not have complex multiplication.Modular form 227136.2.a.gw
sage: E.q_eigenform(10)