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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 272734w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 272734.w1 | 272734w1 | \([1, -1, 0, -1569332, 755084182]\) | \(345893625/1058\) | \(1307408996457446498\) | \([]\) | \(4790016\) | \(2.3446\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 272734w1 has rank \(0\).
Complex multiplication
The elliptic curves in class 272734w do not have complex multiplication.Modular form 272734.2.a.w
sage: E.q_eigenform(10)