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SageMath
E = EllipticCurve("gu1")
E.isogeny_class()
Elliptic curves in class 227136gu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 227136.je1 | 227136gu1 | \([0, 1, 0, -1086835169, -13870185658497]\) | \(-112205650221491190337/745029571313664\) | \(-942700085925100969833529344\) | \([]\) | \(153538560\) | \(4.0115\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 227136gu1 has rank \(1\).
Complex multiplication
The elliptic curves in class 227136gu do not have complex multiplication.Modular form 227136.2.a.gu
sage: E.q_eigenform(10)