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SageMath
E = EllipticCurve("ew1")
E.isogeny_class()
Elliptic curves in class 455175ew
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 455175.ew1 | 455175ew1 | \([1, -1, 0, -37368730917, 2780431649539866]\) | \(-72628961394279272329/24608375505\) | \(-1955338135556343257686640625\) | \([]\) | \(655672320\) | \(4.5938\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 455175ew1 has rank \(0\).
Complex multiplication
The elliptic curves in class 455175ew do not have complex multiplication.Modular form 455175.2.a.ew
sage: E.q_eigenform(10)