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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 106470x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 106470.j1 | 106470x1 | \([1, -1, 0, 603045, -209329925]\) | \(1164854099347679/1581966996750\) | \(-32938085798354850750\) | \([]\) | \(2741760\) | \(2.4308\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 106470x1 has rank \(0\).
Complex multiplication
The elliptic curves in class 106470x do not have complex multiplication.Modular form 106470.2.a.x
sage: E.q_eigenform(10)