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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 55506u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 55506.s1 | 55506u1 | \([1, 0, 1, -612266, -179395054]\) | \(50741013625/1587762\) | \(794272245135783282\) | \([]\) | \(1002240\) | \(2.2098\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 55506u1 has rank \(0\).
Complex multiplication
The elliptic curves in class 55506u do not have complex multiplication.Modular form 55506.2.a.u
sage: E.q_eigenform(10)