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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 9576x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9576.f1 | 9576x1 | \([0, 0, 0, -44598531, 114606150766]\) | \(13141891860831409148932/4237307541832617\) | \(3163133130747881260032\) | \([2]\) | \(752640\) | \(3.0999\) | \(\Gamma_0(N)\)-optimal |
| 9576.f2 | 9576x2 | \([0, 0, 0, -38548011, 146820329350]\) | \(-4242991426585187031506/3781894171664380023\) | \(-5646337743141546059298816\) | \([2]\) | \(1505280\) | \(3.4465\) |
Rank
sage: E.rank()
The elliptic curves in class 9576x have rank \(0\).
Complex multiplication
The elliptic curves in class 9576x do not have complex multiplication.Modular form 9576.2.a.x
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
