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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 9240.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9240.z1 | 9240bc1 | \([0, 1, 0, -308056, 65707520]\) | \(3157287870431675236/673876665\) | \(690049704960\) | \([2]\) | \(49920\) | \(1.6568\) | \(\Gamma_0(N)\)-optimal |
| 9240.z2 | 9240bc2 | \([0, 1, 0, -306976, 66192224]\) | \(-1562098599189850178/23071165962075\) | \(-47249747890329600\) | \([2]\) | \(99840\) | \(2.0034\) |
Rank
sage: E.rank()
The elliptic curves in class 9240.z have rank \(0\).
Complex multiplication
The elliptic curves in class 9240.z do not have complex multiplication.Modular form 9240.2.a.z
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 LMFDB 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 LMFDB labels.
