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SageMath
E = EllipticCurve("fr1")
E.isogeny_class()
Elliptic curves in class 283920fr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 283920.fr1 | 283920fr1 | \([0, 1, 0, -95541, -11398230]\) | \(1248870793216/42525\) | \(3284160843600\) | \([2]\) | \(1036800\) | \(1.4934\) | \(\Gamma_0(N)\)-optimal |
| 283920.fr2 | 283920fr2 | \([0, 1, 0, -91316, -12447720]\) | \(-68150496976/14467005\) | \(-17876344303883520\) | \([2]\) | \(2073600\) | \(1.8399\) |
Rank
sage: E.rank()
The elliptic curves in class 283920fr have rank \(0\).
Complex multiplication
The elliptic curves in class 283920fr do not have complex multiplication.Modular form 283920.2.a.fr
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.
