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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 115920.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115920.e1 | 115920df4 | \([0, 0, 0, -70842603, -130433927398]\) | \(13167998447866683762601/5158996582031250000\) | \(15404681250000000000000000\) | \([2]\) | \(23592960\) | \(3.5317\) | |
| 115920.e2 | 115920df2 | \([0, 0, 0, -31893483, 67887201818]\) | \(1201550658189465626281/28577902500000000\) | \(85333159618560000000000\) | \([2, 2]\) | \(11796480\) | \(3.1851\) | |
| 115920.e3 | 115920df1 | \([0, 0, 0, -31709163, 68726631962]\) | \(1180838681727016392361/692428800000\) | \(2067581317939200000\) | \([2]\) | \(5898240\) | \(2.8385\) | \(\Gamma_0(N)\)-optimal |
| 115920.e4 | 115920df3 | \([0, 0, 0, 4106517, 212484801818]\) | \(2564821295690373719/6533572090396050000\) | \(-19509141724769158963200000\) | \([2]\) | \(23592960\) | \(3.5317\) |
Rank
sage: E.rank()
The elliptic curves in class 115920.e have rank \(0\).
Complex multiplication
The elliptic curves in class 115920.e do not have complex multiplication.Modular form 115920.2.a.e
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
