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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 363726.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 363726.be1 | 363726be4 | \([1, -1, 0, -93116601, -345827521715]\) | \(69138733474448992297/234724512\) | \(303139188787156128\) | \([2]\) | \(25804800\) | \(2.9994\) | |
| 363726.be2 | 363726be3 | \([1, -1, 0, -7739001, -1537714931]\) | \(39691253323129897/22176528704352\) | \(28640276485279678901088\) | \([2]\) | \(25804800\) | \(2.9994\) | |
| 363726.be3 | 363726be2 | \([1, -1, 0, -5822361, -5397444563]\) | \(16901976846788137/31100027904\) | \(40164689873022206976\) | \([2, 2]\) | \(12902400\) | \(2.6528\) | |
| 363726.be4 | 363726be1 | \([1, -1, 0, -246681, -139578323]\) | \(-1285429208617/5778702336\) | \(-7463008969329475584\) | \([2]\) | \(6451200\) | \(2.3062\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 363726.be have rank \(2\).
Complex multiplication
The elliptic curves in class 363726.be do not have complex multiplication.Modular form 363726.2.a.be
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
