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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 25392.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25392.be1 | 25392g6 | \([0, 1, 0, -203312, -35352972]\) | \(3065617154/9\) | \(2728597506048\) | \([2]\) | \(90112\) | \(1.6155\) | |
| 25392.be2 | 25392g4 | \([0, 1, 0, -34032, 2404932]\) | \(28756228/3\) | \(454766251008\) | \([2]\) | \(45056\) | \(1.2690\) | |
| 25392.be3 | 25392g3 | \([0, 1, 0, -12872, -540540]\) | \(1556068/81\) | \(12278688777216\) | \([2, 2]\) | \(45056\) | \(1.2690\) | |
| 25392.be4 | 25392g2 | \([0, 1, 0, -2292, 30780]\) | \(35152/9\) | \(341074688256\) | \([2, 2]\) | \(22528\) | \(0.92239\) | |
| 25392.be5 | 25392g1 | \([0, 1, 0, 353, 3272]\) | \(2048/3\) | \(-7105722672\) | \([2]\) | \(11264\) | \(0.57582\) | \(\Gamma_0(N)\)-optimal |
| 25392.be6 | 25392g5 | \([0, 1, 0, 8288, -2123308]\) | \(207646/6561\) | \(-1989147581908992\) | \([2]\) | \(90112\) | \(1.6155\) |
Rank
sage: E.rank()
The elliptic curves in class 25392.be have rank \(1\).
Complex multiplication
The elliptic curves in class 25392.be do not have complex multiplication.Modular form 25392.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
