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SageMath
sage: E = EllipticCurve("7623.g1")
sage: E.isogeny_class()
Elliptic curves in class 7623p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 7623.g6 | 7623p1 | [1, -1, 1, 1066, -3220] | [2] | 5120 | \(\Gamma_0(N)\)-optimal |
| 7623.g5 | 7623p2 | [1, -1, 1, -4379, -22822] | [2, 2] | 10240 | |
| 7623.g2 | 7623p3 | [1, -1, 1, -53384, -4727302] | [2, 2] | 20480 | |
| 7623.g3 | 7623p4 | [1, -1, 1, -42494, 3361790] | [2] | 20480 | |
| 7623.g1 | 7623p5 | [1, -1, 1, -853799, -303442180] | [2] | 40960 | |
| 7623.g4 | 7623p6 | [1, -1, 1, -37049, -7687204] | [2] | 40960 |
Rank
sage: E.rank()
The elliptic curves in class 7623p have rank \(0\).
Modular form 7623.2.a.g
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
