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SageMath
sage: E = EllipticCurve("7056.bd1")
sage: E.isogeny_class()
Elliptic curves in class 7056.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 7056.bd1 | 7056bp6 | [0, 0, 0, -19266555, 32550241066] | [2] | 165888 | |
| 7056.bd2 | 7056bp5 | [0, 0, 0, -1203195, 509453098] | [2] | 82944 | |
| 7056.bd3 | 7056bp4 | [0, 0, 0, -250635, 39587002] | [2] | 55296 | |
| 7056.bd4 | 7056bp2 | [0, 0, 0, -74235, -7779926] | [2] | 18432 | |
| 7056.bd5 | 7056bp1 | [0, 0, 0, -3675, -173558] | [2] | 9216 | \(\Gamma_0(N)\)-optimal |
| 7056.bd6 | 7056bp3 | [0, 0, 0, 31605, 3629626] | [2] | 27648 |
Rank
sage: E.rank()
The elliptic curves in class 7056.bd have rank \(0\).
Modular form 7056.2.a.bd
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
