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SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 17472.cu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17472.cu1 | 17472cw3 | \([0, 1, 0, -125217, -17093025]\) | \(828279937799497/193444524\) | \(50710321299456\) | \([2]\) | \(73728\) | \(1.6204\) | |
| 17472.cu2 | 17472cw2 | \([0, 1, 0, -8737, -203425]\) | \(281397674377/96589584\) | \(25320379908096\) | \([2, 2]\) | \(36864\) | \(1.2738\) | |
| 17472.cu3 | 17472cw1 | \([0, 1, 0, -3617, 80223]\) | \(19968681097/628992\) | \(164886478848\) | \([2]\) | \(18432\) | \(0.92722\) | \(\Gamma_0(N)\)-optimal |
| 17472.cu4 | 17472cw4 | \([0, 1, 0, 25823, -1385377]\) | \(7264187703863/7406095788\) | \(-1941463574249472\) | \([2]\) | \(73728\) | \(1.6204\) |
Rank
sage: E.rank()
The elliptic curves in class 17472.cu have rank \(0\).
Complex multiplication
The elliptic curves in class 17472.cu do not have complex multiplication.Modular form 17472.2.a.cu
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.
