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SageMath
E = EllipticCurve("cl1")
E.isogeny_class()
Elliptic curves in class 67760cl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 67760.cj4 | 67760cl1 | \([0, -1, 0, 19320, 8441072]\) | \(109902239/4312000\) | \(-31289225347072000\) | \([2]\) | \(552960\) | \(1.8450\) | \(\Gamma_0(N)\)-optimal |
| 67760.cj2 | 67760cl2 | \([0, -1, 0, -522760, 139407600]\) | \(2177286259681/105875000\) | \(768262229504000000\) | \([2]\) | \(1105920\) | \(2.1916\) | |
| 67760.cj3 | 67760cl3 | \([0, -1, 0, -174280, -231003408]\) | \(-80677568161/3131816380\) | \(-22725442592641761280\) | \([2]\) | \(1658880\) | \(2.3943\) | |
| 67760.cj1 | 67760cl4 | \([0, -1, 0, -6814760, -6807734800]\) | \(4823468134087681/30382271150\) | \(220463295122494054400\) | \([2]\) | \(3317760\) | \(2.7409\) |
Rank
sage: E.rank()
The elliptic curves in class 67760cl have rank \(1\).
Complex multiplication
The elliptic curves in class 67760cl do not have complex multiplication.Modular form 67760.2.a.cl
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
