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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 139240.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 139240.c1 | 139240b3 | \([0, 0, 0, -372467, 87491454]\) | \(132304644/5\) | \(215964332241920\) | \([2]\) | \(831488\) | \(1.8366\) | |
| 139240.c2 | 139240b2 | \([0, 0, 0, -24367, 1232274]\) | \(148176/25\) | \(269955415302400\) | \([2, 2]\) | \(415744\) | \(1.4900\) | |
| 139240.c3 | 139240b1 | \([0, 0, 0, -6962, -205379]\) | \(55296/5\) | \(3374442691280\) | \([2]\) | \(207872\) | \(1.1434\) | \(\Gamma_0(N)\)-optimal |
| 139240.c4 | 139240b4 | \([0, 0, 0, 45253, 6982886]\) | \(237276/625\) | \(-26995541530240000\) | \([2]\) | \(831488\) | \(1.8366\) |
Rank
sage: E.rank()
The elliptic curves in class 139240.c have rank \(0\).
Complex multiplication
The elliptic curves in class 139240.c do not have complex multiplication.Modular form 139240.2.a.c
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.
