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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 2736.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2736.o1 | 2736n3 | \([0, 0, 0, -61635, -5889598]\) | \(8671983378625/82308\) | \(245770371072\) | \([2]\) | \(6912\) | \(1.3480\) | |
| 2736.o2 | 2736n4 | \([0, 0, 0, -60195, -6177886]\) | \(-8078253774625/846825858\) | \(-2528608462774272\) | \([2]\) | \(13824\) | \(1.6945\) | |
| 2736.o3 | 2736n1 | \([0, 0, 0, -1155, 1154]\) | \(57066625/32832\) | \(98035826688\) | \([2]\) | \(2304\) | \(0.79865\) | \(\Gamma_0(N)\)-optimal |
| 2736.o4 | 2736n2 | \([0, 0, 0, 4605, 9218]\) | \(3616805375/2105352\) | \(-6286547386368\) | \([2]\) | \(4608\) | \(1.1452\) |
Rank
sage: E.rank()
The elliptic curves in class 2736.o have rank \(1\).
Complex multiplication
The elliptic curves in class 2736.o do not have complex multiplication.Modular form 2736.2.a.o
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
