Show commands:
SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 142296bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
142296.br4 | 142296bo1 | \([0, -1, 0, 3953, 2619520]\) | \(2048/891\) | \(-2971269450548784\) | \([2]\) | \(829440\) | \(1.6481\) | \(\Gamma_0(N)\)-optimal |
142296.br3 | 142296bo2 | \([0, -1, 0, -262852, 50644420]\) | \(37642192/1089\) | \(58104824810731776\) | \([2, 2]\) | \(1658880\) | \(1.9946\) | |
142296.br1 | 142296bo3 | \([0, -1, 0, -4175992, 3286028572]\) | \(37736227588/33\) | \(7043009067967488\) | \([2]\) | \(3317760\) | \(2.3412\) | |
142296.br2 | 142296bo4 | \([0, -1, 0, -618592, -115415012]\) | \(122657188/43923\) | \(9374245069464726528\) | \([2]\) | \(3317760\) | \(2.3412\) |
Rank
sage: E.rank()
The elliptic curves in class 142296bo have rank \(0\).
Complex multiplication
The elliptic curves in class 142296bo do not have complex multiplication.Modular form 142296.2.a.bo
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.