# Properties

 Label 142296.br Number of curves 4 Conductor 142296 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("142296.br1")

sage: E.isogeny_class()

## Elliptic curves in class 142296.br

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
142296.br1 142296bo3 [0, -1, 0, -4175992, 3286028572] [2] 3317760
142296.br2 142296bo4 [0, -1, 0, -618592, -115415012] [2] 3317760
142296.br3 142296bo2 [0, -1, 0, -262852, 50644420] [2, 2] 1658880
142296.br4 142296bo1 [0, -1, 0, 3953, 2619520] [2] 829440 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 142296.br have rank $$0$$.

## Modular form 142296.2.a.br

sage: E.q_eigenform(10)

$$q - q^{3} + 2q^{5} + q^{9} + 6q^{13} - 2q^{15} + 6q^{17} - 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.