# Properties

 Label 11760.br Number of curves $4$ Conductor $11760$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 11760.br

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11760.br1 11760ce3 [0, 1, 0, -88216, -10113580] [2] 49152
11760.br2 11760ce2 [0, 1, 0, -5896, -136396] [2, 2] 24576
11760.br3 11760ce1 [0, 1, 0, -1976, 31380] [2] 12288 $$\Gamma_0(N)$$-optimal
11760.br4 11760ce4 [0, 1, 0, 13704, -834156] [2] 49152

## Rank

sage: E.rank()

The elliptic curves in class 11760.br have rank $$0$$.

## Complex multiplication

The elliptic curves in class 11760.br do not have complex multiplication.

## Modular form 11760.2.a.br

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.