# Properties

 Label 11760.bg Number of curves $4$ Conductor $11760$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bg1")

sage: E.isogeny_class()

## Elliptic curves in class 11760.bg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11760.bg1 11760bx3 [0, -1, 0, -292840, 61092592]  73728
11760.bg2 11760bx2 [0, -1, 0, -18440, 944112] [2, 2] 36864
11760.bg3 11760bx1 [0, -1, 0, -2760, -34320]  18432 $$\Gamma_0(N)$$-optimal
11760.bg4 11760bx4 [0, -1, 0, 5080, 3164400]  73728

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 11760.2.a.bg

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + q^{9} + 4q^{11} + 2q^{13} - q^{15} + 6q^{17} + O(q^{20})$$

## 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. 