# Properties

 Label 11760bo Number of curves $2$ Conductor $11760$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("11760.f1")

sage: E.isogeny_class()

## Elliptic curves in class 11760bo

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11760.f1 11760bo1 [0, -1, 0, -11776, -184064]  32256 $$\Gamma_0(N)$$-optimal
11760.f2 11760bo2 [0, -1, 0, 43104, -1457280]  64512

## Rank

sage: E.rank()

The elliptic curves in class 11760bo have rank $$1$$.

## Modular form 11760.2.a.f

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 