# Properties

 Label 11760e Number of curves $6$ Conductor $11760$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("11760.o1")

sage: E.isogeny_class()

## Elliptic curves in class 11760e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11760.o4 11760e1 [0, -1, 0, -8591, 309366] [2] 12288 $$\Gamma_0(N)$$-optimal
11760.o3 11760e2 [0, -1, 0, -8836, 291040] [2, 2] 24576
11760.o2 11760e3 [0, -1, 0, -33336, -2021760] [2, 2] 49152
11760.o5 11760e4 [0, -1, 0, 11744, 1427056] [2] 49152
11760.o1 11760e5 [0, -1, 0, -513536, -141471840] [2] 98304
11760.o6 11760e6 [0, -1, 0, 54864, -10982880] [2] 98304

## Rank

sage: E.rank()

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

## Modular form 11760.2.a.o

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + q^{9} + 4q^{11} + 2q^{13} + q^{15} - 2q^{17} - 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.