# Properties

 Label 11760co Number of curves $8$ Conductor $11760$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("11760.cl1")

sage: E.isogeny_class()

## Elliptic curves in class 11760co

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11760.cl7 11760co1 [0, 1, 0, -32160, -791820] [2] 55296 $$\Gamma_0(N)$$-optimal
11760.cl5 11760co2 [0, 1, 0, -283040, 57311988] [2, 2] 110592
11760.cl4 11760co3 [0, 1, 0, -2101920, -1173630732] [2] 165888
11760.cl2 11760co4 [0, 1, 0, -4516640, 3693127668] [2] 221184
11760.cl6 11760co5 [0, 1, 0, -63520, 144154100] [4] 221184
11760.cl3 11760co6 [0, 1, 0, -2117600, -1155247500] [2, 2] 331776
11760.cl1 11760co7 [0, 1, 0, -5057600, 2752600500] [2] 663552
11760.cl8 11760co8 [0, 1, 0, 571520, -3886317772] [4] 663552

## Rank

sage: E.rank()

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

## Modular form 11760.2.a.cl

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + q^{9} - 2q^{13} + q^{15} + 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.