# Properties

 Label 11760.b Number of curves $6$ Conductor $11760$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("11760.b1")

sage: E.isogeny_class()

## Elliptic curves in class 11760.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11760.b1 11760br5 [0, -1, 0, -13171216, -18394301120] [2] 294912
11760.b2 11760br3 [0, -1, 0, -823216, -287193920] [2, 2] 147456
11760.b3 11760br6 [0, -1, 0, -768336, -327190464] [2] 294912
11760.b4 11760br4 [0, -1, 0, -290096, 56938176] [2] 147456
11760.b5 11760br2 [0, -1, 0, -54896, -3837504] [2, 2] 73728
11760.b6 11760br1 [0, -1, 0, 7824, -375360] [2] 36864 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 11760.2.a.b

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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.