# Properties

 Label 11760cd Number of curves 8 Conductor 11760 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("11760.bp1")

sage: E.isogeny_class()

## Elliptic curves in class 11760cd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11760.bp7 11760cd1 [0, 1, 0, -390056, 93598644] [2] 110592 $$\Gamma_0(N)$$-optimal
11760.bp6 11760cd2 [0, 1, 0, -452776, 61410740] [2, 2] 221184
11760.bp5 11760cd3 [0, 1, 0, -1154456, -363230316] [2] 331776
11760.bp4 11760cd4 [0, 1, 0, -3416296, -2388827596] [2] 442368
11760.bp8 11760cd5 [0, 1, 0, 1507224, 452626740] [2] 442368
11760.bp2 11760cd6 [0, 1, 0, -17210776, -27485566060] [2, 2] 663552
11760.bp1 11760cd7 [0, 1, 0, -275366296, -1758883007596] [2] 1327104
11760.bp3 11760cd8 [0, 1, 0, -15956376, -31660711020] [2] 1327104

## Rank

sage: E.rank()

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

## Modular form 11760.2.a.bp

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + q^{9} - 2q^{13} - q^{15} + 6q^{17} + 8q^{19} + O(q^{20})$$

## 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.