# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("11760.ci1")

sage: E.isogeny_class()

## Elliptic curves in class 11760cp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11760.ci8 11760cp1 [0, 1, 0, 1160, 47060] [2] 13824 $$\Gamma_0(N)$$-optimal
11760.ci6 11760cp2 [0, 1, 0, -14520, 605268] [2, 2] 27648
11760.ci7 11760cp3 [0, 1, 0, -10600, -1378252] [2] 41472
11760.ci5 11760cp4 [0, 1, 0, -53720, -4145772] [2] 55296
11760.ci4 11760cp5 [0, 1, 0, -226200, 41332500] [2] 55296
11760.ci3 11760cp6 [0, 1, 0, -261480, -51453900] [2, 2] 82944
11760.ci1 11760cp7 [0, 1, 0, -4181480, -3292509900] [2] 165888
11760.ci2 11760cp8 [0, 1, 0, -355560, -11225292] [2] 165888

## Rank

sage: E.rank()

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

## Modular form 11760.2.a.ci

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.