# Properties

 Label 5610t Number of curves 8 Conductor 5610 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("5610.q1")

sage: E.isogeny_class()

## Elliptic curves in class 5610t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5610.q8 5610t1 [1, 0, 1, 43372, -1467502] [6] 55296 $$\Gamma_0(N)$$-optimal
5610.q7 5610t2 [1, 0, 1, -189908, -12291694] [2, 6] 110592
5610.q6 5610t3 [1, 0, 1, -780803, -272099842] [2] 165888
5610.q4 5610t4 [1, 0, 1, -2484908, -1506795694] [6] 221184
5610.q5 5610t5 [1, 0, 1, -1627388, 790397138] [6] 221184
5610.q3 5610t6 [1, 0, 1, -12577283, -17169377794] [2, 2] 331776
5610.q1 5610t7 [1, 0, 1, -201236483, -1098790303234] [2] 663552
5610.q2 5610t8 [1, 0, 1, -12661763, -16927055362] [2] 663552

## Rank

sage: E.rank()

The elliptic curves in class 5610t have rank $$0$$.

## Modular form5610.2.a.q

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - 4q^{7} - q^{8} + q^{9} - q^{10} + q^{11} + q^{12} + 2q^{13} + 4q^{14} + q^{15} + q^{16} - q^{17} - q^{18} - 4q^{19} + O(q^{20})$$

## 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.