# Properties

 Label 69360du Number of curves 8 Conductor 69360 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("69360.cw1")

sage: E.isogeny_class()

## Elliptic curves in class 69360du

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
69360.cw8 69360du1 [0, 1, 0, 6840, -666252] [2] 221184 $$\Gamma_0(N)$$-optimal
69360.cw6 69360du2 [0, 1, 0, -85640, -8767500] [2, 2] 442368
69360.cw7 69360du3 [0, 1, 0, -62520, 19670100] [2] 663552
69360.cw5 69360du4 [0, 1, 0, -316840, 59020340] [2] 884736
69360.cw4 69360du5 [0, 1, 0, -1334120, -593555532] [2] 884736
69360.cw3 69360du6 [0, 1, 0, -1542200, 735243348] [2, 2] 1327104
69360.cw1 69360du7 [0, 1, 0, -24662200, 47132459348] [2] 2654208
69360.cw2 69360du8 [0, 1, 0, -2097080, 158390100] [2] 2654208

## Rank

sage: E.rank()

The elliptic curves in class 69360du have rank $$0$$.

## Modular form 69360.2.a.cw

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} - 4q^{7} + q^{9} + 2q^{13} + q^{15} + 4q^{19} + O(q^{20})$$

## 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.