# Properties

 Label 176610by Number of curves $6$ Conductor $176610$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("176610.bs1")

sage: E.isogeny_class()

## Elliptic curves in class 176610by

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
176610.bs6 176610by1 [1, 0, 1, 8392, -413434] [2] 774144 $$\Gamma_0(N)$$-optimal
176610.bs5 176610by2 [1, 0, 1, -58888, -4288762] [2, 2] 1548288
176610.bs4 176610by3 [1, 0, 1, -311188, 63125798] [2] 3096576
176610.bs2 176610by4 [1, 0, 1, -883068, -319455194] [2, 2] 3096576
176610.bs3 176610by5 [1, 0, 1, -824198, -363866722] [2] 6193152
176610.bs1 176610by6 [1, 0, 1, -14128818, -20442398594] [2] 6193152

## Rank

sage: E.rank()

The elliptic curves in class 176610by have rank $$0$$.

## Modular form 176610.2.a.bs

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.