# Properties

 Label 176610.cy Number of curves $8$ Conductor $176610$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cy1")

sage: E.isogeny_class()

## Elliptic curves in class 176610.cy

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
176610.cy1 176610u8 $$[1, 1, 1, -295386550, -1954166401165]$$ $$4791901410190533590281/41160000$$ $$24482927892360000$$ $$[2]$$ $$27869184$$ $$3.1859$$
176610.cy2 176610u6 $$[1, 1, 1, -18462070, -30538193293]$$ $$1169975873419524361/108425318400$$ $$64493907971170406400$$ $$[2, 2]$$ $$13934592$$ $$2.8393$$
176610.cy3 176610u7 $$[1, 1, 1, -17116470, -35176745613]$$ $$-932348627918877961/358766164249920$$ $$-213402481281568888384320$$ $$[2]$$ $$27869184$$ $$3.1859$$
176610.cy4 176610u5 $$[1, 1, 1, -3664675, -2654284915]$$ $$9150443179640281/184570312500$$ $$109786726239257812500$$ $$[2]$$ $$9289728$$ $$2.6366$$
176610.cy5 176610u3 $$[1, 1, 1, -1238390, -403642765]$$ $$353108405631241/86318776320$$ $$51344421195318558720$$ $$[2]$$ $$6967296$$ $$2.4928$$
176610.cy6 176610u2 $$[1, 1, 1, -485695, 68193557]$$ $$21302308926361/8930250000$$ $$5311920962360250000$$ $$[2, 2]$$ $$4644864$$ $$2.2900$$
176610.cy7 176610u1 $$[1, 1, 1, -418415, 103959605]$$ $$13619385906841/6048000$$ $$3597491445408000$$ $$[2]$$ $$2322432$$ $$1.9435$$ $$\Gamma_0(N)$$-optimal
176610.cy8 176610u4 $$[1, 1, 1, 1616805, 502990557]$$ $$785793873833639/637994920500$$ $$-379494257392940980500$$ $$[2]$$ $$9289728$$ $$2.6366$$

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 176610.cy do not have complex multiplication.

## Modular form 176610.2.a.cy

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.