Properties

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

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 176610u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
176610.cy7 176610u1 \([1, 1, 1, -418415, 103959605]\) \(13619385906841/6048000\) \(3597491445408000\) \([2]\) \(2322432\) \(1.9435\) \(\Gamma_0(N)\)-optimal
176610.cy6 176610u2 \([1, 1, 1, -485695, 68193557]\) \(21302308926361/8930250000\) \(5311920962360250000\) \([2, 2]\) \(4644864\) \(2.2900\)  
176610.cy5 176610u3 \([1, 1, 1, -1238390, -403642765]\) \(353108405631241/86318776320\) \(51344421195318558720\) \([2]\) \(6967296\) \(2.4928\)  
176610.cy8 176610u4 \([1, 1, 1, 1616805, 502990557]\) \(785793873833639/637994920500\) \(-379494257392940980500\) \([2]\) \(9289728\) \(2.6366\)  
176610.cy4 176610u5 \([1, 1, 1, -3664675, -2654284915]\) \(9150443179640281/184570312500\) \(109786726239257812500\) \([2]\) \(9289728\) \(2.6366\)  
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.cy1 176610u8 \([1, 1, 1, -295386550, -1954166401165]\) \(4791901410190533590281/41160000\) \(24482927892360000\) \([2]\) \(27869184\) \(3.1859\)  

Rank

sage: E.rank()
 

The elliptic curves in class 176610u have rank \(0\).

Complex multiplication

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

Modular form 176610.2.a.u

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{7} + q^{8} + q^{9} + q^{10} - q^{12} + 2q^{13} + q^{14} - q^{15} + q^{16} + 6q^{17} + q^{18} - 8q^{19} + O(q^{20})\)  Toggle raw display

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.