Properties

Label 50160.bc
Number of curves $8$
Conductor $50160$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bc1")
 
E.isogeny_class()
 

Elliptic curves in class 50160.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
50160.bc1 50160bo8 \([0, -1, 0, -342788520, -2426162248080]\) \(1087533321226184807035053481/8484255812957933638080\) \(34751511809875696181575680\) \([2]\) \(18579456\) \(3.7294\)  
50160.bc2 50160bo5 \([0, -1, 0, -342144120, -2435798739600]\) \(1081411559614045490773061881/522522049500\) \(2140250314752000\) \([2]\) \(6193152\) \(3.1801\)  
50160.bc3 50160bo6 \([0, -1, 0, -36126120, 20758374000]\) \(1272998045160051207059881/691293848290254950400\) \(2831539602596884276838400\) \([2, 2]\) \(9289728\) \(3.3828\)  
50160.bc4 50160bo3 \([0, -1, 0, -27934120, 56763852400]\) \(588530213343917460371881/861551575695360000\) \(3528915254048194560000\) \([2]\) \(4644864\) \(3.0362\)  
50160.bc5 50160bo2 \([0, -1, 0, -21384120, -38053587600]\) \(264020672568758737421881/5803468580250000\) \(23771007304704000000\) \([2, 2]\) \(3096576\) \(2.8335\)  
50160.bc6 50160bo4 \([0, -1, 0, -20624120, -40884435600]\) \(-236859095231405581781881/39282983014374049500\) \(-160903098426876106752000\) \([2]\) \(6193152\) \(3.1801\)  
50160.bc7 50160bo1 \([0, -1, 0, -1384120, -549587600]\) \(71595431380957421881/9522562500000000\) \(39004416000000000000\) \([2]\) \(1548288\) \(2.4869\) \(\Gamma_0(N)\)-optimal
50160.bc8 50160bo7 \([0, -1, 0, 139464280, 163197306480]\) \(73240740785321709623685719/45195275784938365817280\) \(-185119849615107546387578880\) \([2]\) \(18579456\) \(3.7294\)  

Rank

sage: E.rank()
 

The elliptic curves in class 50160.bc have rank \(0\).

Complex multiplication

The elliptic curves in class 50160.bc do not have complex multiplication.

Modular form 50160.2.a.bc

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + 4 q^{7} + q^{9} + q^{11} + 2 q^{13} - q^{15} + 6 q^{17} - q^{19} + O(q^{20})\) Copy content 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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.