Properties

Label 85176.bs
Number of curves $4$
Conductor $85176$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 85176.bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
85176.bs1 85176ce4 \([0, 0, 0, -454779, -118044810]\) \(1443468546/7\) \(50444710557696\) \([2]\) \(589824\) \(1.8297\)  
85176.bs2 85176ce3 \([0, 0, 0, -89739, 8186022]\) \(11090466/2401\) \(17302535721289728\) \([2]\) \(589824\) \(1.8297\)  
85176.bs3 85176ce2 \([0, 0, 0, -28899, -1779570]\) \(740772/49\) \(176556486951936\) \([2, 2]\) \(294912\) \(1.4832\)  
85176.bs4 85176ce1 \([0, 0, 0, 1521, -118638]\) \(432/7\) \(-6305588819712\) \([2]\) \(147456\) \(1.1366\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 85176.bs have rank \(0\).

Complex multiplication

The elliptic curves in class 85176.bs do not have complex multiplication.

Modular form 85176.2.a.bs

sage: E.q_eigenform(10)
 
\(q + 2q^{5} + q^{7} - 4q^{11} + 6q^{17} - 8q^{19} + O(q^{20})\)  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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.