Properties

Label 17136.bl
Number of curves $4$
Conductor $17136$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("bl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 17136.bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17136.bl1 17136j4 \([0, 0, 0, -1632306819, 25383459170018]\) \(322159999717985454060440834/4250799\) \(6346408900608\) \([2]\) \(2211840\) \(3.4403\)  
17136.bl2 17136j3 \([0, 0, 0, -102281619, 394473389042]\) \(79260902459030376659234/842751810121431609\) \(1258221710496816420784128\) \([2]\) \(2211840\) \(3.4403\)  
17136.bl3 17136j2 \([0, 0, 0, -102019179, 396616526570]\) \(157304700372188331121828/18069292138401\) \(13488654304147792896\) \([2, 2]\) \(1105920\) \(3.0937\)  
17136.bl4 17136j1 \([0, 0, 0, -6359799, 6230596790]\) \(-152435594466395827792/1646846627220711\) \(-307341104958437969664\) \([2]\) \(552960\) \(2.7472\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 17136.bl have rank \(1\).

Complex multiplication

The elliptic curves in class 17136.bl do not have complex multiplication.

Modular form 17136.2.a.bl

sage: E.q_eigenform(10)
 
\(q + 2q^{5} + q^{7} + 2q^{13} - q^{17} + O(q^{20})\)  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.