Properties

Label 17136x
Number of curves $2$
Conductor $17136$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 17136x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17136.be2 17136x1 \([0, 0, 0, -3099, 93130]\) \(-1102302937/616896\) \(-1842041585664\) \([2]\) \(18432\) \(1.0568\) \(\Gamma_0(N)\)-optimal
17136.be1 17136x2 \([0, 0, 0, -54939, 4955722]\) \(6141556990297/1019592\) \(3044485398528\) \([2]\) \(36864\) \(1.4034\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 17136.2.a.x

sage: E.q_eigenform(10)
 
\(q + 2 q^{5} - q^{7} - 2 q^{11} + 4 q^{13} - q^{17} + 2 q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.