Properties

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

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Show commands: SageMath
E = EllipticCurve("bp1")
 
E.isogeny_class()
 

Elliptic curves in class 17136bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17136.l1 17136bp1 \([0, 0, 0, -3036, -64325]\) \(265327034368/297381\) \(3468651984\) \([2]\) \(11520\) \(0.74465\) \(\Gamma_0(N)\)-optimal
17136.l2 17136bp2 \([0, 0, 0, -2271, -97526]\) \(-6940769488/18000297\) \(-3359287427328\) \([2]\) \(23040\) \(1.0912\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 17136.2.a.bp

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} + q^{7} + 6 q^{13} + q^{17} + 2 q^{19} + O(q^{20})\) 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.