Properties

Label 69696bo
Number of curves $2$
Conductor $69696$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bo1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 69696bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
69696.ey2 69696bo1 [0, 0, 0, -17292, 875248] [] 73728 \(\Gamma_0(N)\)-optimal
69696.ey1 69696bo2 [0, 0, 0, -175692, -110803088] [] 811008  

Rank

sage: E.rank()
 

The elliptic curves in class 69696bo have rank \(1\).

Complex multiplication

The elliptic curves in class 69696bo do not have complex multiplication.

Modular form 69696.2.a.bo

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

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.

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.