Properties

Label 69696.er
Number of curves $2$
Conductor $69696$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("er1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 69696.er

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
69696.er1 69696fu2 [0, 0, 0, -175692, 110803088] [] 811008  
69696.er2 69696fu1 [0, 0, 0, -17292, -875248] [] 73728 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 69696.er have rank \(0\).

Complex multiplication

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

Modular form 69696.2.a.er

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 LMFDB 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 LMFDB labels.