Properties

Label 217672.q
Number of curves $2$
Conductor $217672$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 217672.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
217672.q1 217672t2 \([0, -1, 0, -451624, 110706348]\) \(1030541881826/62236321\) \(615225004707203072\) \([2]\) \(2073600\) \(2.1658\)  
217672.q2 217672t1 \([0, -1, 0, -444864, 114354044]\) \(1969910093092/7889\) \(38992584909824\) \([2]\) \(1036800\) \(1.8193\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 217672.q have rank \(0\).

Complex multiplication

The elliptic curves in class 217672.q do not have complex multiplication.

Modular form 217672.2.a.q

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} - 2 q^{5} - q^{7} + q^{9} - 2 q^{11} - 4 q^{15} - 2 q^{17} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.