Properties

Label 2646.q
Number of curves $3$
Conductor $2646$
CM no
Rank $1$
Graph

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

Elliptic curves in class 2646.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2646.q1 2646v3 \([1, -1, 1, -62264, 5995567]\) \(-11527859979/28\) \(-64839187476\) \([]\) \(10368\) \(1.3149\)  
2646.q2 2646v1 \([1, -1, 1, -524, 13647]\) \(-5000211/21952\) \(-69731032896\) \([]\) \(3456\) \(0.76559\) \(\Gamma_0(N)\)-optimal
2646.q3 2646v2 \([1, -1, 1, 4621, -327981]\) \(381790581/1835008\) \(-52460506054656\) \([]\) \(10368\) \(1.3149\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2646.q have rank \(1\).

Complex multiplication

The elliptic curves in class 2646.q do not have complex multiplication.

Modular form 2646.2.a.q

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - 3q^{5} + q^{8} - 3q^{10} - 3q^{11} + 4q^{13} + q^{16} - 6q^{17} + 7q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.