Properties

Label 2646.w
Number of curves $2$
Conductor $2646$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2646.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2646.w1 2646s1 \([1, -1, 1, -20, 39]\) \(-637875/16\) \(-21168\) \([]\) \(288\) \(-0.38564\) \(\Gamma_0(N)\)-optimal
2646.w2 2646s2 \([1, -1, 1, 85, 123]\) \(5767125/4096\) \(-48771072\) \([]\) \(864\) \(0.16367\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2646.2.a.w

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.