Properties

Label 2646.h
Number of curves $2$
Conductor $2646$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2646.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2646.h1 2646i1 \([1, -1, 0, -8682, 320228]\) \(-637875/16\) \(-1815497249328\) \([3]\) \(6048\) \(1.1366\) \(\Gamma_0(N)\)-optimal
2646.h2 2646i2 \([1, -1, 0, 37623, 1329677]\) \(5767125/4096\) \(-4182905662451712\) \([]\) \(18144\) \(1.6859\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2646.h have rank \(0\).

Complex multiplication

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

Modular form 2646.2.a.h

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.