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Properties

Label 26702j
Number of curves $3$
Conductor $26702$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 26702j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26702.k3 26702j1 \([1, 0, 0, -7862, 267656]\) \(11134383337/316\) \(1525271644\) \([]\) \(27360\) \(0.86372\) \(\Gamma_0(N)\)-optimal
26702.k2 26702j2 \([1, 0, 0, -13777, -187799]\) \(59914169497/31554496\) \(152307525283264\) \([]\) \(82080\) \(1.4130\)  
26702.k1 26702j3 \([1, 0, 0, -881592, -318675904]\) \(15698803397448457/20709376\) \(99960202461184\) \([]\) \(246240\) \(1.9623\)  

Rank

sage: E.rank()
 

The elliptic curves in class 26702j have rank \(1\).

Complex multiplication

The elliptic curves in class 26702j do not have complex multiplication.

Modular form 26702.2.a.j

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - 3 q^{5} + q^{6} + q^{7} + q^{8} - 2 q^{9} - 3 q^{10} + q^{12} + q^{14} - 3 q^{15} + q^{16} - 2 q^{18} - 2 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.