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Properties

Label 43602.k
Number of curves $2$
Conductor $43602$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 43602.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43602.k1 43602k2 \([1, 0, 1, -10123273, -12399681760]\) \(-23769846831649063249/3261823333284\) \(-15744198221505210756\) \([]\) \(2074464\) \(2.7014\)  
43602.k2 43602k1 \([1, 0, 1, 26867, 3789320]\) \(444369620591/1540767744\) \(-7436991613648896\) \([]\) \(296352\) \(1.7284\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 43602.k have rank \(1\).

Complex multiplication

The elliptic curves in class 43602.k do not have complex multiplication.

Modular form 43602.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - q^{7} - q^{8} + q^{9} - q^{10} - 5 q^{11} + q^{12} + q^{14} + q^{15} + q^{16} + 4 q^{17} - q^{18} + q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.