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Properties

Label 43681l
Number of curves $2$
Conductor $43681$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 43681l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
43681.c2 43681l1 [1, 0, 0, -910, 41229] [] 39312 \(\Gamma_0(N)\)-optimal
43681.c1 43681l2 [1, 0, 0, -1311340, -578120487] [] 432432  

Rank

sage: E.rank()
 

The elliptic curves in class 43681l have rank \(1\).

Complex multiplication

The elliptic curves in class 43681l do not have complex multiplication.

Modular form 43681.2.a.l

sage: E.q_eigenform(10)
 
\( q - q^{2} - 2q^{3} - q^{4} + q^{5} + 2q^{6} - 2q^{7} + 3q^{8} + q^{9} - q^{10} + 2q^{12} - q^{13} + 2q^{14} - 2q^{15} - q^{16} - 5q^{17} - q^{18} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.