Properties

Label 43758.k
Number of curves $2$
Conductor $43758$
CM no
Rank $1$
Graph

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

Elliptic curves in class 43758.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43758.k1 43758q1 \([1, -1, 1, -842, 6905]\) \(90458382169/25788048\) \(18799486992\) \([2]\) \(51200\) \(0.67806\) \(\Gamma_0(N)\)-optimal
43758.k2 43758q2 \([1, -1, 1, 2218, 43625]\) \(1656015369191/2114999172\) \(-1541834396388\) \([2]\) \(102400\) \(1.0246\)  

Rank

sage: E.rank()
 

The elliptic curves in class 43758.k have rank \(1\).

Complex multiplication

The elliptic curves in class 43758.k do not have complex multiplication.

Modular form 43758.2.a.k

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.