Properties

Label 43190.e
Number of curves $2$
Conductor $43190$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 43190.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43190.e1 43190f1 \([1, 0, 1, -1639933, 1713908056]\) \(-487754906646816354619081/986928523547750000000\) \(-986928523547750000000\) \([3]\) \(1781640\) \(2.7177\) \(\Gamma_0(N)\)-optimal
43190.e2 43190f2 \([1, 0, 1, 14170692, -36821906694]\) \(314700137324290484459710919/767884119673361137664000\) \(-767884119673361137664000\) \([]\) \(5344920\) \(3.2671\)  

Rank

sage: E.rank()
 

The elliptic curves in class 43190.e have rank \(0\).

Complex multiplication

The elliptic curves in class 43190.e do not have complex multiplication.

Modular form 43190.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} + q^{7} - q^{8} - 2 q^{9} - q^{10} + q^{12} + 2 q^{13} - q^{14} + q^{15} + q^{16} + 2 q^{18} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.