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Properties

Label 43890c
Number of curves $2$
Conductor $43890$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 43890c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43890.c2 43890c1 \([1, 1, 0, -33278, 11744628]\) \(-4075827128160594409/57370565777817600\) \(-57370565777817600\) \([2]\) \(456192\) \(1.8972\) \(\Gamma_0(N)\)-optimal
43890.c1 43890c2 \([1, 1, 0, -1006078, 386661748]\) \(112620990763554763909609/446907448384911360\) \(446907448384911360\) \([2]\) \(912384\) \(2.2438\)  

Rank

sage: E.rank()
 

The elliptic curves in class 43890c have rank \(0\).

Complex multiplication

The elliptic curves in class 43890c do not have complex multiplication.

Modular form 43890.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{7} - q^{8} + q^{9} + q^{10} + q^{11} - q^{12} - 2 q^{13} + q^{14} + q^{15} + q^{16} + 4 q^{17} - q^{18} - q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.