Properties

Label 43890.m
Number of curves $4$
Conductor $43890$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 43890.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43890.m1 43890m4 \([1, 1, 0, -356702, -82147404]\) \(5019289526512451088361/13006889280\) \(13006889280\) \([2]\) \(319488\) \(1.6031\)  
43890.m2 43890m2 \([1, 1, 0, -22302, -1289484]\) \(1226833350167030761/1972564070400\) \(1972564070400\) \([2, 2]\) \(159744\) \(1.2565\)  
43890.m3 43890m3 \([1, 1, 0, -15582, -2073036]\) \(-418443533445064681/1602744999240000\) \(-1602744999240000\) \([4]\) \(319488\) \(1.6031\)  
43890.m4 43890m1 \([1, 1, 0, -1822, -7436]\) \(669485563505641/368176005120\) \(368176005120\) \([2]\) \(79872\) \(0.90994\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 43890.2.a.m

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.