Properties

Label 194810.e
Number of curves $2$
Conductor $194810$
CM no
Rank $0$
Graph

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

Elliptic curves in class 194810.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
194810.e1 194810l2 \([1, 0, 1, -3039523, 1482739806]\) \(1753007192038126081/478174101507200\) \(847114589440196739200\) \([2]\) \(12544000\) \(2.7235\)  
194810.e2 194810l1 \([1, 0, 1, -1103523, -427704994]\) \(83890194895342081/3958384640000\) \(7012519851223040000\) \([2]\) \(6272000\) \(2.3769\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 194810.e have rank \(0\).

Complex multiplication

The elliptic curves in class 194810.e do not have complex multiplication.

Modular form 194810.2.a.e

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.