Properties

Label 11913.d
Number of curves $4$
Conductor $11913$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 11913.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11913.d1 11913i3 \([1, 0, 0, -52894, -4682095]\) \(347873904937/395307\) \(18597566080467\) \([2]\) \(43200\) \(1.4596\)  
11913.d2 11913i2 \([1, 0, 0, -4159, -32776]\) \(169112377/88209\) \(4149870117129\) \([2, 2]\) \(21600\) \(1.1130\)  
11913.d3 11913i1 \([1, 0, 0, -2354, 43395]\) \(30664297/297\) \(13972626657\) \([2]\) \(10800\) \(0.76644\) \(\Gamma_0(N)\)-optimal
11913.d4 11913i4 \([1, 0, 0, 15696, -251181]\) \(9090072503/5845851\) \(-275023210489731\) \([2]\) \(43200\) \(1.4596\)  

Rank

sage: E.rank()
 

The elliptic curves in class 11913.d have rank \(0\).

Complex multiplication

The elliptic curves in class 11913.d do not have complex multiplication.

Modular form 11913.2.a.d

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