Properties

Label 1914.p
Number of curves $2$
Conductor $1914$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 1914.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1914.p1 1914p1 \([1, 0, 0, -217350, 38984004]\) \(-1135540872025530818401/1611210069216\) \(-1611210069216\) \([5]\) \(10800\) \(1.6141\) \(\Gamma_0(N)\)-optimal
1914.p2 1914p2 \([1, 0, 0, 540540, 207657054]\) \(17466551704682106586559/28728344556038333646\) \(-28728344556038333646\) \([]\) \(54000\) \(2.4188\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1914.p have rank \(0\).

Complex multiplication

The elliptic curves in class 1914.p do not have complex multiplication.

Modular form 1914.2.a.p

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

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.