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Properties

Label 13794.p
Number of curves $4$
Conductor $13794$
CM no
Rank $1$
Graph

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

Elliptic curves in class 13794.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13794.p1 13794m3 \([1, 0, 1, -51791, 4532174]\) \(8671983378625/82308\) \(145813642788\) \([2]\) \(51840\) \(1.3044\)  
13794.p2 13794m4 \([1, 0, 1, -50581, 4754330]\) \(-8078253774625/846825858\) \(-1500203663824338\) \([2]\) \(103680\) \(1.6510\)  
13794.p3 13794m1 \([1, 0, 1, -971, -970]\) \(57066625/32832\) \(58163890752\) \([2]\) \(17280\) \(0.75514\) \(\Gamma_0(N)\)-optimal
13794.p4 13794m2 \([1, 0, 1, 3869, -6778]\) \(3616805375/2105352\) \(-3729759494472\) \([2]\) \(34560\) \(1.1017\)  

Rank

sage: E.rank()
 

The elliptic curves in class 13794.p have rank \(1\).

Complex multiplication

The elliptic curves in class 13794.p do not have complex multiplication.

Modular form 13794.2.a.p

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.