Properties

Label 19800.e
Number of curves 4
Conductor 19800
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("19800.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 19800.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19800.e1 19800n3 [0, 0, 0, -158475, -24282250] [2] 98304  
19800.e2 19800n4 [0, 0, 0, -23475, 854750] [2] 98304  
19800.e3 19800n2 [0, 0, 0, -9975, -373750] [2, 2] 49152  
19800.e4 19800n1 [0, 0, 0, 150, -19375] [2] 24576 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 19800.e have rank \(1\).

Modular form 19800.2.a.e

sage: E.q_eigenform(10)
 
\( q - 4q^{7} + q^{11} - 6q^{13} + 6q^{17} - 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.