Properties

Label 19074.a
Number of curves 4
Conductor 19074
CM no
Rank 2
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("19074.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 19074.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19074.a1 19074b3 [1, 1, 0, -23270, -1370796] [2] 55296  
19074.a2 19074b4 [1, 1, 0, -11710, -2718692] [2] 110592  
19074.a3 19074b1 [1, 1, 0, -1595, 22473] [2] 18432 \(\Gamma_0(N)\)-optimal
19074.a4 19074b2 [1, 1, 0, 1295, 98191] [2] 36864  

Rank

sage: E.rank()
 

The elliptic curves in class 19074.a have rank \(2\).

Modular form 19074.2.a.a

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.