Properties

Label 19074f
Number of curves 4
Conductor 19074
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("19074.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 19074f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19074.k4 19074f1 [1, 0, 1, -1926625, 774195284] [2] 774144 \(\Gamma_0(N)\)-optimal
19074.k2 19074f2 [1, 0, 1, -28653345, 59027754196] [2, 2] 1548288  
19074.k1 19074f3 [1, 0, 1, -458442585, 3778080005764] [2] 3096576  
19074.k3 19074f4 [1, 0, 1, -26491625, 68310179876] [2] 3096576  

Rank

sage: E.rank()
 

The elliptic curves in class 19074f have rank \(0\).

Modular form 19074.2.a.k

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

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 Cremona 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 Cremona labels.