Properties

Label 19074c
Number of curves 2
Conductor 19074
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("19074.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 19074c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19074.e2 19074c1 [1, 1, 0, -33674, 2294880] [2] 104448 \(\Gamma_0(N)\)-optimal
19074.e1 19074c2 [1, 1, 0, -82804, -6008090] [2] 208896  

Rank

sage: E.rank()
 

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

Modular form 19074.2.a.e

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.