Properties

Label 19350ba
Number of curves $4$
Conductor $19350$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 19350ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19350.e3 19350ba1 [1, -1, 0, -15417, 739741] [2] 36864 \(\Gamma_0(N)\)-optimal
19350.e2 19350ba2 [1, -1, 0, -19917, 276241] [2, 2] 73728  
19350.e1 19350ba3 [1, -1, 0, -188667, -31280009] [2] 147456  
19350.e4 19350ba4 [1, -1, 0, 76833, 2114491] [2] 147456  

Rank

sage: E.rank()
 

The elliptic curves in class 19350ba have rank \(1\).

Complex multiplication

The elliptic curves in class 19350ba do not have complex multiplication.

Modular form 19350.2.a.ba

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

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.