Properties

Label 15246i
Number of curves 6
Conductor 15246
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("15246.m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 15246i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
15246.m5 15246i1 [1, -1, 0, -567, 10665] [2] 11520 \(\Gamma_0(N)\)-optimal
15246.m4 15246i2 [1, -1, 0, -11457, 474579] [2] 23040  
15246.m6 15246i3 [1, -1, 0, 4878, -221292] [2] 34560  
15246.m3 15246i4 [1, -1, 0, -38682, -2390580] [2] 69120  
15246.m2 15246i5 [1, -1, 0, -185697, -30842883] [2] 103680  
15246.m1 15246i6 [1, -1, 0, -2973537, -1972852227] [2] 207360  

Rank

sage: E.rank()
 

The elliptic curves in class 15246i have rank \(1\).

Modular form 15246.2.a.m

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{7} - q^{8} + 4q^{13} + q^{14} + q^{16} + 6q^{17} - 2q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 6 & 9 & 18 \\ 2 & 1 & 6 & 3 & 18 & 9 \\ 3 & 6 & 1 & 2 & 3 & 6 \\ 6 & 3 & 2 & 1 & 6 & 3 \\ 9 & 18 & 3 & 6 & 1 & 2 \\ 18 & 9 & 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.