Properties

Label 15246.bo
Number of curves $6$
Conductor $15246$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bo1")
 
E.isogeny_class()
 

Elliptic curves in class 15246.bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15246.bo1 15246bs4 \([1, -1, 1, -1463639, 681917811]\) \(268498407453697/252\) \(325449928188\) \([2]\) \(163840\) \(1.9374\)  
15246.bo2 15246bs5 \([1, -1, 1, -995369, -378310809]\) \(84448510979617/933897762\) \(1206099045943785378\) \([2]\) \(327680\) \(2.2839\)  
15246.bo3 15246bs3 \([1, -1, 1, -113279, 5221923]\) \(124475734657/63011844\) \(81377778193624836\) \([2, 2]\) \(163840\) \(1.9374\)  
15246.bo4 15246bs2 \([1, -1, 1, -91499, 10666923]\) \(65597103937/63504\) \(82013381903376\) \([2, 2]\) \(81920\) \(1.5908\)  
15246.bo5 15246bs1 \([1, -1, 1, -4379, 247371]\) \(-7189057/16128\) \(-20828795404032\) \([2]\) \(40960\) \(1.2442\) \(\Gamma_0(N)\)-optimal
15246.bo6 15246bs6 \([1, -1, 1, 420331, 40013295]\) \(6359387729183/4218578658\) \(-5448159211514005602\) \([2]\) \(327680\) \(2.2839\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 15246.bo do not have complex multiplication.

Modular form 15246.2.a.bo

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + 2 q^{5} + q^{7} + q^{8} + 2 q^{10} - 6 q^{13} + q^{14} + q^{16} + 2 q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.