↑

Properties

Label 286650.j
Number of curves $4$
Conductor $286650$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("j1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 286650.j have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(3\)\(1\)
\(5\)\(1\)
\(7\)\(1\)
\(13\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 + 6 T + 11 T^{2}\) 1.11.g
\(17\) \( 1 + 17 T^{2}\) 1.17.a
\(19\) \( 1 + 8 T + 19 T^{2}\) 1.19.i
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 - 6 T + 29 T^{2}\) 1.29.ag
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 286650.j do not have complex multiplication.

Modular form 286650.2.a.j

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{8} - 6 q^{11} + q^{13} + q^{16} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 286650.j

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
286650.j1 286650j3 \([1, -1, 0, -567495567, -5203311064659]\) \(15082569606665230489/7751016000\) \(10387102752014625000000\) \([2]\) \(95551488\) \(3.5566\)  
286650.j2 286650j4 \([1, -1, 0, -564408567, -5262720379659]\) \(-14837772556740428569/342100087875000\) \(-458446836418716919921875000\) \([2]\) \(191102976\) \(3.9032\)  
286650.j3 286650j1 \([1, -1, 0, -8362692, -4177561284]\) \(48264326765929/22299191460\) \(29883049265008229062500\) \([2]\) \(31850496\) \(3.0073\) \(\Gamma_0(N)\)-optimal
286650.j4 286650j2 \([1, -1, 0, 29453058, -31518348534]\) \(2108526614950391/1540302022350\) \(-2064152025397106317968750\) \([2]\) \(63700992\) \(3.3539\)