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Properties

Label 286650.ji
Number of curves $2$
Conductor $286650$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("ji1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 286650.ji 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 \(\mathbb{F}_p\)
\(11\) \( 1 + 4 T + 11 T^{2}\) 1.11.e
\(17\) \( 1 + 8 T + 17 T^{2}\) 1.17.i
\(19\) \( 1 - 6 T + 19 T^{2}\) 1.19.ag
\(23\) \( 1 - 6 T + 23 T^{2}\) 1.23.ag
\(29\) \( 1 - 4 T + 29 T^{2}\) 1.29.ae
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

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

Modular form 286650.2.a.ji

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{8} - 4 q^{11} - q^{13} + q^{16} - 8 q^{17} + 6 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 286650.ji

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
286650.ji1 286650ji2 \([1, -1, 1, -507380, -124488003]\) \(10779215329/1232010\) \(1651011230206406250\) \([2]\) \(6635520\) \(2.2279\)  
286650.ji2 286650ji1 \([1, -1, 1, 43870, -9828003]\) \(6967871/35100\) \(-47037356985937500\) \([2]\) \(3317760\) \(1.8814\) \(\Gamma_0(N)\)-optimal