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Properties

Label 265200.bo
Number of curves $6$
Conductor $265200$
CM no
Rank $0$
Graph

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

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 265200.bo have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 + T\)
\(5\)\(1\)
\(13\)\(1 + T\)
\(17\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 + 7 T^{2}\) 1.7.a
\(11\) \( 1 + 4 T + 11 T^{2}\) 1.11.e
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 + 2 T + 29 T^{2}\) 1.29.c
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 265200.bo do not have complex multiplication.

Modular form 265200.2.a.bo

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} + q^{9} - 4 q^{11} - q^{13} - q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 265200.bo

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
265200.bo1 265200bo5 \([0, -1, 0, -8069608, 8824545712]\) \(908031902324522977/161726530797\) \(10350497971008000000\) \([2]\) \(8388608\) \(2.6530\)  
265200.bo2 265200bo3 \([0, -1, 0, -555608, 108305712]\) \(296380748763217/92608836489\) \(5926965535296000000\) \([2, 2]\) \(4194304\) \(2.3064\)  
265200.bo3 265200bo2 \([0, -1, 0, -217608, -37710288]\) \(17806161424897/668584449\) \(42789404736000000\) \([2, 2]\) \(2097152\) \(1.9599\)  
265200.bo4 265200bo1 \([0, -1, 0, -215608, -38462288]\) \(17319700013617/25857\) \(1654848000000\) \([2]\) \(1048576\) \(1.6133\) \(\Gamma_0(N)\)-optimal
265200.bo5 265200bo4 \([0, -1, 0, 88392, -135630288]\) \(1193377118543/124806800313\) \(-7987635220032000000\) \([2]\) \(4194304\) \(2.3064\)  
265200.bo6 265200bo6 \([0, -1, 0, 1550392, 731681712]\) \(6439735268725823/7345472585373\) \(-470110245463872000000\) \([2]\) \(8388608\) \(2.6530\)