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Properties

Label 3150.bo
Number of curves $6$
Conductor $3150$
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 3150.bo have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(3\)\(1\)
\(5\)\(1\)
\(7\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 - 4 T + 11 T^{2}\) 1.11.ae
\(13\) \( 1 + 6 T + 13 T^{2}\) 1.13.g
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(19\) \( 1 + 4 T + 19 T^{2}\) 1.19.e
\(23\) \( 1 - 8 T + 23 T^{2}\) 1.23.ai
\(29\) \( 1 - 2 T + 29 T^{2}\) 1.29.ac
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 3150.bo do not have complex multiplication.

Modular form 3150.2.a.bo

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{7} + q^{8} + 4 q^{11} - 6 q^{13} + q^{14} + q^{16} + 2 q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 3150.bo

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3150.bo1 3150bl3 \([1, -1, 1, -302405, -63931903]\) \(268498407453697/252\) \(2870437500\) \([2]\) \(16384\) \(1.5431\)  
3150.bo2 3150bl5 \([1, -1, 1, -205655, 35603597]\) \(84448510979617/933897762\) \(10637679195281250\) \([2]\) \(32768\) \(1.8897\)  
3150.bo3 3150bl4 \([1, -1, 1, -23405, -481903]\) \(124475734657/63011844\) \(717744285562500\) \([2, 2]\) \(16384\) \(1.5431\)  
3150.bo4 3150bl2 \([1, -1, 1, -18905, -994903]\) \(65597103937/63504\) \(723350250000\) \([2, 2]\) \(8192\) \(1.1966\)  
3150.bo5 3150bl1 \([1, -1, 1, -905, -22903]\) \(-7189057/16128\) \(-183708000000\) \([2]\) \(4096\) \(0.84998\) \(\Gamma_0(N)\)-optimal
3150.bo6 3150bl6 \([1, -1, 1, 86845, -3789403]\) \(6359387729183/4218578658\) \(-48052247526281250\) \([2]\) \(32768\) \(1.8897\)