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Properties

Label 14994bi
Number of curves $6$
Conductor $14994$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bi1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 14994bi have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(3\)\(1\)
\(7\)\(1\)
\(17\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 - 3 T + 5 T^{2}\) 1.5.ad
\(11\) \( 1 - T + 11 T^{2}\) 1.11.ab
\(13\) \( 1 + 3 T + 13 T^{2}\) 1.13.d
\(19\) \( 1 - 6 T + 19 T^{2}\) 1.19.ag
\(23\) \( 1 - 2 T + 23 T^{2}\) 1.23.ac
\(29\) \( 1 + 6 T + 29 T^{2}\) 1.29.g
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 14994bi do not have complex multiplication.

Modular form 14994.2.a.bi

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 2 q^{5} - q^{8} + 2 q^{10} - 4 q^{11} + 2 q^{13} + q^{16} + q^{17} - 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 14994bi

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14994.g5 14994bi1 \([1, -1, 0, -30977613, 66286809189]\) \(38331145780597164097/55468445663232\) \(4757313422434680963072\) \([2]\) \(1474560\) \(3.0617\) \(\Gamma_0(N)\)-optimal
14994.g4 14994bi2 \([1, -1, 0, -40009293, 24490000485]\) \(82582985847542515777/44772582831427584\) \(3839970756602740772081664\) \([2, 2]\) \(2949120\) \(3.4082\)  
14994.g2 14994bi3 \([1, -1, 0, -378838413, -2818625145435]\) \(70108386184777836280897/552468975892674624\) \(47383121035157214815613504\) \([2, 2]\) \(5898240\) \(3.7548\)  
14994.g6 14994bi4 \([1, -1, 0, 154312947, 192501009189]\) \(4738217997934888496063/2928751705237796928\) \(-251187673130381225100276288\) \([2]\) \(5898240\) \(3.7548\)  
14994.g1 14994bi5 \([1, -1, 0, -6049904373, -181120341567411]\) \(285531136548675601769470657/17941034271597192\) \(1538732916202951632332232\) \([2]\) \(11796480\) \(4.1014\)  
14994.g3 14994bi6 \([1, -1, 0, -129038373, -6480344011779]\) \(-2770540998624539614657/209924951154647363208\) \(-18004448761648575465228276168\) \([2]\) \(11796480\) \(4.1014\)