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Properties

Label 8190.bi
Number of curves $3$
Conductor $8190$
CM no
Rank $1$
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 8190.bi have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(3\)\(1\)
\(5\)\(1 + T\)
\(7\)\(1 - T\)
\(13\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 - 3 T + 11 T^{2}\) 1.11.ad
\(17\) \( 1 + 6 T + 17 T^{2}\) 1.17.g
\(19\) \( 1 - 2 T + 19 T^{2}\) 1.19.ac
\(23\) \( 1 + 9 T + 23 T^{2}\) 1.23.j
\(29\) \( 1 + 6 T + 29 T^{2}\) 1.29.g
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 8190.bi do not have complex multiplication.

Modular form 8190.2.a.bi

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} + q^{7} + q^{8} - q^{10} + 3 q^{11} + q^{13} + q^{14} + q^{16} - 6 q^{17} + 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 8190.bi

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8190.bi1 8190bl3 \([1, -1, 1, -454528778, 3955711147337]\) \(-14245586655234650511684983641/1028175397808386133196800\) \(-749539865002313491100467200\) \([3]\) \(5715360\) \(3.9065\)  
8190.bi2 8190bl1 \([1, -1, 1, -5206028, -4956262513]\) \(-21405018343206000779641/2177246093750000000\) \(-1587212402343750000000\) \([]\) \(635040\) \(2.8078\) \(\Gamma_0(N)\)-optimal
8190.bi3 8190bl2 \([1, -1, 1, 32059597, 4539299987]\) \(4998853083179567995470359/2905108466204672000000\) \(-2117824071863205888000000\) \([3]\) \(1905120\) \(3.3571\)