Elliptic curve isogeny class with Cremona label 8190bp (LMFDB label 8190.bn)

• Label: 8190bp
• Number of curves: $4$
• Conductor: $8190$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 8190bp 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 \(\mathbb{F}_p\)
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 8190.2.a.bp

Isogeny 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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 8190bp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
8190.bn4	8190bp1	\([1, -1, 1, -6480392, -3215030709]\)	\(41285728533151645510969/17760741842188800000\)	\(12947580802955635200000\)	\([4]\)	\(921600\)	\(2.9393\)	\(\Gamma_0(N)\)-optimal
8190.bn2	8190bp2	\([1, -1, 1, -88736072, -321577414581]\)	\(105997782562506306791694649/51649016225625000000\)	\(37652132828480625000000\)	\([2, 2]\)	\(1843200\)	\(3.2859\)
8190.bn1	8190bp3	\([1, -1, 1, -1419611072, -20587077214581]\)	\(434014578033107719741685694649/103121648659575000\)	\(75175681872830175000\)	\([2]\)	\(3686400\)	\(3.6325\)
8190.bn3	8190bp4	\([1, -1, 1, -73951952, -432257250549]\)	\(-61354313914516350666047929/75227254486083984375000\)	\(-54840668520355224609375000\)	\([2]\)	\(3686400\)	\(3.6325\)