Elliptic curve isogeny class with LMFDB label 107800.bk (Cremona label 107800bn)

• Label: 107800.bk
• Number of curves: $4$
• Conductor: $107800$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 107800.bk have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1\)
\(11\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 107800.bk do not have complex multiplication.

Modular form 107800.2.a.bk

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 LMFDB 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 LMFDB labels.

Elliptic curves in class 107800.bk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
107800.bk1	107800bn4	\([0, 0, 0, -9245075, 556774750]\)	\(46424454082884/26794860125\)	\(50438215981538000000000\)	\([2]\)	\(7962624\)	\(3.0458\)
107800.bk2	107800bn2	\([0, 0, 0, -6182575, -5895912750]\)	\(55537159171536/228765625\)	\(107656188062500000000\)	\([2, 2]\)	\(3981312\)	\(2.6992\)
107800.bk3	107800bn1	\([0, 0, 0, -6176450, -5908217875]\)	\(885956203616256/15125\)	\(444860281250000\)	\([2]\)	\(1990656\)	\(2.3526\)	\(\Gamma_0(N)\)-optimal
107800.bk4	107800bn3	\([0, 0, 0, -3218075, -11561072250]\)	\(-1957960715364/29541015625\)	\(-55607535156250000000000\)	\([2]\)	\(7962624\)	\(3.0458\)