Elliptic curve isogeny class with Cremona label 110946bm (LMFDB label 110946.bo)

• Label: 110946bm
• Number of curves: $4$
• Conductor: $110946$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 110946bm have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(11\)	\(1 + T\)
\(41\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 4 T + 23 T^{2}\)	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 110946bm do not have complex multiplication.

Modular form 110946.2.a.bm

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 110946bm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
110946.bo4	110946bm1	\([1, 0, 0, -3397, 1073]\)	\(912673/528\)	\(2508055039248\)	\([2]\)	\(276480\)	\(1.0687\)	\(\Gamma_0(N)\)-optimal
110946.bo2	110946bm2	\([1, 0, 0, -37017, -2735595]\)	\(1180932193/4356\)	\(20691454073796\)	\([2, 2]\)	\(552960\)	\(1.4153\)
110946.bo3	110946bm3	\([1, 0, 0, -20207, -5226837]\)	\(-192100033/2371842\)	\(-11266496743181922\)	\([2]\)	\(1105920\)	\(1.7618\)
110946.bo1	110946bm4	\([1, 0, 0, -591747, -175256625]\)	\(4824238966273/66\)	\(313506879906\)	\([2]\)	\(1105920\)	\(1.7618\)