Elliptic curve isogeny class with Cremona label 110110bu (LMFDB label 110110.cc)

• Label: 110110bu
• Number of curves: $4$
• Conductor: $110110$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 110110bu have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(5\)	\(1 - T\)
\(7\)	\(1 - T\)
\(11\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 110110bu do not have complex multiplication.

Modular form 110110.2.a.bu

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 110110bu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
110110.cc3	110110bu1	\([1, -1, 1, -242023, -41865953]\)	\(884984855328729/83492864000\)	\(147912701640704000\)	\([2]\)	\(1228800\)	\(2.0328\)	\(\Gamma_0(N)\)-optimal
110110.cc2	110110bu2	\([1, -1, 1, -861543, 261203231]\)	\(39920686684059609/6492304000000\)	\(11501512566544000000\)	\([2, 2]\)	\(2457600\)	\(2.3793\)
110110.cc4	110110bu3	\([1, -1, 1, 1558457, 1462491231]\)	\(236293804275620391/658593925444000\)	\(-1166739313153498084000\)	\([2]\)	\(4915200\)	\(2.7259\)
110110.cc1	110110bu4	\([1, -1, 1, -13193863, 18448908767]\)	\(143378317900125424089/4976562500000\)	\(8816284039062500000\)	\([2]\)	\(4915200\)	\(2.7259\)