Elliptic curve isogeny class with LMFDB label 46827.o (Cremona label 46827q)

• Label: 46827.o
• Number of curves: $4$
• Conductor: $46827$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 46827.o have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(11\)	\(1\)
\(43\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - T + 2 T^{2}\)	1.2.ab
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 46827.o do not have complex multiplication.

Modular form 46827.2.a.o

Isogeny matrix

The \((i,j)\)-th 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, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 46827.o

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
46827.o1	46827q4	\([1, -1, 0, -266283, 52305534]\)	\(1616855892553/22851963\)	\(29512578243273147\)	\([2]\)	\(345600\)	\(1.9651\)
46827.o2	46827q2	\([1, -1, 0, -32148, -936765]\)	\(2845178713/1347921\)	\(1740796796242449\)	\([2, 2]\)	\(172800\)	\(1.6185\)
46827.o3	46827q1	\([1, -1, 0, -26703, -1671840]\)	\(1630532233/1161\)	\(1499394312009\)	\([2]\)	\(86400\)	\(1.2719\)	\(\Gamma_0(N)\)-optimal
46827.o4	46827q3	\([1, -1, 0, 114867, -7199604]\)	\(129784785047/92307627\)	\(-119212343564899563\)	\([2]\)	\(345600\)	\(1.9651\)