Elliptic curve isogeny class with LMFDB label 46569.c (Cremona label 46569c)

• Label: 46569.c
• Number of curves: $4$
• Conductor: $46569$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 46569.c have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 + T\)
\(19\)	\(1\)
\(43\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + T + 2 T^{2}\)	1.2.b
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 46569.c do not have complex multiplication.

Modular form 46569.2.a.c

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 46569.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
46569.c1	46569c4	\([1, 1, 1, -88272, -10007202]\)	\(1616855892553/22851963\)	\(1075090731914403\)	\([2]\)	\(207360\)	\(1.6890\)
46569.c2	46569c2	\([1, 1, 1, -10657, 175886]\)	\(2845178713/1347921\)	\(63414130963401\)	\([2, 2]\)	\(103680\)	\(1.3425\)
46569.c3	46569c1	\([1, 1, 1, -8852, 316676]\)	\(1630532233/1161\)	\(54620267841\)	\([2]\)	\(51840\)	\(0.99590\)	\(\Gamma_0(N)\)-optimal
46569.c4	46569c3	\([1, 1, 1, 38078, 1384514]\)	\(129784785047/92307627\)	\(-4342693635234387\)	\([2]\)	\(207360\)	\(1.6890\)