Elliptic curve isogeny class with Cremona label 85176ce (LMFDB label 85176.bs)

• Label: 85176ce
• Number of curves: $4$
• Conductor: $85176$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 85176ce have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1 + T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 4 T + 5 T^{2}\)	1.5.ae
\(11\)	\( 1 - 5 T + 11 T^{2}\)	1.11.af
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 85176ce do not have complex multiplication.

Modular form 85176.2.a.ce

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 85176ce

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
85176.bs4	85176ce1	\([0, 0, 0, 1521, -118638]\)	\(432/7\)	\(-6305588819712\)	\([2]\)	\(147456\)	\(1.1366\)	\(\Gamma_0(N)\)-optimal
85176.bs3	85176ce2	\([0, 0, 0, -28899, -1779570]\)	\(740772/49\)	\(176556486951936\)	\([2, 2]\)	\(294912\)	\(1.4832\)
85176.bs2	85176ce3	\([0, 0, 0, -89739, 8186022]\)	\(11090466/2401\)	\(17302535721289728\)	\([2]\)	\(589824\)	\(1.8297\)
85176.bs1	85176ce4	\([0, 0, 0, -454779, -118044810]\)	\(1443468546/7\)	\(50444710557696\)	\([2]\)	\(589824\)	\(1.8297\)