Elliptic curve isogeny class with LMFDB label 83942.c (Cremona label 83942a)

• Label: 83942.c
• Number of curves: $3$
• Conductor: $83942$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 83942.c have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(19\)	\(1 + T\)
\(47\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(13\)	\( 1 + 5 T + 13 T^{2}\)	1.13.f
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 83942.c do not have complex multiplication.

Modular form 83942.2.a.c

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 LMFDB numbering.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 83942.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
83942.c1	83942a3	\([1, 0, 1, -188916, 254207730]\)	\(-69173457625/2550136832\)	\(-27488474030541897728\)	\([]\)	\(1907712\)	\(2.4102\)
83942.c2	83942a1	\([1, 0, 1, -34286, -2447144]\)	\(-413493625/152\)	\(-1638440730008\)	\([]\)	\(211968\)	\(1.3116\)	\(\Gamma_0(N)\)-optimal
83942.c3	83942a2	\([1, 0, 1, 20939, -9286208]\)	\(94196375/3511808\)	\(-37854534626104832\)	\([]\)	\(635904\)	\(1.8609\)