Modular curve $X_{\mathrm{arith}}(43)$

• Label: 43.79464.2850-43.i.1.1
• Level: $43$
• Index: $79464$
• Genus: $2850$
• Analytic rank: $62$
• Cusps: $924$
• $\Q$-cusps: $21$

Invariants

Level:	$43$		$\SL_2$-level:	$43$		Newform level:	$1849$
Index:	$79464$		$\PSL_2$-index:	$39732$
Genus:	$2850 = 1 + \frac{ 39732 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 924 }{2}$
Cusps:	$924$ (of which $21$ are rational)		Cusp widths	$43^{924}$		Cusp orbits	$1^{21}\cdot21\cdot42^{21}$
Elliptic points:	$0$ of order $2$ and $0$ of order $3$
Analytic rank:	$62$
$\Q$-gonality:	$395 \le \gamma \le 1935$
$\overline{\Q}$-gonality:	$395 \le \gamma \le 1935$
Rational cusps:	$21$
Rational CM points:	none

Other labels

Rouse, Sutherland, and Zureick-Brown (RSZB) label:	43.79464.2850.1
Sutherland (S) label:	43Cs.1.1

Level structure

$\GL_2(\Z/43\Z)$-generators:	$\begin{bmatrix}34&0\\0&1\end{bmatrix}$
$\GL_2(\Z/43\Z)$-subgroup:	$C_{42}$
Contains $-I$:	no $\quad$ (see 43.39732.2850.i.1 for the level structure with $-I$)
Cyclic 43-isogeny field degree:	$1$
Cyclic 43-torsion field degree:	$1$
Full 43-torsion field degree:	$42$

Jacobian

Conductor:	$43^{5586}$
Simple:	no
Squarefree:	no
Decomposition:	$1^{6}\cdot2^{12}\cdot3^{4}\cdot4^{6}\cdot6^{23}\cdot10\cdot12^{22}\cdot18^{2}\cdot20^{4}\cdot24^{5}\cdot36^{21}\cdot40^{3}\cdot60\cdot120^{4}\cdot240^{3}$
Newforms:	43.2.a.a$^{2}$, 43.2.a.b$^{2}$, 43.2.c.a$^{2}$, 43.2.c.b$^{2}$, 43.2.e.a$^{2}$, 43.2.e.b$^{2}$, 43.2.g.a$^{2}$, 1849.2.a.a, 1849.2.a.b, 1849.2.a.c, 1849.2.a.d, 1849.2.a.e, 1849.2.a.f, 1849.2.a.g, 1849.2.a.h, 1849.2.a.i, 1849.2.a.j, 1849.2.a.k, 1849.2.a.l, 1849.2.a.m, 1849.2.a.n, 1849.2.a.o, 1849.2.a.p, 1849.2.a.q, 1849.2.a.r, 1849.2.c.a, 1849.2.c.b, 1849.2.c.c, 1849.2.c.d, 1849.2.c.e, 1849.2.c.f, 1849.2.c.g, 1849.2.c.h, 1849.2.c.i, 1849.2.c.j, 1849.2.c.k, 1849.2.c.l, 1849.2.c.m, 1849.2.c.n, 1849.2.c.o, 1849.2.c.p, 1849.2.c.q, 1849.2.c.r, 1849.2.e.a, 1849.2.e.b, 1849.2.e.ba, 1849.2.e.bb, 1849.2.e.bc, 1849.2.e.bd, 1849.2.e.c, 1849.2.e.d, 1849.2.e.e, 1849.2.e.f, 1849.2.e.g, 1849.2.e.h, 1849.2.e.i, 1849.2.e.j, 1849.2.e.k, 1849.2.e.l, 1849.2.e.m, 1849.2.e.n, 1849.2.e.o, 1849.2.e.p, 1849.2.e.q, 1849.2.e.r, 1849.2.e.s, 1849.2.e.t, 1849.2.e.u, 1849.2.e.v, 1849.2.e.w, 1849.2.e.x, 1849.2.e.y, 1849.2.e.z, 1849.2.g.a, 1849.2.g.b, 1849.2.g.ba, 1849.2.g.bb, 1849.2.g.bc, 1849.2.g.bd, 1849.2.g.be, 1849.2.g.bf, 1849.2.g.bg, 1849.2.g.bh, 1849.2.g.bi, 1849.2.g.bj, 1849.2.g.bk, 1849.2.g.c, 1849.2.g.d, 1849.2.g.e, 1849.2.g.f, 1849.2.g.g, 1849.2.g.h, 1849.2.g.i, 1849.2.g.j, 1849.2.g.k, 1849.2.g.l, 1849.2.g.m, 1849.2.g.n, 1849.2.g.o, 1849.2.g.p, 1849.2.g.q, 1849.2.g.r, 1849.2.g.s, 1849.2.g.t, 1849.2.g.u, 1849.2.g.v, 1849.2.g.w, 1849.2.g.x, 1849.2.g.y, 1849.2.g.z

Rational points

This modular curve has 21 rational cusps but no known non-cuspidal rational points.

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank	Kernel decomposition
43.1848.57-43.i.1.2	$43$	$43$	$43$	$57$	$1$	$1^{5}\cdot2^{10}\cdot3^{4}\cdot4^{5}\cdot6^{21}\cdot10\cdot12^{22}\cdot18^{2}\cdot20^{4}\cdot24^{5}\cdot36^{20}\cdot40^{3}\cdot60\cdot120^{4}\cdot240^{3}$
$X_1(43)$	$43$	$43$	$43$	$57$	$1$	$1^{5}\cdot2^{10}\cdot3^{4}\cdot4^{5}\cdot6^{21}\cdot10\cdot12^{22}\cdot18^{2}\cdot20^{4}\cdot24^{5}\cdot36^{20}\cdot40^{3}\cdot60\cdot120^{4}\cdot240^{3}$
43.11352.408-43.a.1.2	$43$	$7$	$7$	$408$	$62$	$6^{19}\cdot12^{22}\cdot24^{5}\cdot36^{19}\cdot60\cdot120^{4}\cdot240^{3}$
43.26488.946-43.b.1.2	$43$	$3$	$3$	$946$	$62$	$2^{6}\cdot4^{6}\cdot6^{4}\cdot12^{17}\cdot20\cdot24^{5}\cdot36^{15}\cdot40^{3}\cdot120\cdot240^{3}$