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Properties

Label 46.72864.2641-46.e.1.2
Level $46$
Index $72864$
Genus $2641$
Analytic rank $95$
Cusps $792$
$\Q$-cusps $33$

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Invariants

Level: $46$ $\SL_2$-level: $46$ Newform level: $2116$
Index: $72864$ $\PSL_2$-index:$36432$
Genus: $2641 = 1 + \frac{ 36432 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 792 }{2}$
Cusps: $792$ (of which $33$ are rational) Cusp widths $46^{792}$ Cusp orbits $1^{33}\cdot11^{3}\cdot22^{33}$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
Analytic rank: $95$
$\Q$-gonality: $362 \le \gamma \le 1012$
$\overline{\Q}$-gonality: $362 \le \gamma \le 1012$
Rational cusps: $33$
Rational CM points: none

Other labels

Rouse, Sutherland, and Zureick-Brown (RSZB) label: 46.72864.2641.1

Level structure

$\GL_2(\Z/46\Z)$-generators: $\begin{bmatrix}11&0\\0&1\end{bmatrix}$
$\GL_2(\Z/46\Z)$-subgroup: $C_{22}$
Contains $-I$: no $\quad$ (see 46.36432.2641.e.1 for the level structure with $-I$)
Cyclic 46-isogeny field degree: $1$
Cyclic 46-torsion field degree: $1$
Full 46-torsion field degree: $22$

Jacobian

Conductor: $2^{2022}\cdot23^{5082}$
Simple: no
Squarefree: no
Decomposition: $1^{22}\cdot2^{29}\cdot3^{3}\cdot4^{8}\cdot5^{14}\cdot6\cdot8^{3}\cdot10^{97}\cdot20^{37}\cdot30^{3}\cdot40^{8}\cdot60\cdot80^{3}$
Newforms: 23.2.a.a$^{6}$, 23.2.c.a$^{6}$, 46.2.a.a$^{4}$, 46.2.c.a$^{4}$, 46.2.c.b$^{4}$, 92.2.a.a$^{2}$, 92.2.a.b$^{2}$, 92.2.e.a$^{2}$, 529.2.a.a$^{3}$, 529.2.a.b$^{3}$, 529.2.a.c$^{3}$, 529.2.a.d$^{3}$, 529.2.a.e$^{3}$, 529.2.a.f$^{3}$, 529.2.a.g$^{3}$, 529.2.a.h$^{3}$, 529.2.a.i$^{3}$, 529.2.a.j$^{3}$, 529.2.c.a$^{3}$, 529.2.c.b$^{3}$, 529.2.c.c$^{3}$, 529.2.c.d$^{3}$, 529.2.c.e$^{3}$, 529.2.c.f$^{3}$, 529.2.c.g$^{3}$, 529.2.c.h$^{3}$, 529.2.c.i$^{3}$, 529.2.c.j$^{3}$, 529.2.c.k$^{3}$, 529.2.c.l$^{3}$, 529.2.c.m$^{3}$, 529.2.c.n$^{3}$, 529.2.c.o$^{3}$, 529.2.c.p$^{3}$, 529.2.c.q$^{3}$, 529.2.c.r$^{3}$, 1058.2.a.a$^{2}$, 1058.2.a.b$^{2}$, 1058.2.a.c$^{2}$, 1058.2.a.d$^{2}$, 1058.2.a.e$^{2}$, 1058.2.a.f$^{2}$, 1058.2.a.g$^{2}$, 1058.2.a.h$^{2}$, 1058.2.a.i$^{2}$, 1058.2.a.j$^{2}$, 1058.2.a.k$^{2}$, 1058.2.a.l$^{2}$, 1058.2.a.m$^{2}$, 1058.2.a.n$^{2}$, 1058.2.c.a$^{2}$, 1058.2.c.b$^{2}$, 1058.2.c.ba$^{2}$, 1058.2.c.bb$^{2}$, 1058.2.c.bc$^{2}$, 1058.2.c.c$^{2}$, 1058.2.c.d$^{2}$, 1058.2.c.e$^{2}$, 1058.2.c.f$^{2}$, 1058.2.c.g$^{2}$, 1058.2.c.h$^{2}$, 1058.2.c.i$^{2}$, 1058.2.c.j$^{2}$, 1058.2.c.k$^{2}$, 1058.2.c.l$^{2}$, 1058.2.c.m$^{2}$, 1058.2.c.n$^{2}$, 1058.2.c.o$^{2}$, 1058.2.c.p$^{2}$, 1058.2.c.q$^{2}$, 1058.2.c.r$^{2}$, 1058.2.c.s$^{2}$, 1058.2.c.t$^{2}$, 1058.2.c.u$^{2}$, 1058.2.c.v$^{2}$, 1058.2.c.w$^{2}$, 1058.2.c.x$^{2}$, 1058.2.c.y$^{2}$, 1058.2.c.z$^{2}$, 2116.2.a.a, 2116.2.a.b, 2116.2.a.c, 2116.2.a.d, 2116.2.a.e, 2116.2.a.f, 2116.2.a.g, 2116.2.a.h, 2116.2.a.i, 2116.2.a.j, 2116.2.e.a, 2116.2.e.b, 2116.2.e.c, 2116.2.e.d, 2116.2.e.e, 2116.2.e.f, 2116.2.e.g, 2116.2.e.h, 2116.2.e.i, 2116.2.e.j, 2116.2.e.k, 2116.2.e.l, 2116.2.e.m, 2116.2.e.n, 2116.2.e.o, 2116.2.e.p, 2116.2.e.q, 2116.2.e.r, 2116.2.e.s

Rational points

This modular curve has 33 rational cusps but no known non-cuspidal rational points.

Modular covers

The following modular covers realize this modular curve as a fiber product over $X(1)$.

Factor curve Level Index Degree Genus Rank Kernel decomposition
$X(2)$ $2$ $12144$ $6072$ $0$ $0$ full Jacobian
$X_{\mathrm{arith}}(23)$ $23$ $6$ $6$ $375$ $13$ $1^{22}\cdot2^{22}\cdot3^{2}\cdot4^{6}\cdot5^{12}\cdot6\cdot8^{3}\cdot10^{86}\cdot20^{31}\cdot30^{2}\cdot40^{6}\cdot60\cdot80^{3}$

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank Kernel decomposition
$X_1(2,46)$ $46$ $23$ $23$ $100$ $1$ $1^{18}\cdot2^{26}\cdot3^{3}\cdot4^{8}\cdot5^{14}\cdot6\cdot8^{3}\cdot10^{90}\cdot20^{36}\cdot30^{3}\cdot40^{8}\cdot60\cdot80^{3}$
46.3168.100-46.e.2.1 $46$ $23$ $23$ $100$ $1$ $1^{18}\cdot2^{26}\cdot3^{3}\cdot4^{8}\cdot5^{14}\cdot6\cdot8^{3}\cdot10^{90}\cdot20^{36}\cdot30^{3}\cdot40^{8}\cdot60\cdot80^{3}$
46.6624.241-46.a.1.1 $46$ $11$ $11$ $241$ $95$ $10^{95}\cdot20^{37}\cdot30^{3}\cdot40^{8}\cdot60\cdot80^{3}$
46.24288.881-46.f.1.1 $46$ $3$ $3$ $881$ $33$ $1^{14}\cdot2^{20}\cdot3^{2}\cdot4^{6}\cdot5^{12}\cdot8^{2}\cdot10^{78}\cdot20^{18}\cdot30^{2}\cdot40^{6}\cdot80^{2}$
46.36432.1255-46.e.1.1 $46$ $2$ $2$ $1255$ $44$ $1^{15}\cdot2^{12}\cdot3\cdot4^{3}\cdot5^{6}\cdot6\cdot8^{2}\cdot10^{47}\cdot20^{22}\cdot30\cdot40^{3}\cdot60\cdot80^{2}$
46.36432.1255-46.e.1.4 $46$ $2$ $2$ $1255$ $44$ $1^{15}\cdot2^{12}\cdot3\cdot4^{3}\cdot5^{6}\cdot6\cdot8^{2}\cdot10^{47}\cdot20^{22}\cdot30\cdot40^{3}\cdot60\cdot80^{2}$