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Properties

Label 24.1152.73.cg.1
Level $24$
Index $1152$
Genus $73$
Analytic rank $9$
Cusps $48$
$\Q$-cusps $8$

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Invariants

Level: $24$ $\SL_2$-level: $24$ Newform level: $576$
Index: $1152$ $\PSL_2$-index:$1152$
Genus: $73 = 1 + \frac{ 1152 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 48 }{2}$
Cusps: $48$ (of which $8$ are rational) Cusp widths $24^{48}$ Cusp orbits $1^{8}\cdot2^{8}\cdot4^{4}\cdot8$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
Analytic rank: $9$
$\Q$-gonality: $17 \le \gamma \le 24$
$\overline{\Q}$-gonality: $17 \le \gamma \le 24$
Rational cusps: $8$
Rational CM points: none

Other labels

Rouse, Sutherland, and Zureick-Brown (RSZB) label: 24.1152.73.20

Level structure

$\GL_2(\Z/24\Z)$-generators: $\begin{bmatrix}1&0\\0&17\end{bmatrix}$, $\begin{bmatrix}7&0\\0&13\end{bmatrix}$, $\begin{bmatrix}13&0\\0&1\end{bmatrix}$, $\begin{bmatrix}13&0\\0&13\end{bmatrix}$, $\begin{bmatrix}17&0\\0&17\end{bmatrix}$, $\begin{bmatrix}19&0\\0&19\end{bmatrix}$
$\GL_2(\Z/24\Z)$-subgroup: $C_2^6$
Contains $-I$: yes
Quadratic refinements: 24.2304.73-24.cg.1.1, 24.2304.73-24.cg.1.2, 24.2304.73-24.cg.1.3, 24.2304.73-24.cg.1.4, 24.2304.73-24.cg.1.5, 24.2304.73-24.cg.1.6, 24.2304.73-24.cg.1.7, 24.2304.73-24.cg.1.8, 24.2304.73-24.cg.1.9, 24.2304.73-24.cg.1.10, 24.2304.73-24.cg.1.11, 24.2304.73-24.cg.1.12, 24.2304.73-24.cg.1.13, 24.2304.73-24.cg.1.14, 48.2304.73-24.cg.1.1, 48.2304.73-24.cg.1.2, 48.2304.73-24.cg.1.3, 48.2304.73-24.cg.1.4, 48.2304.73-24.cg.1.5, 48.2304.73-24.cg.1.6, 48.2304.73-24.cg.1.7, 48.2304.73-24.cg.1.8, 48.2304.73-24.cg.1.9, 48.2304.73-24.cg.1.10, 48.2304.73-24.cg.1.11, 48.2304.73-24.cg.1.12, 48.2304.73-24.cg.1.13, 48.2304.73-24.cg.1.14, 48.2304.73-24.cg.1.15, 48.2304.73-24.cg.1.16, 48.2304.73-24.cg.1.17, 48.2304.73-24.cg.1.18, 48.2304.73-24.cg.1.19, 48.2304.73-24.cg.1.20, 48.2304.73-24.cg.1.21
Cyclic 24-isogeny field degree: $1$
Cyclic 24-torsion field degree: $8$
Full 24-torsion field degree: $64$

Jacobian

Conductor: $2^{334}\cdot3^{98}$
Simple: no
Squarefree: no
Decomposition: $1^{73}$
Newforms: 24.2.a.a$^{8}$, 32.2.a.a$^{6}$, 36.2.a.a$^{5}$, 48.2.a.a$^{6}$, 64.2.a.a$^{3}$, 72.2.a.a$^{4}$, 96.2.a.a$^{4}$, 96.2.a.b$^{4}$, 144.2.a.a$^{3}$, 144.2.a.b$^{3}$, 192.2.a.a$^{2}$, 192.2.a.b$^{2}$, 192.2.a.c$^{2}$, 192.2.a.d$^{2}$, 288.2.a.a$^{2}$, 288.2.a.b$^{2}$, 288.2.a.c$^{2}$, 288.2.a.d$^{2}$, 288.2.a.e$^{2}$, 576.2.a.a, 576.2.a.b, 576.2.a.c, 576.2.a.d, 576.2.a.e, 576.2.a.f, 576.2.a.g, 576.2.a.h, 576.2.a.i

Rational points

This modular curve has 8 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
$X_{\mathrm{sp}}(3)$ $3$ $96$ $96$ $0$ $0$ full Jacobian
$X_{\mathrm{sp}}(8)$ $8$ $12$ $12$ $3$ $0$ $1^{70}$

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank Kernel decomposition
24.384.21.bm.2 $24$ $3$ $3$ $21$ $1$ $1^{52}$
24.576.33.cx.2 $24$ $2$ $2$ $33$ $5$ $1^{40}$
24.576.33.cy.1 $24$ $2$ $2$ $33$ $2$ $1^{40}$
$X_{\mathrm{sp}}^+(24)$ $24$ $2$ $2$ $33$ $6$ $1^{40}$
24.576.37.fu.2 $24$ $2$ $2$ $37$ $4$ $1^{36}$
24.576.37.gf.2 $24$ $2$ $2$ $37$ $4$ $1^{36}$
24.576.37.gj.1 $24$ $2$ $2$ $37$ $5$ $1^{36}$
24.576.37.bgv.1 $24$ $2$ $2$ $37$ $5$ $1^{36}$

This modular curve is minimally covered by the modular curves in the database listed below.

Covering curve Level Index Degree Genus Rank Kernel decomposition
24.2304.145.bg.1 $24$ $2$ $2$ $145$ $9$ $2^{12}\cdot4^{10}\cdot8$
24.2304.145.cv.1 $24$ $2$ $2$ $145$ $9$ $2^{28}\cdot4^{4}$
24.2304.145.dy.1 $24$ $2$ $2$ $145$ $9$ $2^{28}\cdot4^{4}$
24.2304.145.et.1 $24$ $2$ $2$ $145$ $9$ $2^{18}\cdot4^{9}$
24.2304.145.ew.1 $24$ $2$ $2$ $145$ $9$ $2^{18}\cdot4^{9}$
24.2304.145.fs.1 $24$ $2$ $2$ $145$ $9$ $2^{28}\cdot4^{4}$
24.2304.145.gt.1 $24$ $2$ $2$ $145$ $9$ $2^{28}\cdot4^{4}$
24.2304.145.iu.1 $24$ $2$ $2$ $145$ $9$ $2^{12}\cdot4^{10}\cdot8$
48.2304.161.cav.1 $48$ $2$ $2$ $161$ $43$ $1^{44}\cdot2^{20}\cdot4$
48.2304.161.cav.2 $48$ $2$ $2$ $161$ $43$ $1^{44}\cdot2^{20}\cdot4$
48.2304.161.caw.1 $48$ $2$ $2$ $161$ $19$ $2^{44}$
48.2304.161.cax.1 $48$ $2$ $2$ $161$ $32$ $1^{88}$
48.2304.161.cax.3 $48$ $2$ $2$ $161$ $32$ $1^{88}$
48.2304.161.cay.1 $48$ $2$ $2$ $161$ $9$ $2^{28}\cdot4^{8}$
48.2304.161.cay.2 $48$ $2$ $2$ $161$ $9$ $2^{28}\cdot4^{8}$
48.2304.161.caz.1 $48$ $2$ $2$ $161$ $9$ $4^{22}$
48.2304.161.cba.1 $48$ $2$ $2$ $161$ $15$ $2^{20}\cdot4^{8}\cdot8^{2}$
48.2304.161.cba.2 $48$ $2$ $2$ $161$ $15$ $2^{20}\cdot4^{8}\cdot8^{2}$
48.2304.161.cbb.1 $48$ $2$ $2$ $161$ $9$ $2^{4}\cdot4^{18}\cdot8$
48.2304.161.cbb.2 $48$ $2$ $2$ $161$ $9$ $2^{4}\cdot4^{18}\cdot8$
48.2304.161.cbc.1 $48$ $2$ $2$ $161$ $9$ $2^{8}\cdot4^{18}$
48.2304.161.cbc.2 $48$ $2$ $2$ $161$ $9$ $2^{8}\cdot4^{18}$
48.2304.161.cbd.1 $48$ $2$ $2$ $161$ $9$ $2^{28}\cdot4^{8}$
48.2304.161.cbd.2 $48$ $2$ $2$ $161$ $9$ $2^{28}\cdot4^{8}$
48.2304.161.cbe.1 $48$ $2$ $2$ $161$ $37$ $1^{88}$
48.2304.161.cbe.3 $48$ $2$ $2$ $161$ $37$ $1^{88}$
48.2304.161.cbf.1 $48$ $2$ $2$ $161$ $21$ $2^{44}$
48.2304.161.cbg.1 $48$ $2$ $2$ $161$ $47$ $1^{44}\cdot2^{20}\cdot4$
48.2304.161.cbg.2 $48$ $2$ $2$ $161$ $47$ $1^{44}\cdot2^{20}\cdot4$