Properties

Label 70.6720.257-70.cl.1.2
Level $70$
Index $6720$
Genus $257$
Analytic rank $56$
Cusps $48$
$\Q$-cusps $2$

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Invariants

Level: $70$ $\SL_2$-level: $70$ Newform level: $4900$
Index: $6720$ $\PSL_2$-index:$3360$
Genus: $257 = 1 + \frac{ 3360 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 48 }{2}$
Cusps: $48$ (of which $2$ are rational) Cusp widths $70^{48}$ Cusp orbits $1^{2}\cdot2\cdot3^{2}\cdot4^{2}\cdot6\cdot12^{2}$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
Analytic rank: $56$
$\Q$-gonality: $34 \le \gamma \le 56$
$\overline{\Q}$-gonality: $34 \le \gamma \le 56$
Rational cusps: $2$
Rational CM points: none

Other labels

Rouse, Sutherland, and Zureick-Brown (RSZB) label: 70.6720.257.22

Level structure

$\GL_2(\Z/70\Z)$-generators: $\begin{bmatrix}31&65\\15&46\end{bmatrix}$, $\begin{bmatrix}42&37\\55&21\end{bmatrix}$, $\begin{bmatrix}58&9\\15&66\end{bmatrix}$
$\GL_2(\Z/70\Z)$-subgroup: $C_6^3.C_2^2$
Contains $-I$: no $\quad$ (see 70.3360.257.cl.1 for the level structure with $-I$)
Cyclic 70-isogeny field degree: $6$
Cyclic 70-torsion field degree: $36$
Full 70-torsion field degree: $864$

Jacobian

Conductor: $2^{280}\cdot5^{428}\cdot7^{445}$
Simple: no
Squarefree: no
Decomposition: $1^{61}\cdot2^{46}\cdot3^{4}\cdot4^{18}\cdot6^{2}\cdot8$
Newforms: 20.2.a.a, 35.2.a.a$^{2}$, 35.2.a.b$^{2}$, 35.2.b.a$^{2}$, 100.2.a.a$^{2}$, 100.2.c.a, 140.2.a.a, 140.2.a.b, 140.2.e.a$^{2}$, 140.2.e.b$^{2}$, 175.2.a.a, 175.2.a.b, 175.2.a.c, 175.2.a.d, 175.2.a.e, 175.2.a.f, 175.2.b.a, 175.2.b.b, 175.2.b.c, 196.2.a.a, 245.2.a.e$^{2}$, 245.2.a.f$^{2}$, 245.2.a.h$^{2}$, 245.2.b.c$^{2}$, 245.2.b.e$^{2}$, 245.2.b.f$^{2}$, 700.2.a.a, 700.2.a.b$^{2}$, 700.2.a.c, 700.2.a.d$^{2}$, 700.2.a.e, 700.2.a.f, 700.2.a.g, 700.2.a.h, 700.2.a.i, 700.2.a.j, 700.2.e.a, 700.2.e.b, 700.2.e.c, 700.2.e.d, 980.2.a.b, 980.2.a.c, 980.2.a.d, 980.2.a.e, 980.2.a.f, 980.2.a.h, 980.2.a.i, 980.2.e.a$^{2}$, 980.2.e.b$^{2}$, 980.2.e.c$^{2}$, 980.2.e.d$^{2}$, 1225.2.a.ba, 1225.2.a.bb, 1225.2.a.bc, 1225.2.a.d, 1225.2.a.f, 1225.2.a.k, 1225.2.a.l, 1225.2.a.p, 1225.2.a.r, 1225.2.a.v, 1225.2.a.x, 1225.2.a.y, 1225.2.b.g, 1225.2.b.i, 1225.2.b.j, 1225.2.b.l, 1225.2.b.n, 4900.2.a.a$^{2}$, 4900.2.a.b, 4900.2.a.bb, 4900.2.a.bd, 4900.2.a.bf, 4900.2.a.bj, 4900.2.a.c, 4900.2.a.d, 4900.2.a.e$^{2}$, 4900.2.a.f, 4900.2.a.h$^{2}$, 4900.2.a.j, 4900.2.a.k, 4900.2.a.l, 4900.2.a.m, 4900.2.a.n$^{3}$, 4900.2.a.o$^{2}$, 4900.2.a.p$^{2}$, 4900.2.a.q$^{2}$, 4900.2.a.r, 4900.2.a.s, 4900.2.a.t, 4900.2.a.u$^{2}$, 4900.2.a.w, 4900.2.e.a, 4900.2.e.b, 4900.2.e.d, 4900.2.e.e, 4900.2.e.f, 4900.2.e.g, 4900.2.e.h, 4900.2.e.j, 4900.2.e.k, 4900.2.e.l, 4900.2.e.n, 4900.2.e.o, 4900.2.e.s

Rational points

This modular curve has 2 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
35.3360.117-35.a.1.7 $35$ $2$ $2$ $117$ $19$ $1^{54}\cdot2^{25}\cdot3^{2}\cdot4^{6}\cdot6$
70.1344.49-70.u.1.7 $70$ $5$ $5$ $49$ $12$ $1^{48}\cdot2^{36}\cdot3^{4}\cdot4^{14}\cdot6^{2}\cdot8$
70.1344.49-70.u.2.5 $70$ $5$ $5$ $49$ $12$ $1^{48}\cdot2^{36}\cdot3^{4}\cdot4^{14}\cdot6^{2}\cdot8$
70.3360.117-35.a.1.5 $70$ $2$ $2$ $117$ $19$ $1^{54}\cdot2^{25}\cdot3^{2}\cdot4^{6}\cdot6$

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

Covering curve Level Index Degree Genus Rank Kernel decomposition
70.13440.513-70.t.1.4 $70$ $2$ $2$ $513$ $98$ $1^{52}\cdot2^{52}\cdot3^{4}\cdot4^{17}\cdot6^{2}\cdot8$
70.13440.513-70.cn.1.4 $70$ $2$ $2$ $513$ $109$ $1^{52}\cdot2^{52}\cdot3^{4}\cdot4^{17}\cdot6^{2}\cdot8$
70.13440.513-70.cv.1.2 $70$ $2$ $2$ $513$ $111$ $1^{52}\cdot2^{52}\cdot3^{4}\cdot4^{17}\cdot6^{2}\cdot8$
70.13440.513-70.cw.1.3 $70$ $2$ $2$ $513$ $98$ $1^{52}\cdot2^{52}\cdot3^{4}\cdot4^{17}\cdot6^{2}\cdot8$
70.20160.769-70.em.1.6 $70$ $3$ $3$ $769$ $158$ $1^{100}\cdot2^{88}\cdot3^{12}\cdot4^{37}\cdot6^{6}\cdot8^{2}$
70.20160.769-70.ev.1.6 $70$ $3$ $3$ $769$ $138$ $1^{116}\cdot2^{110}\cdot3^{4}\cdot4^{34}\cdot6^{2}\cdot8^{2}$