Label |
Cremona label |
Class |
Cremona class |
Class size |
Class degree |
Conductor |
Discriminant |
Rank |
Torsion |
$\textrm{End}^0(E_{\overline\Q})$ |
CM |
Sato-Tate |
Semistable |
Potentially good |
Nonmax $\ell$ |
$\ell$-adic images |
mod-$\ell$ images |
Adelic level |
Adelic index |
Adelic genus |
Regulator |
$Ш_{\textrm{an}}$ |
Ш primes |
Integral points |
Modular degree |
Faltings height |
j-invariant |
$abc$ quality |
Szpiro ratio |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
MW-generators |
156.b4 |
156b1 |
156.b |
156b |
$4$ |
$6$ |
\( 2^{2} \cdot 3 \cdot 13 \) |
\( 2^{4} \cdot 3^{6} \cdot 13 \) |
$0$ |
$\Z/6\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.8.0.1 |
2B, 3B.1.1 |
$156$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$5$ |
$12$ |
$-0.316421$ |
$16384000/9477$ |
$1.48887$ |
$3.83861$ |
$[0, 1, 0, -13, -4]$ |
\(y^2=x^3+x^2-13x-4\) |
2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 12.48.0-12.i.1.8, 26.6.0.b.1, $\ldots$ |
$[]$ |
468.c4 |
468d1 |
468.c |
468d |
$4$ |
$6$ |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{4} \cdot 3^{12} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.8.0.2 |
2B, 3B.1.2 |
$156$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$96$ |
$0.232885$ |
$16384000/9477$ |
$1.48887$ |
$4.22480$ |
$[0, 0, 0, -120, -11]$ |
\(y^2=x^3-120x-11\) |
2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 12.48.0-12.i.1.6, 26.6.0.b.1, $\ldots$ |
$[]$ |
624.b4 |
624g1 |
624.b |
624g |
$4$ |
$6$ |
\( 2^{4} \cdot 3 \cdot 13 \) |
\( 2^{4} \cdot 3^{6} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$156$ |
$96$ |
$1$ |
$1.331439434$ |
$1$ |
|
$3$ |
$48$ |
$-0.316421$ |
$16384000/9477$ |
$1.48887$ |
$3.01180$ |
$[0, -1, 0, -13, 4]$ |
\(y^2=x^3-x^2-13x+4\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.48.0-12.i.1.4, 26.6.0.b.1, $\ldots$ |
$[(0, 2)]$ |
1872.i4 |
1872p1 |
1872.i |
1872p |
$4$ |
$6$ |
\( 2^{4} \cdot 3^{2} \cdot 13 \) |
\( 2^{4} \cdot 3^{12} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$156$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$384$ |
$0.232885$ |
$16384000/9477$ |
$1.48887$ |
$3.44750$ |
$[0, 0, 0, -120, 11]$ |
\(y^2=x^3-120x+11\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.48.0-12.i.1.2, 26.6.0.b.1, $\ldots$ |
$[]$ |
2028.e4 |
2028d1 |
2028.e |
2028d |
$4$ |
$6$ |
\( 2^{2} \cdot 3 \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 13^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$156$ |
$96$ |
$1$ |
$0.736272345$ |
$1$ |
|
$5$ |
$2016$ |
$0.966053$ |
$16384000/9477$ |
$1.48887$ |
$4.56664$ |
$[0, 1, 0, -2253, 144]$ |
\(y^2=x^3+x^2-2253x+144\) |
2.3.0.a.1, 3.4.0.a.1, 6.24.0-6.a.1.1, 12.48.0-12.i.1.1, 26.6.0.b.1, $\ldots$ |
$[(108, 1014)]$ |
2496.h4 |
2496a1 |
2496.h |
2496a |
$4$ |
$6$ |
\( 2^{6} \cdot 3 \cdot 13 \) |
\( 2^{10} \cdot 3^{6} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$312$ |
$96$ |
$1$ |
$1.480230472$ |
$1$ |
|
$5$ |
$384$ |
$0.030152$ |
$16384000/9477$ |
$1.48887$ |
$3.00971$ |
$[0, -1, 0, -53, 21]$ |
\(y^2=x^3-x^2-53x+21\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 24.48.0-12.i.1.3, $\ldots$ |
$[(-3, 12)]$ |
2496.v4 |
2496ba1 |
2496.v |
2496ba |
$4$ |
$6$ |
\( 2^{6} \cdot 3 \cdot 13 \) |
\( 2^{10} \cdot 3^{6} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$312$ |
$96$ |
$1$ |
$0.615690421$ |
$1$ |
|
$7$ |
$384$ |
$0.030152$ |
$16384000/9477$ |
$1.48887$ |
$3.00971$ |
$[0, 1, 0, -53, -21]$ |
\(y^2=x^3+x^2-53x-21\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 24.48.0-12.i.1.7, $\ldots$ |
$[(-2, 9)]$ |
3900.a4 |
3900c1 |
3900.a |
3900c |
$4$ |
$6$ |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 \) |
\( 2^{4} \cdot 3^{6} \cdot 5^{6} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$780$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$1728$ |
$0.488297$ |
$16384000/9477$ |
$1.48887$ |
$3.51215$ |
$[0, -1, 0, -333, 162]$ |
\(y^2=x^3-x^2-333x+162\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 15.8.0-3.a.1.2, $\ldots$ |
$[]$ |
6084.h4 |
6084f1 |
6084.h |
6084f |
$4$ |
$6$ |
\( 2^{2} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 13^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$156$ |
$96$ |
$1$ |
$0.724512777$ |
$1$ |
|
$9$ |
$16128$ |
$1.515360$ |
$16384000/9477$ |
$1.48887$ |
$4.74737$ |
$[0, 0, 0, -20280, -24167]$ |
\(y^2=x^3-20280x-24167\) |
2.3.0.a.1, 3.4.0.a.1, 6.24.0-6.a.1.3, 12.48.0-12.i.1.3, 26.6.0.b.1, $\ldots$ |
$[(182, 1521)]$ |
7488.bb4 |
7488bp1 |
7488.bb |
7488bp |
$4$ |
$6$ |
\( 2^{6} \cdot 3^{2} \cdot 13 \) |
\( 2^{10} \cdot 3^{12} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$312$ |
$96$ |
$1$ |
$1.766052509$ |
$1$ |
|
$3$ |
$3072$ |
$0.579458$ |
$16384000/9477$ |
$1.48887$ |
$3.37796$ |
$[0, 0, 0, -480, 88]$ |
\(y^2=x^3-480x+88\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 24.48.0-12.i.1.5, $\ldots$ |
$[(26, 72)]$ |
7488.bf4 |
7488k1 |
7488.bf |
7488k |
$4$ |
$6$ |
\( 2^{6} \cdot 3^{2} \cdot 13 \) |
\( 2^{10} \cdot 3^{12} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$312$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$3072$ |
$0.579458$ |
$16384000/9477$ |
$1.48887$ |
$3.37796$ |
$[0, 0, 0, -480, -88]$ |
\(y^2=x^3-480x-88\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 24.48.0-12.i.1.1, $\ldots$ |
$[]$ |
7644.a4 |
7644a1 |
7644.a |
7644a |
$4$ |
$6$ |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13 \) |
\( 2^{4} \cdot 3^{6} \cdot 7^{6} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$1092$ |
$96$ |
$1$ |
$1.150414570$ |
$1$ |
|
$7$ |
$4320$ |
$0.656534$ |
$16384000/9477$ |
$1.48887$ |
$3.47361$ |
$[0, -1, 0, -653, 78]$ |
\(y^2=x^3-x^2-653x+78\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 21.8.0-3.a.1.1, $\ldots$ |
$[(-1, 27)]$ |
8112.i4 |
8112t1 |
8112.i |
8112t |
$4$ |
$6$ |
\( 2^{4} \cdot 3 \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 13^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$156$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$8064$ |
$0.966053$ |
$16384000/9477$ |
$1.48887$ |
$3.86332$ |
$[0, -1, 0, -2253, -144]$ |
\(y^2=x^3-x^2-2253x-144\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.48.0-12.i.1.5, 26.6.0.b.1, $\ldots$ |
$[]$ |
11700.h4 |
11700j1 |
11700.h |
11700j |
$4$ |
$6$ |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 13 \) |
\( 2^{4} \cdot 3^{12} \cdot 5^{6} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$780$ |
$96$ |
$1$ |
$0.976745768$ |
$1$ |
|
$9$ |
$13824$ |
$1.037603$ |
$16384000/9477$ |
$1.48887$ |
$3.80393$ |
$[0, 0, 0, -3000, -1375]$ |
\(y^2=x^3-3000x-1375\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 15.8.0-3.a.1.1, $\ldots$ |
$[(-26, 243)]$ |
15600.cv4 |
15600ce1 |
15600.cv |
15600ce |
$4$ |
$6$ |
\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 13 \) |
\( 2^{4} \cdot 3^{6} \cdot 5^{6} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$780$ |
$96$ |
$1$ |
$1.772312437$ |
$1$ |
|
$3$ |
$6912$ |
$0.488297$ |
$16384000/9477$ |
$1.48887$ |
$3.00787$ |
$[0, 1, 0, -333, -162]$ |
\(y^2=x^3+x^2-333x-162\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 26.6.0.b.1, $\ldots$ |
$[(-18, 18)]$ |
18876.k4 |
18876h1 |
18876.k |
18876h |
$4$ |
$6$ |
\( 2^{2} \cdot 3 \cdot 11^{2} \cdot 13 \) |
\( 2^{4} \cdot 3^{6} \cdot 11^{6} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$1716$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$17280$ |
$0.882526$ |
$16384000/9477$ |
$1.48887$ |
$3.43012$ |
$[0, 1, 0, -1613, -1080]$ |
\(y^2=x^3+x^2-1613x-1080\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 26.6.0.b.1, $\ldots$ |
$[]$ |
22932.n4 |
22932k1 |
22932.n |
22932k |
$4$ |
$6$ |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 13 \) |
\( 2^{4} \cdot 3^{12} \cdot 7^{6} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$1092$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$34560$ |
$1.205839$ |
$16384000/9477$ |
$1.48887$ |
$3.75005$ |
$[0, 0, 0, -5880, 3773]$ |
\(y^2=x^3-5880x+3773\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 21.8.0-3.a.1.2, $\ldots$ |
$[]$ |
24336.bi4 |
24336bh1 |
24336.bi |
24336bh |
$4$ |
$6$ |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 13^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$156$ |
$96$ |
$1$ |
$3.485354479$ |
$1$ |
|
$3$ |
$64512$ |
$1.515360$ |
$16384000/9477$ |
$1.48887$ |
$4.09574$ |
$[0, 0, 0, -20280, 24167]$ |
\(y^2=x^3-20280x+24167\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.48.0-12.i.1.7, 26.6.0.b.1, $\ldots$ |
$[(12493, 1396278)]$ |
30576.cm4 |
30576cl1 |
30576.cm |
30576cl |
$4$ |
$6$ |
\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 13 \) |
\( 2^{4} \cdot 3^{6} \cdot 7^{6} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$1092$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$17280$ |
$0.656534$ |
$16384000/9477$ |
$1.48887$ |
$3.00735$ |
$[0, 1, 0, -653, -78]$ |
\(y^2=x^3+x^2-653x-78\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 26.6.0.b.1, $\ldots$ |
$[]$ |
32448.u4 |
32448b1 |
32448.u |
32448b |
$4$ |
$6$ |
\( 2^{6} \cdot 3 \cdot 13^{2} \) |
\( 2^{10} \cdot 3^{6} \cdot 13^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$312$ |
$96$ |
$1$ |
$3.587062305$ |
$1$ |
|
$3$ |
$64512$ |
$1.312628$ |
$16384000/9477$ |
$1.48887$ |
$3.74810$ |
$[0, -1, 0, -9013, 10165]$ |
\(y^2=x^3-x^2-9013x+10165\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 24.48.0-12.i.1.6, $\ldots$ |
$[(148, 1377)]$ |
32448.cu4 |
32448cy1 |
32448.cu |
32448cy |
$4$ |
$6$ |
\( 2^{6} \cdot 3 \cdot 13^{2} \) |
\( 2^{10} \cdot 3^{6} \cdot 13^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$312$ |
$96$ |
$1$ |
$2.266200839$ |
$1$ |
|
$5$ |
$64512$ |
$1.312628$ |
$16384000/9477$ |
$1.48887$ |
$3.74810$ |
$[0, 1, 0, -9013, -10165]$ |
\(y^2=x^3+x^2-9013x-10165\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 24.48.0-12.i.1.2, $\ldots$ |
$[(-74, 507)]$ |
45084.d4 |
45084g1 |
45084.d |
45084g |
$4$ |
$6$ |
\( 2^{2} \cdot 3 \cdot 13 \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 13 \cdot 17^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$2652$ |
$96$ |
$1$ |
$1.107076207$ |
$1$ |
|
$7$ |
$55296$ |
$1.100185$ |
$16384000/9477$ |
$1.48887$ |
$3.39518$ |
$[0, -1, 0, -3853, 3286]$ |
\(y^2=x^3-x^2-3853x+3286\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 26.6.0.b.1, $\ldots$ |
$[(-45, 289)]$ |
46800.ec4 |
46800de1 |
46800.ec |
46800de |
$4$ |
$6$ |
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 13 \) |
\( 2^{4} \cdot 3^{12} \cdot 5^{6} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$780$ |
$96$ |
$1$ |
$4.356432561$ |
$1$ |
|
$3$ |
$55296$ |
$1.037603$ |
$16384000/9477$ |
$1.48887$ |
$3.31355$ |
$[0, 0, 0, -3000, 1375]$ |
\(y^2=x^3-3000x+1375\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 26.6.0.b.1, $\ldots$ |
$[(1145, 38700)]$ |
50700.n4 |
50700d1 |
50700.n |
50700d |
$4$ |
$6$ |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 5^{6} \cdot 13^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$780$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$290304$ |
$1.770773$ |
$16384000/9477$ |
$1.48887$ |
$4.10117$ |
$[0, -1, 0, -56333, 130662]$ |
\(y^2=x^3-x^2-56333x+130662\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 26.6.0.b.1, $\ldots$ |
$[]$ |
56316.f4 |
56316d1 |
56316.f |
56316d |
$4$ |
$6$ |
\( 2^{2} \cdot 3 \cdot 13 \cdot 19^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 13 \cdot 19^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$2964$ |
$96$ |
$1$ |
$8.114198318$ |
$1$ |
|
$1$ |
$85536$ |
$1.155798$ |
$16384000/9477$ |
$1.48887$ |
$3.38714$ |
$[0, -1, 0, -4813, -1190]$ |
\(y^2=x^3-x^2-4813x-1190\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 26.6.0.b.1, $\ldots$ |
$[(-8987/14, 954477/14)]$ |
56628.i4 |
56628k1 |
56628.i |
56628k |
$4$ |
$6$ |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \cdot 13 \) |
\( 2^{4} \cdot 3^{12} \cdot 11^{6} \cdot 13 \) |
$2$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$1716$ |
$96$ |
$1$ |
$3.317405721$ |
$1$ |
|
$17$ |
$138240$ |
$1.431833$ |
$16384000/9477$ |
$1.48887$ |
$3.68809$ |
$[0, 0, 0, -14520, 14641]$ |
\(y^2=x^3-14520x+14641\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 26.6.0.b.1, $\ldots$ |
$[(-40, 729), (0, 121)]$ |
62400.ds4 |
62400ex1 |
62400.ds |
62400ex |
$4$ |
$6$ |
\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 13 \) |
\( 2^{10} \cdot 3^{6} \cdot 5^{6} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$1560$ |
$96$ |
$1$ |
$3.731449865$ |
$1$ |
|
$3$ |
$55296$ |
$0.834871$ |
$16384000/9477$ |
$1.48887$ |
$3.00688$ |
$[0, -1, 0, -1333, 37]$ |
\(y^2=x^3-x^2-1333x+37\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 26.6.0.b.1, $\ldots$ |
$[(-12, 119)]$ |
62400.et4 |
62400cz1 |
62400.et |
62400cz |
$4$ |
$6$ |
\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 13 \) |
\( 2^{10} \cdot 3^{6} \cdot 5^{6} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$1560$ |
$96$ |
$1$ |
$1.451831642$ |
$1$ |
|
$5$ |
$55296$ |
$0.834871$ |
$16384000/9477$ |
$1.48887$ |
$3.00688$ |
$[0, 1, 0, -1333, -37]$ |
\(y^2=x^3+x^2-1333x-37\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 26.6.0.b.1, $\ldots$ |
$[(-1, 36)]$ |
75504.ba4 |
75504bf1 |
75504.ba |
75504bf |
$4$ |
$6$ |
\( 2^{4} \cdot 3 \cdot 11^{2} \cdot 13 \) |
\( 2^{4} \cdot 3^{6} \cdot 11^{6} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$1716$ |
$96$ |
$1$ |
$7.707936777$ |
$1$ |
|
$1$ |
$69120$ |
$0.882526$ |
$16384000/9477$ |
$1.48887$ |
$3.00676$ |
$[0, -1, 0, -1613, 1080]$ |
\(y^2=x^3-x^2-1613x+1080\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 26.6.0.b.1, $\ldots$ |
$[(8792/13, 516456/13)]$ |
82524.j4 |
82524j1 |
82524.j |
82524j |
$4$ |
$6$ |
\( 2^{2} \cdot 3 \cdot 13 \cdot 23^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 13 \cdot 23^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$3588$ |
$96$ |
$1$ |
$0.732748970$ |
$1$ |
|
$9$ |
$152064$ |
$1.251326$ |
$16384000/9477$ |
$1.48887$ |
$3.37407$ |
$[0, 1, 0, -7053, -7308]$ |
\(y^2=x^3+x^2-7053x-7308\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 26.6.0.b.1, $\ldots$ |
$[(291, 4761)]$ |
91728.dh4 |
91728ds1 |
91728.dh |
91728ds |
$4$ |
$6$ |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 13 \) |
\( 2^{4} \cdot 3^{12} \cdot 7^{6} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$1092$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$138240$ |
$1.205839$ |
$16384000/9477$ |
$1.48887$ |
$3.29508$ |
$[0, 0, 0, -5880, -3773]$ |
\(y^2=x^3-5880x-3773\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 26.6.0.b.1, $\ldots$ |
$[]$ |
97344.dc4 |
97344y1 |
97344.dc |
97344y |
$4$ |
$6$ |
\( 2^{6} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{10} \cdot 3^{12} \cdot 13^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$312$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$516096$ |
$1.861933$ |
$16384000/9477$ |
$1.48887$ |
$3.96349$ |
$[0, 0, 0, -81120, -193336]$ |
\(y^2=x^3-81120x-193336\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 24.48.0-12.i.1.8, $\ldots$ |
$[]$ |
97344.do4 |
97344en1 |
97344.do |
97344en |
$4$ |
$6$ |
\( 2^{6} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{10} \cdot 3^{12} \cdot 13^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$312$ |
$96$ |
$1$ |
$6.025835274$ |
$1$ |
|
$3$ |
$516096$ |
$1.861933$ |
$16384000/9477$ |
$1.48887$ |
$3.96349$ |
$[0, 0, 0, -81120, 193336]$ |
\(y^2=x^3-81120x+193336\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 24.48.0-12.i.1.4, $\ldots$ |
$[(32162, 5767632)]$ |
99372.n4 |
99372f1 |
99372.n |
99372f |
$4$ |
$6$ |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 7^{6} \cdot 13^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$1092$ |
$96$ |
$1$ |
$9.856215655$ |
$1$ |
|
$1$ |
$725760$ |
$1.939009$ |
$16384000/9477$ |
$1.48887$ |
$4.03677$ |
$[0, -1, 0, -110413, -270206]$ |
\(y^2=x^3-x^2-110413x-270206\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 26.6.0.b.1, $\ldots$ |
$[(-91830/17, 7968674/17)]$ |
122304.ch4 |
122304fw1 |
122304.ch |
122304fw |
$4$ |
$6$ |
\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 13 \) |
\( 2^{10} \cdot 3^{6} \cdot 7^{6} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$2184$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$138240$ |
$1.003107$ |
$16384000/9477$ |
$1.48887$ |
$3.00648$ |
$[0, -1, 0, -2613, 1989]$ |
\(y^2=x^3-x^2-2613x+1989\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 26.6.0.b.1, $\ldots$ |
$[]$ |
122304.gp4 |
122304dz1 |
122304.gp |
122304dz |
$4$ |
$6$ |
\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 13 \) |
\( 2^{10} \cdot 3^{6} \cdot 7^{6} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$2184$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$138240$ |
$1.003107$ |
$16384000/9477$ |
$1.48887$ |
$3.00648$ |
$[0, 1, 0, -2613, -1989]$ |
\(y^2=x^3+x^2-2613x-1989\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 26.6.0.b.1, $\ldots$ |
$[]$ |
131196.e4 |
131196n1 |
131196.e |
131196n |
$4$ |
$6$ |
\( 2^{2} \cdot 3 \cdot 13 \cdot 29^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 13 \cdot 29^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$4524$ |
$96$ |
$1$ |
$6.806533822$ |
$1$ |
|
$1$ |
$290304$ |
$1.367228$ |
$16384000/9477$ |
$1.48887$ |
$3.35936$ |
$[0, -1, 0, -11213, 13674]$ |
\(y^2=x^3-x^2-11213x+13674\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 26.6.0.b.1, $\ldots$ |
$[(-12395/14, 1872907/14)]$ |
135252.l4 |
135252i1 |
135252.l |
135252i |
$4$ |
$6$ |
\( 2^{2} \cdot 3^{2} \cdot 13 \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 13 \cdot 17^{6} \) |
$2$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$2652$ |
$96$ |
$1$ |
$8.033067283$ |
$1$ |
|
$5$ |
$442368$ |
$1.649492$ |
$16384000/9477$ |
$1.48887$ |
$3.63739$ |
$[0, 0, 0, -34680, -54043]$ |
\(y^2=x^3-34680x-54043\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 26.6.0.b.1, $\ldots$ |
$[(-137, 1458), (1003, 31212)]$ |
149916.d4 |
149916j1 |
149916.d |
149916j |
$4$ |
$6$ |
\( 2^{2} \cdot 3 \cdot 13 \cdot 31^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 13 \cdot 31^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$4836$ |
$96$ |
$1$ |
$4.653746139$ |
$1$ |
|
$1$ |
$367200$ |
$1.400572$ |
$16384000/9477$ |
$1.48887$ |
$3.35534$ |
$[0, -1, 0, -12813, -7866]$ |
\(y^2=x^3-x^2-12813x-7866\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 26.6.0.b.1, $\ldots$ |
$[(-219/2, 5805/2)]$ |
152100.ct4 |
152100bx1 |
152100.ct |
152100bx |
$4$ |
$6$ |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 5^{6} \cdot 13^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$780$ |
$96$ |
$1$ |
$9.478356550$ |
$1$ |
|
$1$ |
$2322432$ |
$2.320080$ |
$16384000/9477$ |
$1.48887$ |
$4.27599$ |
$[0, 0, 0, -507000, -3020875]$ |
\(y^2=x^3-507000x-3020875\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 26.6.0.b.1, $\ldots$ |
$[(-138935/14, 1194075/14)]$ |
168948.s4 |
168948o1 |
168948.s |
168948o |
$4$ |
$6$ |
\( 2^{2} \cdot 3^{2} \cdot 13 \cdot 19^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 13 \cdot 19^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$2964$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$684288$ |
$1.705105$ |
$16384000/9477$ |
$1.48887$ |
$3.62561$ |
$[0, 0, 0, -43320, 75449]$ |
\(y^2=x^3-43320x+75449\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 26.6.0.b.1, $\ldots$ |
$[]$ |
180336.cq4 |
180336o1 |
180336.cq |
180336o |
$4$ |
$6$ |
\( 2^{4} \cdot 3 \cdot 13 \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 13 \cdot 17^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$2652$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$221184$ |
$1.100185$ |
$16384000/9477$ |
$1.48887$ |
$3.00628$ |
$[0, 1, 0, -3853, -3286]$ |
\(y^2=x^3+x^2-3853x-3286\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 26.6.0.b.1, $\ldots$ |
$[]$ |
187200.eh4 |
187200lk1 |
187200.eh |
187200lk |
$4$ |
$6$ |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 \) |
\( 2^{10} \cdot 3^{12} \cdot 5^{6} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$1560$ |
$96$ |
$1$ |
$2.740196446$ |
$1$ |
|
$5$ |
$442368$ |
$1.384178$ |
$16384000/9477$ |
$1.48887$ |
$3.27774$ |
$[0, 0, 0, -12000, -11000]$ |
\(y^2=x^3-12000x-11000\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 26.6.0.b.1, $\ldots$ |
$[(185, 2025)]$ |
187200.me4 |
187200fj1 |
187200.me |
187200fj |
$4$ |
$6$ |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13 \) |
\( 2^{10} \cdot 3^{12} \cdot 5^{6} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$1560$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$442368$ |
$1.384178$ |
$16384000/9477$ |
$1.48887$ |
$3.27774$ |
$[0, 0, 0, -12000, 11000]$ |
\(y^2=x^3-12000x+11000\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 26.6.0.b.1, $\ldots$ |
$[]$ |
191100.ce4 |
191100r1 |
191100.ce |
191100r |
$4$ |
$6$ |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 13 \) |
\( 2^{4} \cdot 3^{6} \cdot 5^{6} \cdot 7^{6} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$5460$ |
$96$ |
$1$ |
$3.105202790$ |
$1$ |
|
$3$ |
$622080$ |
$1.461252$ |
$16384000/9477$ |
$1.48887$ |
$3.34824$ |
$[0, 1, 0, -16333, -22912]$ |
\(y^2=x^3+x^2-16333x-22912\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 26.6.0.b.1, $\ldots$ |
$[(-68, 882)]$ |
202800.gv4 |
202800bz1 |
202800.gv |
202800bz |
$4$ |
$6$ |
\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 5^{6} \cdot 13^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$780$ |
$96$ |
$1$ |
$4.664290094$ |
$1$ |
|
$1$ |
$1161216$ |
$1.770773$ |
$16384000/9477$ |
$1.48887$ |
$3.63591$ |
$[0, 1, 0, -56333, -130662]$ |
\(y^2=x^3+x^2-56333x-130662\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 26.6.0.b.1, $\ldots$ |
$[(-923/2, 6375/2)]$ |
213564.g4 |
213564b1 |
213564.g |
213564b |
$4$ |
$6$ |
\( 2^{2} \cdot 3 \cdot 13 \cdot 37^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 13 \cdot 37^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$5772$ |
$96$ |
$1$ |
$8.081473790$ |
$1$ |
|
$1$ |
$622080$ |
$1.489038$ |
$16384000/9477$ |
$1.48887$ |
$3.34509$ |
$[0, 1, 0, -18253, 14552]$ |
\(y^2=x^3+x^2-18253x+14552\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 26.6.0.b.1, $\ldots$ |
$[(-904/11, 516456/11)]$ |
225264.bz4 |
225264k1 |
225264.bz |
225264k |
$4$ |
$6$ |
\( 2^{4} \cdot 3 \cdot 13 \cdot 19^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 13 \cdot 19^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$2964$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$342144$ |
$1.155798$ |
$16384000/9477$ |
$1.48887$ |
$3.00616$ |
$[0, 1, 0, -4813, 1190]$ |
\(y^2=x^3+x^2-4813x+1190\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 26.6.0.b.1, $\ldots$ |
$[]$ |
226512.do4 |
226512bt1 |
226512.do |
226512bt |
$4$ |
$6$ |
\( 2^{4} \cdot 3^{2} \cdot 11^{2} \cdot 13 \) |
\( 2^{4} \cdot 3^{12} \cdot 11^{6} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$1716$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$552960$ |
$1.431833$ |
$16384000/9477$ |
$1.48887$ |
$3.27345$ |
$[0, 0, 0, -14520, -14641]$ |
\(y^2=x^3-14520x-14641\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 26.6.0.b.1, $\ldots$ |
$[]$ |
245388.v4 |
245388v1 |
245388.v |
245388v |
$4$ |
$6$ |
\( 2^{2} \cdot 3 \cdot 11^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 11^{6} \cdot 13^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$1716$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$2903040$ |
$2.165001$ |
$16384000/9477$ |
$1.48887$ |
$3.96125$ |
$[0, 1, 0, -272653, -1282228]$ |
\(y^2=x^3+x^2-272653x-1282228\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 26.6.0.b.1, $\ldots$ |
$[]$ |