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 |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
19.a2 |
19a1 |
19.a |
19a |
$3$ |
$9$ |
\( 19 \) |
\( - 19^{3} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.72.0.3 |
3Cs.1.1 |
$1026$ |
$1296$ |
$43$ |
$1$ |
$1$ |
|
$2$ |
$1$ |
$-0.515867$ |
$-89915392/6859$ |
$[0, 1, 1, -9, -15]$ |
\(y^2+y=x^3+x^2-9x-15\) |
3.24.0-3.a.1.1, 9.72.0-9.b.1.1, 38.2.0.a.1, 114.48.1.?, 171.216.4.?, $\ldots$ |
19.a3 |
19a3 |
19.a |
19a |
$3$ |
$9$ |
\( 19 \) |
\( -19 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
27.72.0.1 |
3B.1.1 |
$1026$ |
$1296$ |
$43$ |
$1$ |
$1$ |
|
$2$ |
$3$ |
$-1.065172$ |
$32768/19$ |
$[0, 1, 1, 1, 0]$ |
\(y^2+y=x^3+x^2+x\) |
3.8.0-3.a.1.2, 9.24.0-9.a.1.2, 27.72.0-27.a.1.2, 38.2.0.a.1, 114.16.0.?, $\ldots$ |
26.a2 |
26a1 |
26.a |
26a |
$3$ |
$9$ |
\( 2 \cdot 13 \) |
\( - 2^{3} \cdot 13^{3} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.24.0.1 |
3Cs.1.1 |
$936$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$2$ |
$2$ |
$-0.494920$ |
$-10218313/17576$ |
$[1, 0, 1, -5, -8]$ |
\(y^2+xy+y=x^3-5x-8\) |
3.24.0-3.a.1.1, 104.2.0.?, 117.72.0.?, 312.48.1.?, 936.144.3.? |
26.a3 |
26a3 |
26.a |
26a |
$3$ |
$9$ |
\( 2 \cdot 13 \) |
\( - 2 \cdot 13 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.24.0.1 |
3B.1.1 |
$936$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$2$ |
$6$ |
$-1.044226$ |
$12167/26$ |
$[1, 0, 1, 0, 0]$ |
\(y^2+xy+y=x^3\) |
3.8.0-3.a.1.2, 9.24.0-9.a.1.2, 104.2.0.?, 117.72.0.?, 312.16.0.?, $\ldots$ |
27.a2 |
27a4 |
27.a |
27a |
$4$ |
$27$ |
\( 3^{3} \) |
\( - 3^{5} \) |
$0$ |
$\Z/3\Z$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.13.25 |
3B.1.1 |
$$ |
$$ |
$$ |
$1$ |
$1$ |
|
$2$ |
$9$ |
$-0.497158$ |
$-12288000$ |
$[0, 0, 1, -30, 63]$ |
\(y^2+y=x^3-30x+63\) |
|
27.a3 |
27a1 |
27.a |
27a |
$4$ |
$27$ |
\( 3^{3} \) |
\( - 3^{9} \) |
$0$ |
$\Z/3\Z$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.1944.55.37 |
3Cs.1.1 |
$$ |
$$ |
$$ |
$1$ |
$1$ |
|
$2$ |
$1$ |
$-0.497158$ |
$0$ |
$[0, 0, 1, 0, -7]$ |
\(y^2+y=x^3-7\) |
|
27.a4 |
27a3 |
27.a |
27a |
$4$ |
$27$ |
\( 3^{3} \) |
\( - 3^{3} \) |
$0$ |
$\Z/3\Z$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.1944.55.31 |
3Cs.1.1 |
$$ |
$$ |
$$ |
$1$ |
$1$ |
|
$2$ |
$3$ |
$-1.046465$ |
$0$ |
$[0, 0, 1, 0, 0]$ |
\(y^2+y=x^3\) |
|
35.a2 |
35a3 |
35.a |
35a |
$3$ |
$9$ |
\( 5 \cdot 7 \) |
\( - 5 \cdot 7 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.24.0.1 |
3B.1.1 |
$630$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$2$ |
$6$ |
$-0.971150$ |
$-262144/35$ |
$[0, 1, 1, -1, 0]$ |
\(y^2+y=x^3+x^2-x\) |
3.8.0-3.a.1.2, 9.24.0-9.a.1.2, 63.72.0-63.e.1.2, 70.2.0.a.1, 210.16.0.?, $\ldots$ |
35.a3 |
35a1 |
35.a |
35a |
$3$ |
$9$ |
\( 5 \cdot 7 \) |
\( - 5^{3} \cdot 7^{3} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.24.0.1 |
3Cs.1.1 |
$630$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$2$ |
$2$ |
$-0.421844$ |
$71991296/42875$ |
$[0, 1, 1, 9, 1]$ |
\(y^2+y=x^3+x^2+9x+1\) |
3.24.0-3.a.1.1, 63.72.0-63.b.1.3, 70.2.0.a.1, 210.48.1.?, 630.144.3.? |
37.b2 |
37b1 |
37.b |
37b |
$3$ |
$9$ |
\( 37 \) |
\( 37^{3} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.72.0.3 |
3Cs.1.1 |
$1998$ |
$1296$ |
$43$ |
$1$ |
$1$ |
|
$2$ |
$2$ |
$-0.327225$ |
$1404928000/50653$ |
$[0, 1, 1, -23, -50]$ |
\(y^2+y=x^3+x^2-23x-50\) |
3.24.0-3.a.1.1, 9.72.0-9.b.1.1, 74.2.0.?, 222.48.1.?, 333.216.4.?, $\ldots$ |
37.b3 |
37b3 |
37.b |
37b |
$3$ |
$9$ |
\( 37 \) |
\( 37 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
27.72.0.1 |
3B.1.1 |
$1998$ |
$1296$ |
$43$ |
$1$ |
$1$ |
|
$2$ |
$6$ |
$-0.876531$ |
$4096000/37$ |
$[0, 1, 1, -3, 1]$ |
\(y^2+y=x^3+x^2-3x+1\) |
3.8.0-3.a.1.2, 9.24.0-9.a.1.2, 27.72.0-27.a.1.2, 74.2.0.?, 222.16.0.?, $\ldots$ |
38.a2 |
38a3 |
38.a |
38a |
$3$ |
$9$ |
\( 2 \cdot 19 \) |
\( - 2^{3} \cdot 19 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
27.72.0.1 |
3B.1.1 |
$4104$ |
$1296$ |
$43$ |
$1$ |
$1$ |
|
$2$ |
$18$ |
$-0.613442$ |
$-413493625/152$ |
$[1, 0, 1, -16, 22]$ |
\(y^2+xy+y=x^3-16x+22\) |
3.8.0-3.a.1.2, 9.24.0-9.a.1.2, 27.72.0-27.a.1.2, 152.2.0.?, 171.72.0.?, $\ldots$ |
38.a3 |
38a1 |
38.a |
38a |
$3$ |
$9$ |
\( 2 \cdot 19 \) |
\( - 2^{9} \cdot 19^{3} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.72.0.3 |
3Cs.1.1 |
$4104$ |
$1296$ |
$43$ |
$1$ |
$1$ |
|
$2$ |
$6$ |
$-0.064137$ |
$94196375/3511808$ |
$[1, 0, 1, 9, 90]$ |
\(y^2+xy+y=x^3+9x+90\) |
3.24.0-3.a.1.1, 9.72.0-9.b.1.1, 152.2.0.?, 171.216.4.?, 456.48.1.?, $\ldots$ |
44.a2 |
44a1 |
44.a |
44a |
$2$ |
$3$ |
\( 2^{2} \cdot 11 \) |
\( - 2^{8} \cdot 11 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$66$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$2$ |
$-0.652294$ |
$8192/11$ |
$[0, 1, 0, 3, -1]$ |
\(y^2=x^3+x^2+3x-1\) |
3.8.0-3.a.1.2, 22.2.0.a.1, 66.16.0-66.a.1.4 |
50.a2 |
50a3 |
50.a |
50a |
$4$ |
$15$ |
\( 2 \cdot 5^{2} \) |
\( - 2^{5} \cdot 5^{8} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3, 5$ |
8.2.0.1, 3.8.0.1, 5.24.0.2 |
3B.1.1, 5B.1.4 |
$120$ |
$384$ |
$9$ |
$1$ |
$1$ |
|
$2$ |
$10$ |
$0.078619$ |
$-121945/32$ |
$[1, 0, 1, -76, 298]$ |
\(y^2+xy+y=x^3-76x+298\) |
3.8.0-3.a.1.2, 5.24.0-5.a.1.1, 8.2.0.a.1, 15.192.1-15.a.4.4, 24.16.0-24.a.1.8, $\ldots$ |
50.a3 |
50a1 |
50.a |
50a |
$4$ |
$15$ |
\( 2 \cdot 5^{2} \) |
\( - 2 \cdot 5^{4} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3, 5$ |
8.2.0.1, 3.8.0.1, 5.24.0.4 |
3B.1.1, 5B.1.3 |
$120$ |
$384$ |
$9$ |
$1$ |
$1$ |
|
$2$ |
$2$ |
$-0.726100$ |
$-25/2$ |
$[1, 0, 1, -1, -2]$ |
\(y^2+xy+y=x^3-x-2\) |
3.8.0-3.a.1.2, 5.24.0-5.a.2.1, 8.2.0.a.1, 15.192.1-15.a.2.3, 24.16.0-24.a.1.8, $\ldots$ |
51.a2 |
51a1 |
51.a |
51a |
$2$ |
$3$ |
\( 3 \cdot 17 \) |
\( - 3^{3} \cdot 17 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.8.0.1 |
3B.1.1 |
$102$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$2$ |
$-0.808530$ |
$32768/459$ |
$[0, 1, 1, 1, -1]$ |
\(y^2+y=x^3+x^2+x-1\) |
3.8.0-3.a.1.2, 102.16.0.? |
54.a2 |
54a3 |
54.a |
54a |
$3$ |
$9$ |
\( 2 \cdot 3^{3} \) |
\( - 2 \cdot 3^{3} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.72.0.6 |
3B.1.1 |
$72$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$2$ |
$18$ |
$-0.864511$ |
$-132651/2$ |
$[1, -1, 0, -3, 3]$ |
\(y^2+xy=x^3-x^2-3x+3\) |
3.8.0-3.a.1.2, 9.72.0-9.d.2.1, 24.16.0-24.d.1.8, 72.144.3.? |
54.a3 |
54a1 |
54.a |
54a |
$3$ |
$9$ |
\( 2 \cdot 3^{3} \) |
\( - 2^{3} \cdot 3^{9} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.72.0.2 |
3Cs.1.1 |
$72$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$2$ |
$6$ |
$-0.315205$ |
$9261/8$ |
$[1, -1, 0, 12, 8]$ |
\(y^2+xy=x^3-x^2+12x+8\) |
3.24.0-3.a.1.1, 9.72.0-9.a.1.2, 24.48.1-24.ci.1.1, 72.144.3.? |
54.b3 |
54b1 |
54.b |
54b |
$3$ |
$9$ |
\( 2 \cdot 3^{3} \) |
\( - 2^{3} \cdot 3^{3} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.72.0.1 |
3Cs.1.1 |
$72$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$2$ |
$2$ |
$-0.864511$ |
$9261/8$ |
$[1, -1, 1, 1, -1]$ |
\(y^2+xy+y=x^3-x^2+x-1\) |
3.24.0-3.a.1.1, 9.72.0-9.a.1.1, 24.48.1-24.ci.1.1, 72.144.3.? |
77.b1 |
77b3 |
77.b |
77b |
$3$ |
$9$ |
\( 7 \cdot 11 \) |
\( - 7^{2} \cdot 11 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.24.0.1 |
3B.1.1 |
$1386$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$2$ |
$60$ |
$-0.295000$ |
$-78843215872/539$ |
$[0, 1, 1, -89, 295]$ |
\(y^2+y=x^3+x^2-89x+295\) |
3.8.0-3.a.1.2, 9.24.0-9.a.1.2, 22.2.0.a.1, 63.72.0-63.e.1.2, 66.16.0-66.a.1.4, $\ldots$ |
77.b2 |
77b1 |
77.b |
77b |
$3$ |
$9$ |
\( 7 \cdot 11 \) |
\( - 7^{6} \cdot 11^{3} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.24.0.1 |
3Cs.1.1 |
$1386$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$2$ |
$20$ |
$0.254306$ |
$-13278380032/156590819$ |
$[0, 1, 1, -49, 600]$ |
\(y^2+y=x^3+x^2-49x+600\) |
3.24.0-3.a.1.1, 22.2.0.a.1, 63.72.0-63.b.1.3, 66.48.1-66.b.1.1, 1386.144.3.? |
91.b2 |
91b1 |
91.b |
91b |
$3$ |
$9$ |
\( 7 \cdot 13 \) |
\( - 7 \cdot 13 \) |
$1$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.24.0.1 |
3B.1.1 |
$1638$ |
$144$ |
$3$ |
$1.059245086$ |
$1$ |
|
$6$ |
$4$ |
$-0.738508$ |
$-43614208/91$ |
$[0, 1, 1, -7, 5]$ |
\(y^2+y=x^3+x^2-7x+5\) |
3.8.0-3.a.1.2, 9.24.0-9.a.1.2, 117.72.0.?, 182.2.0.?, 546.16.0.?, $\ldots$ |
91.b3 |
91b2 |
91.b |
91b |
$3$ |
$9$ |
\( 7 \cdot 13 \) |
\( - 7^{3} \cdot 13^{3} \) |
$1$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.24.0.1 |
3Cs.1.1 |
$1638$ |
$144$ |
$3$ |
$0.353081695$ |
$1$ |
|
$10$ |
$12$ |
$-0.189202$ |
$224755712/753571$ |
$[0, 1, 1, 13, 42]$ |
\(y^2+y=x^3+x^2+13x+42\) |
3.24.0-3.a.1.1, 117.72.0.?, 182.2.0.?, 546.48.1.?, 1638.144.3.? |
92.b2 |
92a1 |
92.b |
92a |
$2$ |
$3$ |
\( 2^{2} \cdot 23 \) |
\( - 2^{4} \cdot 23 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$138$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$2$ |
$-0.819269$ |
$32000/23$ |
$[0, 1, 0, 2, 1]$ |
\(y^2=x^3+x^2+2x+1\) |
3.8.0-3.a.1.2, 46.2.0.a.1, 138.16.0.? |
106.c2 |
106a1 |
106.c |
106a |
$2$ |
$3$ |
\( 2 \cdot 53 \) |
\( - 2^{3} \cdot 53 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.8.0.1 |
3B.1.1 |
$1272$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$6$ |
$-0.813213$ |
$103823/424$ |
$[1, 0, 0, 1, 1]$ |
\(y^2+xy=x^3+x+1\) |
3.8.0-3.a.1.2, 424.2.0.?, 1272.16.0.? |
106.d2 |
106c1 |
106.d |
106c |
$2$ |
$3$ |
\( 2 \cdot 53 \) |
\( - 2^{24} \cdot 53 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.8.0.1 |
3B.1.1 |
$636$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$48$ |
$0.428091$ |
$-2507141976625/889192448$ |
$[1, 0, 0, -283, -2351]$ |
\(y^2+xy=x^3-283x-2351\) |
3.8.0-3.a.1.2, 212.2.0.?, 636.16.0.? |
108.a2 |
108a1 |
108.a |
108a |
$2$ |
$3$ |
\( 2^{2} \cdot 3^{3} \) |
\( - 2^{8} \cdot 3^{3} \) |
$0$ |
$\Z/3\Z$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.18.1 |
3B.1.1 |
$$ |
$$ |
$$ |
$1$ |
$1$ |
|
$2$ |
$6$ |
$-0.584366$ |
$0$ |
$[0, 0, 0, 0, 4]$ |
\(y^2=x^3+4\) |
|
110.a1 |
110c1 |
110.a |
110c |
$2$ |
$3$ |
\( 2 \cdot 5 \cdot 11 \) |
\( - 2^{7} \cdot 5 \cdot 11^{3} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.8.0.1 |
3B.1.1 |
$1320$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$28$ |
$-0.047191$ |
$-76711450249/851840$ |
$[1, 0, 1, -89, 316]$ |
\(y^2+xy+y=x^3-89x+316\) |
3.8.0-3.a.1.2, 440.2.0.?, 1320.16.0.? |
110.c1 |
110b1 |
110.c |
110b |
$2$ |
$3$ |
\( 2 \cdot 5 \cdot 11 \) |
\( - 2^{3} \cdot 5 \cdot 11 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.8.0.1 |
3B.1.1 |
$1320$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$4$ |
$-0.807105$ |
$-117649/440$ |
$[1, 0, 0, -1, 1]$ |
\(y^2+xy=x^3-x+1\) |
3.8.0-3.a.1.2, 440.2.0.?, 1320.16.0.? |
116.b1 |
116b1 |
116.b |
116b |
$2$ |
$3$ |
\( 2^{2} \cdot 29 \) |
\( - 2^{8} \cdot 29 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$348$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$8$ |
$-0.559319$ |
$-35152/29$ |
$[0, 1, 0, -4, 4]$ |
\(y^2=x^3+x^2-4x+4\) |
3.8.0-3.a.1.2, 116.2.0.?, 348.16.0.? |
124.a1 |
124a1 |
124.a |
124a |
$2$ |
$3$ |
\( 2^{2} \cdot 31 \) |
\( - 2^{4} \cdot 31 \) |
$1$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$186$ |
$16$ |
$0$ |
$0.520530693$ |
$1$ |
|
$10$ |
$6$ |
$-0.771762$ |
$-87808/31$ |
$[0, 1, 0, -2, 1]$ |
\(y^2=x^3+x^2-2x+1\) |
3.8.0-3.a.1.2, 62.2.0.a.1, 186.16.0.? |
140.a2 |
140a1 |
140.a |
140a |
$2$ |
$3$ |
\( 2^{2} \cdot 5 \cdot 7 \) |
\( - 2^{8} \cdot 5^{3} \cdot 7 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$210$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$12$ |
$-0.291759$ |
$-65536/875$ |
$[0, 1, 0, -5, -25]$ |
\(y^2=x^3+x^2-5x-25\) |
3.8.0-3.a.1.2, 70.2.0.a.1, 210.16.0.? |
142.e2 |
142d1 |
142.e |
142d |
$2$ |
$3$ |
\( 2 \cdot 71 \) |
\( 2^{3} \cdot 71 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.8.0.1 |
3B.1.1 |
$1704$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$4$ |
$-0.652843$ |
$57066625/568$ |
$[1, 0, 0, -8, 8]$ |
\(y^2+xy=x^3-8x+8\) |
3.8.0-3.a.1.2, 568.2.0.?, 1704.16.0.? |
153.b1 |
153b2 |
153.b |
153b |
$2$ |
$3$ |
\( 3^{2} \cdot 17 \) |
\( - 3^{7} \cdot 17^{3} \) |
$1$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$102$ |
$16$ |
$0$ |
$0.338669215$ |
$1$ |
|
$10$ |
$48$ |
$0.290082$ |
$-23100424192/14739$ |
$[0, 0, 1, -534, 4752]$ |
\(y^2+y=x^3-534x+4752\) |
3.8.0-3.a.1.2, 102.16.0.? |
158.b2 |
158d1 |
158.b |
158d |
$3$ |
$9$ |
\( 2 \cdot 79 \) |
\( 2^{6} \cdot 79^{3} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.24.0.1 |
3Cs.1.1 |
$2844$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$2$ |
$40$ |
$0.130552$ |
$59914169497/31554496$ |
$[1, 0, 1, -82, -92]$ |
\(y^2+xy+y=x^3-82x-92\) |
3.24.0-3.a.1.1, 316.2.0.?, 711.72.0.?, 948.48.1.?, 2844.144.3.? |
158.b3 |
158d3 |
158.b |
158d |
$3$ |
$9$ |
\( 2 \cdot 79 \) |
\( 2^{2} \cdot 79 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.24.0.1 |
3B.1.1 |
$2844$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$2$ |
$120$ |
$-0.418754$ |
$11134383337/316$ |
$[1, 0, 1, -47, 118]$ |
\(y^2+xy+y=x^3-47x+118\) |
3.8.0-3.a.1.2, 9.24.0-9.a.1.2, 316.2.0.?, 711.72.0.?, 948.16.0.?, $\ldots$ |
162.a1 |
162a1 |
162.a |
162a |
$2$ |
$3$ |
\( 2 \cdot 3^{4} \) |
\( - 2^{2} \cdot 3^{6} \) |
$1$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.8.0.2, 3.8.0.1 |
3B.1.1 |
$12$ |
$128$ |
$1$ |
$0.305934883$ |
$1$ |
|
$14$ |
$12$ |
$-0.597807$ |
$-35937/4$ |
$[1, -1, 0, -6, 8]$ |
\(y^2+xy=x^3-x^2-6x+8\) |
3.8.0-3.a.1.2, 4.8.0.b.1, 12.128.1-12.b.2.3 |
162.b1 |
162c3 |
162.b |
162c |
$4$ |
$21$ |
\( 2 \cdot 3^{4} \) |
\( - 2^{7} \cdot 3^{6} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3, 7$ |
8.2.0.1, 3.8.0.1, 7.8.0.1 |
3B.1.1, 7B |
$504$ |
$768$ |
$21$ |
$1$ |
$1$ |
|
$2$ |
$42$ |
$0.269368$ |
$-189613868625/128$ |
$[1, -1, 0, -1077, 13877]$ |
\(y^2+xy=x^3-x^2-1077x+13877\) |
3.8.0-3.a.1.2, 7.8.0.a.1, 8.2.0.a.1, 21.128.1-21.a.4.2, 24.16.0-24.a.1.8, $\ldots$ |
162.b4 |
162c1 |
162.b |
162c |
$4$ |
$21$ |
\( 2 \cdot 3^{4} \) |
\( - 2 \cdot 3^{6} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3, 7$ |
8.2.0.1, 3.8.0.1, 7.8.0.1 |
3B.1.1, 7B |
$504$ |
$768$ |
$21$ |
$1$ |
$1$ |
|
$2$ |
$6$ |
$-0.703587$ |
$3375/2$ |
$[1, -1, 0, 3, -1]$ |
\(y^2+xy=x^3-x^2+3x-1\) |
3.8.0-3.a.1.2, 7.8.0.a.1, 8.2.0.a.1, 21.128.1-21.a.2.2, 24.16.0-24.a.1.8, $\ldots$ |
162.c2 |
162b3 |
162.c |
162b |
$4$ |
$21$ |
\( 2 \cdot 3^{4} \) |
\( - 2^{21} \cdot 3^{4} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3, 7$ |
8.2.0.1, 3.8.0.1, 7.16.0.2 |
3B.1.1, 7B.2.3 |
$504$ |
$768$ |
$21$ |
$1$ |
$1$ |
|
$2$ |
$42$ |
$0.269368$ |
$-1159088625/2097152$ |
$[1, -1, 1, -95, -697]$ |
\(y^2+xy+y=x^3-x^2-95x-697\) |
3.8.0-3.a.1.2, 7.16.0-7.a.1.1, 8.2.0.a.1, 21.128.1-21.a.1.2, 24.16.0-24.a.1.8, $\ldots$ |
162.c3 |
162b1 |
162.c |
162b |
$4$ |
$21$ |
\( 2 \cdot 3^{4} \) |
\( - 2^{3} \cdot 3^{4} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3, 7$ |
8.2.0.1, 3.8.0.1, 7.16.0.1 |
3B.1.1, 7B.2.1 |
$504$ |
$768$ |
$21$ |
$1$ |
$1$ |
|
$2$ |
$6$ |
$-0.703587$ |
$-140625/8$ |
$[1, -1, 1, -5, 5]$ |
\(y^2+xy+y=x^3-x^2-5x+5\) |
3.8.0-3.a.1.2, 7.16.0-7.a.1.2, 8.2.0.a.1, 21.128.1-21.a.3.3, 24.16.0-24.a.1.8, $\ldots$ |
162.d2 |
162d1 |
162.d |
162d |
$2$ |
$3$ |
\( 2 \cdot 3^{4} \) |
\( - 2^{6} \cdot 3^{4} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.16.0.2, 3.8.0.1 |
3B.1.1 |
$12$ |
$128$ |
$1$ |
$1$ |
$1$ |
|
$2$ |
$12$ |
$-0.597807$ |
$109503/64$ |
$[1, -1, 1, 4, -1]$ |
\(y^2+xy+y=x^3-x^2+4x-1\) |
3.8.0-3.a.1.2, 4.16.0-4.b.1.1, 12.128.1-12.b.1.4 |
170.c1 |
170d1 |
170.c |
170d |
$2$ |
$3$ |
\( 2 \cdot 5 \cdot 17 \) |
\( - 2^{3} \cdot 5^{3} \cdot 17 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.8.0.1 |
3B.1.1 |
$2040$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$12$ |
$-0.505901$ |
$-1771561/17000$ |
$[1, 0, 1, -3, 6]$ |
\(y^2+xy+y=x^3-3x+6\) |
3.8.0-3.a.1.2, 680.2.0.?, 2040.16.0.? |
170.e2 |
170c1 |
170.e |
170c |
$2$ |
$3$ |
\( 2 \cdot 5 \cdot 17 \) |
\( - 2^{21} \cdot 5^{3} \cdot 17 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.8.0.1 |
3B.1.1 |
$2040$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$84$ |
$0.540466$ |
$7023836099951/4456448000$ |
$[1, 0, 0, 399, -919]$ |
\(y^2+xy=x^3+399x-919\) |
3.8.0-3.a.1.2, 680.2.0.?, 2040.16.0.? |
171.b1 |
171b3 |
171.b |
171b |
$3$ |
$9$ |
\( 3^{2} \cdot 19 \) |
\( - 3^{6} \cdot 19 \) |
$1$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
27.72.0.1 |
3B.1.1 |
$1026$ |
$1296$ |
$43$ |
$2.033701819$ |
$1$ |
|
$4$ |
$72$ |
$0.582746$ |
$-50357871050752/19$ |
$[0, 0, 1, -6924, 221760]$ |
\(y^2+y=x^3-6924x+221760\) |
3.8.0-3.a.1.2, 9.24.0-9.a.1.2, 27.72.0-27.a.1.2, 38.2.0.a.1, 114.16.0.?, $\ldots$ |
171.b2 |
171b2 |
171.b |
171b |
$3$ |
$9$ |
\( 3^{2} \cdot 19 \) |
\( - 3^{6} \cdot 19^{3} \) |
$1$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.72.0.3 |
3Cs.1.1 |
$1026$ |
$1296$ |
$43$ |
$0.677900606$ |
$1$ |
|
$8$ |
$24$ |
$0.033439$ |
$-89915392/6859$ |
$[0, 0, 1, -84, 315]$ |
\(y^2+y=x^3-84x+315\) |
3.24.0-3.a.1.1, 9.72.0-9.b.1.1, 38.2.0.a.1, 114.48.1.?, 171.216.4.?, $\ldots$ |
172.a1 |
172a1 |
172.a |
172a |
$2$ |
$3$ |
\( 2^{2} \cdot 43 \) |
\( - 2^{8} \cdot 43 \) |
$1$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$258$ |
$16$ |
$0$ |
$0.760139663$ |
$1$ |
|
$10$ |
$12$ |
$-0.457803$ |
$-1024000/43$ |
$[0, 1, 0, -13, 15]$ |
\(y^2=x^3+x^2-13x+15\) |
3.8.0-3.a.1.2, 86.2.0.?, 258.16.0.? |
174.b1 |
174a1 |
174.b |
174a |
$2$ |
$3$ |
\( 2 \cdot 3 \cdot 29 \) |
\( - 2^{11} \cdot 3^{21} \cdot 29 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.8.0.1 |
3B.1.1 |
$696$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$1540$ |
$1.520357$ |
$-50577879066661513/621261297432576$ |
$[1, 0, 1, -7705, 1226492]$ |
\(y^2+xy+y=x^3-7705x+1226492\) |
3.8.0-3.a.1.2, 696.16.0.? |
178.b2 |
178a1 |
178.b |
178a |
$2$ |
$3$ |
\( 2 \cdot 89 \) |
\( - 2^{12} \cdot 89 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.8.0.1 |
3B.1.1 |
$1068$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$32$ |
$-0.252186$ |
$23639903/364544$ |
$[1, 0, 0, 6, -28]$ |
\(y^2+xy=x^3+6x-28\) |
3.8.0-3.a.1.2, 356.2.0.?, 1068.16.0.? |