| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 36.1-a1 |
36.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{205}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{2} \cdot 3^{16} \) |
$3.13394$ |
$(3,a), (3,a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$25.41455941$ |
1.775029824 |
\( \frac{18541}{54} a + \frac{21025}{9} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -8 a + 198\) , \( -680 a + 5605\bigr] \) |
${y}^2+w{x}{y}+w{y}={x}^3+w{x}^2+\left(-8w+198\right){x}-680w+5605$ |
| 36.1-b1 |
36.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{205}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{2} \) |
$3.13394$ |
$(3,a), (3,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2 \) |
$6.251824599$ |
$6.999515039$ |
3.056312836 |
\( -\frac{24389}{12} \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( 17 a + 69\) , \( 53 a + 261\bigr] \) |
${y}^2+\left(w+1\right){x}{y}+w{y}={x}^3+w{x}^2+\left(17w+69\right){x}+53w+261$ |
| 36.1-b2 |
36.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{205}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{10} \) |
$3.13394$ |
$(3,a), (3,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \cdot 5 \) |
$1.250364919$ |
$6.999515039$ |
3.056312836 |
\( -\frac{19465109}{248832} \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( 32 a - 46\) , \( -428 a + 3944\bigr] \) |
${y}^2+\left(w+1\right){x}{y}+w{y}={x}^3+w{x}^2+\left(32w-46\right){x}-428w+3944$ |
| 36.1-b3 |
36.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{205}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{20} \) |
$3.13394$ |
$(3,a), (3,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.625182459$ |
$6.999515039$ |
3.056312836 |
\( \frac{502270291349}{1889568} \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( 512 a - 3726\) , \( -15820 a + 121800\bigr] \) |
${y}^2+\left(w+1\right){x}{y}+w{y}={x}^3+w{x}^2+\left(512w-3726\right){x}-15820w+121800$ |
| 36.1-b4 |
36.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{205}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{4} \) |
$3.13394$ |
$(3,a), (3,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{2} \) |
$3.125912299$ |
$6.999515039$ |
3.056312836 |
\( \frac{131872229}{18} \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( 47 a - 161\) , \( 323 a - 1809\bigr] \) |
${y}^2+\left(w+1\right){x}{y}+w{y}={x}^3+w{x}^2+\left(47w-161\right){x}+323w-1809$ |
| 36.1-c1 |
36.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{205}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{6} \) |
$3.13394$ |
$(3,a), (3,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$4.624531899$ |
$14.80331963$ |
4.781343722 |
\( \frac{13085}{972} a - \frac{3365}{81} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 2 a + 27\) , \( -8 a - 63\bigr] \) |
${y}^2+{x}{y}={x}^3+w{x}^2+\left(2w+27\right){x}-8w-63$ |
| 36.1-c2 |
36.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{205}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{12} \) |
$3.13394$ |
$(3,a), (3,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.312265949$ |
$14.80331963$ |
4.781343722 |
\( -\frac{2896081915}{118098} a + \frac{7989323965}{39366} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -28 a - 173\) , \( -282 a - 1887\bigr] \) |
${y}^2+{x}{y}={x}^3+w{x}^2+\left(-28w-173\right){x}-282w-1887$ |
| 36.1-d1 |
36.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{205}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{6} \cdot 3^{20} \) |
$3.13394$ |
$(3,a), (3,a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$8.421093020$ |
0.588154648 |
\( -\frac{22469832701}{8748} a + \frac{344100904375}{17496} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 188 a - 1200\) , \( 3457 a - 25764\bigr] \) |
${y}^2+\left(w+1\right){x}{y}+{y}={x}^3+\left(w+1\right){x}^2+\left(188w-1200\right){x}+3457w-25764$ |
| 36.1-e1 |
36.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{205}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{6} \) |
$3.13394$ |
$(3,a), (3,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$4.624531899$ |
$14.80331963$ |
4.781343722 |
\( -\frac{13085}{972} a - \frac{27295}{972} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -2 a + 29\) , \( 8 a - 71\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(-w+1\right){x}^2+\left(-2w+29\right){x}+8w-71$ |
| 36.1-e2 |
36.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{205}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{12} \) |
$3.13394$ |
$(3,a), (3,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.312265949$ |
$14.80331963$ |
4.781343722 |
\( \frac{2896081915}{118098} a + \frac{10535944990}{59049} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 28 a - 201\) , \( 282 a - 2169\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(-w+1\right){x}^2+\left(28w-201\right){x}+282w-2169$ |
| 36.1-f1 |
36.1-f |
$2$ |
$5$ |
\(\Q(\sqrt{205}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{18} \) |
$3.13394$ |
$(3,a), (3,a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 3 \cdot 5 \) |
$1$ |
$2.701629609$ |
2.830349950 |
\( -\frac{9129329}{864} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -7 a + 9\) , \( -38 a - 263\bigr] \) |
${y}^2+\left(w+1\right){x}{y}+{y}={x}^3-w{x}^2+\left(-7w+9\right){x}-38w-263$ |
| 36.1-f2 |
36.1-f |
$2$ |
$5$ |
\(\Q(\sqrt{205}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{42} \) |
$3.13394$ |
$(3,a), (3,a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 3 \cdot 5 \) |
$1$ |
$2.701629609$ |
2.830349950 |
\( \frac{19902511}{28697814} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 3 a + 119\) , \( 1302 a + 11237\bigr] \) |
${y}^2+\left(w+1\right){x}{y}+{y}={x}^3-w{x}^2+\left(3w+119\right){x}+1302w+11237$ |
| 36.1-g1 |
36.1-g |
$1$ |
$1$ |
\(\Q(\sqrt{205}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{2} \cdot 3^{16} \) |
$3.13394$ |
$(3,a), (3,a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$25.41455941$ |
1.775029824 |
\( -\frac{18541}{54} a + \frac{144691}{54} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 35 a + 216\) , \( 904 a + 6009\bigr] \) |
${y}^2+\left(w+1\right){x}{y}+w{y}={x}^3+\left(w+1\right){x}^2+\left(35w+216\right){x}+904w+6009$ |
| 36.1-h1 |
36.1-h |
$1$ |
$1$ |
\(\Q(\sqrt{205}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{6} \cdot 3^{20} \) |
$3.13394$ |
$(3,a), (3,a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$8.421093020$ |
0.588154648 |
\( \frac{22469832701}{8748} a + \frac{99720412991}{5832} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -160 a - 1065\) , \( -4521 a - 30104\bigr] \) |
${y}^2+w{x}{y}={x}^3+w{x}^2+\left(-160w-1065\right){x}-4521w-30104$ |
| 36.1-i1 |
36.1-i |
$1$ |
$1$ |
\(\Q(\sqrt{205}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{2} \cdot 3^{16} \) |
$3.13394$ |
$(3,a), (3,a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$1$ |
$25.41455941$ |
5.325089474 |
\( -\frac{18541}{54} a + \frac{144691}{54} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( 7 a - 39\) , \( 38 a - 321\bigr] \) |
${y}^2+{x}{y}+w{y}={x}^3-w{x}^2+\left(7w-39\right){x}+38w-321$ |
| 36.1-j1 |
36.1-j |
$1$ |
$1$ |
\(\Q(\sqrt{205}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{6} \cdot 3^{20} \) |
$3.13394$ |
$(3,a), (3,a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 7 \) |
$1$ |
$8.421093020$ |
4.117082542 |
\( \frac{22469832701}{8748} a + \frac{99720412991}{5832} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 802 a - 5933\) , \( -37181 a + 285361\bigr] \) |
${y}^2+\left(w+1\right){x}{y}+{y}={x}^3+\left(w-1\right){x}^2+\left(802w-5933\right){x}-37181w+285361$ |
| 36.1-k1 |
36.1-k |
$2$ |
$5$ |
\(\Q(\sqrt{205}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{18} \) |
$3.13394$ |
$(3,a), (3,a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 3 \cdot 5 \) |
$1$ |
$2.701629609$ |
2.830349950 |
\( -\frac{9129329}{864} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( 6 a + 3\) , \( 38 a - 301\bigr] \) |
${y}^2+w{x}{y}+{y}={x}^3+\left(6w+3\right){x}+38w-301$ |
| 36.1-k2 |
36.1-k |
$2$ |
$5$ |
\(\Q(\sqrt{205}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{42} \) |
$3.13394$ |
$(3,a), (3,a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 3 \cdot 5 \) |
$1$ |
$2.701629609$ |
2.830349950 |
\( \frac{19902511}{28697814} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( -4 a + 123\) , \( -1302 a + 12539\bigr] \) |
${y}^2+w{x}{y}+{y}={x}^3+\left(-4w+123\right){x}-1302w+12539$ |
| 36.1-l1 |
36.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{205}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{6} \) |
$3.13394$ |
$(3,a), (3,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$0.742529693$ |
$14.80331963$ |
3.838539514 |
\( -\frac{13085}{972} a - \frac{27295}{972} \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( 14 a + 75\) , \( 44 a + 282\bigr] \) |
${y}^2+\left(w+1\right){x}{y}+w{y}={x}^3+w{x}^2+\left(14w+75\right){x}+44w+282$ |
| 36.1-l2 |
36.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{205}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{12} \) |
$3.13394$ |
$(3,a), (3,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.371264846$ |
$14.80331963$ |
3.838539514 |
\( \frac{2896081915}{118098} a + \frac{10535944990}{59049} \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( -16 a - 125\) , \( 26 a + 162\bigr] \) |
${y}^2+\left(w+1\right){x}{y}+w{y}={x}^3+w{x}^2+\left(-16w-125\right){x}+26w+162$ |
| 36.1-m1 |
36.1-m |
$1$ |
$1$ |
\(\Q(\sqrt{205}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{6} \cdot 3^{20} \) |
$3.13394$ |
$(3,a), (3,a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 7 \) |
$1$ |
$8.421093020$ |
4.117082542 |
\( -\frac{22469832701}{8748} a + \frac{344100904375}{17496} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -776 a - 5181\) , \( 31223 a + 207903\bigr] \) |
${y}^2+w{x}{y}+w{y}={x}^3+\left(w+1\right){x}^2+\left(-776w-5181\right){x}+31223w+207903$ |
| 36.1-n1 |
36.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{205}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{6} \) |
$3.13394$ |
$(3,a), (3,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$0.742529693$ |
$14.80331963$ |
3.838539514 |
\( \frac{13085}{972} a - \frac{3365}{81} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 11 a + 38\) , \( 19 a + 199\bigr] \) |
${y}^2+w{x}{y}+w{y}={x}^3+\left(w-1\right){x}^2+\left(11w+38\right){x}+19w+199$ |
| 36.1-n2 |
36.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{205}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{12} \) |
$3.13394$ |
$(3,a), (3,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.371264846$ |
$14.80331963$ |
3.838539514 |
\( -\frac{2896081915}{118098} a + \frac{7989323965}{39366} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 41 a - 192\) , \( -193 a + 1821\bigr] \) |
${y}^2+w{x}{y}+w{y}={x}^3+\left(w-1\right){x}^2+\left(41w-192\right){x}-193w+1821$ |
| 36.1-o1 |
36.1-o |
$1$ |
$1$ |
\(\Q(\sqrt{205}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{2} \cdot 3^{16} \) |
$3.13394$ |
$(3,a), (3,a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$1$ |
$25.41455941$ |
5.325089474 |
\( \frac{18541}{54} a + \frac{21025}{9} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -8 a - 32\) , \( -39 a - 283\bigr] \) |
${y}^2+{x}{y}+\left(w+1\right){y}={x}^3+\left(w-1\right){x}^2+\left(-8w-32\right){x}-39w-283$ |
| 36.1-p1 |
36.1-p |
$4$ |
$10$ |
\(\Q(\sqrt{205}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{2} \) |
$3.13394$ |
$(3,a), (3,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2 \) |
$6.251824599$ |
$6.999515039$ |
3.056312836 |
\( -\frac{24389}{12} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 8 a + 35\) , \( 7 a + 37\bigr] \) |
${y}^2+w{x}{y}+w{y}={x}^3+\left(w-1\right){x}^2+\left(8w+35\right){x}+7w+37$ |
| 36.1-p2 |
36.1-p |
$4$ |
$10$ |
\(\Q(\sqrt{205}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{10} \) |
$3.13394$ |
$(3,a), (3,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \cdot 5 \) |
$1.250364919$ |
$6.999515039$ |
3.056312836 |
\( -\frac{19465109}{248832} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -7 a - 65\) , \( 388 a + 2574\bigr] \) |
${y}^2+w{x}{y}+w{y}={x}^3+\left(w-1\right){x}^2+\left(-7w-65\right){x}+388w+2574$ |
| 36.1-p3 |
36.1-p |
$4$ |
$10$ |
\(\Q(\sqrt{205}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{20} \) |
$3.13394$ |
$(3,a), (3,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.625182459$ |
$6.999515039$ |
3.056312836 |
\( \frac{502270291349}{1889568} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -487 a - 3265\) , \( 12580 a + 83758\bigr] \) |
${y}^2+w{x}{y}+w{y}={x}^3+\left(w-1\right){x}^2+\left(-487w-3265\right){x}+12580w+83758$ |
| 36.1-p4 |
36.1-p |
$4$ |
$10$ |
\(\Q(\sqrt{205}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{4} \) |
$3.13394$ |
$(3,a), (3,a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{2} \) |
$3.125912299$ |
$6.999515039$ |
3.056312836 |
\( \frac{131872229}{18} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -22 a - 165\) , \( -463 a - 3093\bigr] \) |
${y}^2+w{x}{y}+w{y}={x}^3+\left(w-1\right){x}^2+\left(-22w-165\right){x}-463w-3093$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.
