| 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 |
| 145.2-a1 |
145.2-a |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5^{3} \cdot 29^{3} \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 3^{2} \) |
$1$ |
$42.29533189$ |
1.261003163 |
\( -\frac{7871515703585209609195898722853052}{121945} a^{3} - \frac{2662628447821281878668749836092631}{121945} a^{2} + \frac{27922770438742838812706397721202301}{121945} a + \frac{1176379563089911167697232592695285}{24389} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{2} - 2\) , \( 1099 a^{3} + 913 a^{2} - 3824 a - 2786\) , \( -37826 a^{3} - 3784 a^{2} + 135356 a - 3950\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(1099a^{3}+913a^{2}-3824a-2786\right){x}-37826a^{3}-3784a^{2}+135356a-3950$ |
| 145.2-a2 |
145.2-a |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5 \cdot 29 \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 1 \) |
$1$ |
$42.29533189$ |
1.261003163 |
\( \frac{346583852229899708}{145} a^{3} - \frac{419040095774382771}{145} a^{2} - \frac{1298732343116544231}{145} a + \frac{1657846139782373138}{145} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{2} - 2\) , \( -336 a^{3} + 433 a^{2} + 1271 a - 1711\) , \( -5858 a^{3} + 7041 a^{2} + 21967 a - 27908\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(-336a^{3}+433a^{2}+1271a-1711\right){x}-5858a^{3}+7041a^{2}+21967a-27908$ |
| 145.2-a3 |
145.2-a |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5^{6} \cdot 29^{6} \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$169.1813275$ |
1.261003163 |
\( -\frac{478672083353676504338649}{2974116605} a^{3} - \frac{809580996115760937062801}{14870583025} a^{2} + \frac{8490010818666806724963358}{14870583025} a + \frac{1788410508787560069693424}{14870583025} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{2} - 2\) , \( 59 a^{3} + 68 a^{2} - 194 a - 226\) , \( -383 a^{3} - 170 a^{2} + 1345 a + 448\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(59a^{3}+68a^{2}-194a-226\right){x}-383a^{3}-170a^{2}+1345a+448$ |
| 145.2-a4 |
145.2-a |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5^{3} \cdot 29^{3} \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$676.7253102$ |
1.261003163 |
\( -\frac{962236778381448}{121945} a^{3} + \frac{2847898353244631}{121945} a^{2} - \frac{1721306864641051}{121945} a - \frac{98613401759628}{24389} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{2} - 2\) , \( -16 a^{3} + 28 a^{2} + 71 a - 116\) , \( 116 a^{3} - 136 a^{2} - 441 a + 560\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(-16a^{3}+28a^{2}+71a-116\right){x}+116a^{3}-136a^{2}-441a+560$ |
| 145.2-a5 |
145.2-a |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5^{2} \cdot 29^{2} \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$169.1813275$ |
1.261003163 |
\( \frac{159685226823}{4205} a^{3} - \frac{46270475307}{4205} a^{2} - \frac{507570391608}{4205} a + \frac{379717285087}{4205} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{2} - 2\) , \( -21 a^{3} + 28 a^{2} + 81 a - 106\) , \( -81 a^{3} + 99 a^{2} + 305 a - 391\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(-21a^{3}+28a^{2}+81a-106\right){x}-81a^{3}+99a^{2}+305a-391$ |
| 145.2-a6 |
145.2-a |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5^{4} \cdot 29^{4} \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$1$ |
$10.57383297$ |
1.261003163 |
\( \frac{3924815332575135346772}{3536405} a^{3} + \frac{3246179105759555460927}{3536405} a^{2} - \frac{9768196976794187673789}{3536405} a - \frac{2148122624770386650058}{3536405} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{2} - 2\) , \( -26 a^{3} + 23 a^{2} + 91 a - 101\) , \( -108 a^{3} + 85 a^{2} + 375 a - 402\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(-26a^{3}+23a^{2}+91a-101\right){x}-108a^{3}+85a^{2}+375a-402$ |
| 145.2-a7 |
145.2-a |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5 \cdot 29 \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$676.7253102$ |
1.261003163 |
\( -\frac{21858}{145} a^{3} - \frac{473679}{145} a^{2} - \frac{506319}{145} a + \frac{1578197}{145} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{2} - 2\) , \( -a^{3} + 3 a^{2} + 6 a - 6\) , \( 2 a^{2} + 2 a - 4\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(-a^{3}+3a^{2}+6a-6\right){x}+2a^{2}+2a-4$ |
| 145.2-a8 |
145.2-a |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5^{12} \cdot 29^{12} \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$10.57383297$ |
1.261003163 |
\( -\frac{353532504082336352769040404}{44226847900683630125} a^{3} - \frac{118679748424393055933104957}{44226847900683630125} a^{2} + \frac{1256102902688268113794656607}{44226847900683630125} a + \frac{264629891574656984861820211}{44226847900683630125} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{2} - 2\) , \( 219 a^{3} - 137 a^{2} - 804 a + 574\) , \( -436 a^{3} - 152 a^{2} + 1498 a + 338\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(219a^{3}-137a^{2}-804a+574\right){x}-436a^{3}-152a^{2}+1498a+338$ |
| 145.2-b1 |
145.2-b |
$4$ |
$14$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5^{14} \cdot 29^{2} \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.6.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$37.12204626$ |
1.106765585 |
\( \frac{230503164291}{525625} a^{3} - \frac{277729455896}{525625} a^{2} - \frac{172985895152}{105125} a + \frac{1102426552392}{525625} \) |
\( \bigl[a^{3} + a^{2} - 2 a - 1\) , \( -a^{2} + a + 1\) , \( a + 1\) , \( 6 a^{3} + 6 a^{2} - 16 a - 6\) , \( 12 a^{3} + 9 a^{2} - 33 a - 10\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}+\left(6a^{3}+6a^{2}-16a-6\right){x}+12a^{3}+9a^{2}-33a-10$ |
| 145.2-b2 |
145.2-b |
$4$ |
$14$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5^{7} \cdot 29 \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.6.1 |
$1$ |
\( 1 \) |
$1$ |
$148.4881850$ |
1.106765585 |
\( -\frac{46928367}{725} a^{3} - \frac{15506749}{725} a^{2} + \frac{166828287}{725} a + \frac{34453039}{725} \) |
\( \bigl[a^{3} + a^{2} - 2 a - 1\) , \( -a^{2} + a + 1\) , \( a + 1\) , \( a^{3} + a^{2} - 6 a - 1\) , \( a^{3} - a^{2} - 4 a - 1\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}+\left(a^{3}+a^{2}-6a-1\right){x}+a^{3}-a^{2}-4a-1$ |
| 145.2-b3 |
145.2-b |
$4$ |
$14$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5^{2} \cdot 29^{14} \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.6.3 |
$1$ |
\( 2^{2} \) |
$1$ |
$37.12204626$ |
1.106765585 |
\( -\frac{661087751739463381331431886538563}{1487791163378997317405} a^{3} + \frac{1951571521407985923989420889160237}{1487791163378997317405} a^{2} - \frac{1175955155785562213942162207539017}{1487791163378997317405} a - \frac{336956637773880289733582668124757}{1487791163378997317405} \) |
\( \bigl[a^{3} - 3 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{2} + a - 1\) , \( -2217840 a^{3} - 1835159 a^{2} + 5518084 a + 1213528\) , \( 2470158781 a^{3} + 2043066146 a^{2} - 6147760682 a - 1351954420\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(-2217840a^{3}-1835159a^{2}+5518084a+1213528\right){x}+2470158781a^{3}+2043066146a^{2}-6147760682a-1351954420$ |
| 145.2-b4 |
145.2-b |
$4$ |
$14$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5 \cdot 29^{7} \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.6.3 |
$1$ |
\( 1 \) |
$1$ |
$148.4881850$ |
1.106765585 |
\( \frac{84345529948654163101422494794}{86249381545} a^{3} + \frac{69761421738141200017547121122}{86249381545} a^{2} - \frac{209921659840910908051054641353}{86249381545} a - \frac{46163838435148922680899820821}{86249381545} \) |
\( \bigl[a^{3} - 3 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{2} + a - 1\) , \( -2217835 a^{3} - 1835159 a^{2} + 5518064 a + 1213533\) , \( 2470158335 a^{3} + 2043065677 a^{2} - 6147759783 a - 1351954219\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(-2217835a^{3}-1835159a^{2}+5518064a+1213533\right){x}+2470158335a^{3}+2043065677a^{2}-6147759783a-1351954219$ |
| 145.2-c1 |
145.2-c |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5^{3} \cdot 29^{3} \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$36$ |
\( 1 \) |
$1$ |
$3.606037203$ |
0.967601317 |
\( -\frac{7871515703585209609195898722853052}{121945} a^{3} - \frac{2662628447821281878668749836092631}{121945} a^{2} + \frac{27922770438742838812706397721202301}{121945} a + \frac{1176379563089911167697232592695285}{24389} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{2} + a + 3\) , \( a^{2} + a - 2\) , \( 22808 a^{3} + 7709 a^{2} - 80944 a - 17107\) , \( 2125579 a^{3} + 718864 a^{2} - 7540346 a - 1588249\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(22808a^{3}+7709a^{2}-80944a-17107\right){x}+2125579a^{3}+718864a^{2}-7540346a-1588249$ |
| 145.2-c2 |
145.2-c |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5^{6} \cdot 29^{6} \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$14.42414881$ |
0.967601317 |
\( -\frac{478672083353676504338649}{2974116605} a^{3} - \frac{809580996115760937062801}{14870583025} a^{2} + \frac{8490010818666806724963358}{14870583025} a + \frac{1788410508787560069693424}{14870583025} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{2} + a + 3\) , \( a^{2} + a - 2\) , \( 1423 a^{3} + 479 a^{2} - 5049 a - 1067\) , \( 34418 a^{3} + 11641 a^{2} - 122094 a - 25725\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(1423a^{3}+479a^{2}-5049a-1067\right){x}+34418a^{3}+11641a^{2}-122094a-25725$ |
| 145.2-c3 |
145.2-c |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5^{12} \cdot 29^{12} \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$3.606037203$ |
0.967601317 |
\( -\frac{353532504082336352769040404}{44226847900683630125} a^{3} - \frac{118679748424393055933104957}{44226847900683630125} a^{2} + \frac{1256102902688268113794656607}{44226847900683630125} a + \frac{264629891574656984861820211}{44226847900683630125} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{2} + a + 3\) , \( a^{2} + a - 2\) , \( 1398 a^{3} + 449 a^{2} - 4994 a - 1027\) , \( 34541 a^{3} + 11730 a^{2} - 122402 a - 25765\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(1398a^{3}+449a^{2}-4994a-1027\right){x}+34541a^{3}+11730a^{2}-122402a-25765$ |
| 145.2-c4 |
145.2-c |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5 \cdot 29 \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 1 \) |
$1$ |
$292.0890134$ |
0.967601317 |
\( \frac{346583852229899708}{145} a^{3} - \frac{419040095774382771}{145} a^{2} - \frac{1298732343116544231}{145} a + \frac{1657846139782373138}{145} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{2} + a + 3\) , \( a^{2} + a - 2\) , \( 268 a^{3} + 104 a^{2} - 949 a - 257\) , \( 3217 a^{3} + 1061 a^{2} - 11422 a - 2295\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(268a^{3}+104a^{2}-949a-257\right){x}+3217a^{3}+1061a^{2}-11422a-2295$ |
| 145.2-c5 |
145.2-c |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5^{3} \cdot 29^{3} \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$14.42414881$ |
0.967601317 |
\( -\frac{962236778381448}{121945} a^{3} + \frac{2847898353244631}{121945} a^{2} - \frac{1721306864641051}{121945} a - \frac{98613401759628}{24389} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{2} + a + 3\) , \( a^{2} + a - 2\) , \( 88 a^{3} + 29 a^{2} - 309 a - 67\) , \( 612 a^{3} + 208 a^{2} - 2169 a - 464\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(88a^{3}+29a^{2}-309a-67\right){x}+612a^{3}+208a^{2}-2169a-464$ |
| 145.2-c6 |
145.2-c |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5^{2} \cdot 29^{2} \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$1168.356053$ |
0.967601317 |
\( \frac{159685226823}{4205} a^{3} - \frac{46270475307}{4205} a^{2} - \frac{507570391608}{4205} a + \frac{379717285087}{4205} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{2} + a + 3\) , \( a^{2} + a - 2\) , \( 13 a^{3} + 4 a^{2} - 49 a - 12\) , \( 64 a^{3} + 22 a^{2} - 227 a - 49\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(13a^{3}+4a^{2}-49a-12\right){x}+64a^{3}+22a^{2}-227a-49$ |
| 145.2-c7 |
145.2-c |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5^{4} \cdot 29^{4} \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$292.0890134$ |
0.967601317 |
\( \frac{3924815332575135346772}{3536405} a^{3} + \frac{3246179105759555460927}{3536405} a^{2} - \frac{9768196976794187673789}{3536405} a - \frac{2148122624770386650058}{3536405} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{2} + a + 3\) , \( a^{2} + a - 2\) , \( -2 a^{3} - 16 a^{2} - 29 a - 7\) , \( 103 a^{3} + 91 a^{2} - 244 a - 55\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-2a^{3}-16a^{2}-29a-7\right){x}+103a^{3}+91a^{2}-244a-55$ |
| 145.2-c8 |
145.2-c |
$8$ |
$12$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5 \cdot 29 \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$1168.356053$ |
0.967601317 |
\( -\frac{21858}{145} a^{3} - \frac{473679}{145} a^{2} - \frac{506319}{145} a + \frac{1578197}{145} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{2} + a + 3\) , \( a^{2} + a - 2\) , \( -2 a^{3} - a^{2} + 6 a + 3\) , \( a^{3} - 4 a - 1\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-2a^{3}-a^{2}+6a+3\right){x}+a^{3}-4a-1$ |
| 145.2-d1 |
145.2-d |
$4$ |
$14$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5^{2} \cdot 29^{14} \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.3 |
$49$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$0.104447754$ |
1.068112419 |
\( -\frac{661087751739463381331431886538563}{1487791163378997317405} a^{3} + \frac{1951571521407985923989420889160237}{1487791163378997317405} a^{2} - \frac{1175955155785562213942162207539017}{1487791163378997317405} a - \frac{336956637773880289733582668124757}{1487791163378997317405} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{2} + a - 2\) , \( 0\) , \( -454771 a^{3} - 376071 a^{2} + 1131814 a + 248570\) , \( -229727262 a^{3} - 190004926 a^{2} + 571751738 a + 125731744\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(-454771a^{3}-376071a^{2}+1131814a+248570\right){x}-229727262a^{3}-190004926a^{2}+571751738a+125731744$ |
| 145.2-d2 |
145.2-d |
$4$ |
$14$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5 \cdot 29^{7} \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.3 |
$49$ |
\( 7 \) |
$1$ |
$0.417791016$ |
1.068112419 |
\( \frac{84345529948654163101422494794}{86249381545} a^{3} + \frac{69761421738141200017547121122}{86249381545} a^{2} - \frac{209921659840910908051054641353}{86249381545} a - \frac{46163838435148922680899820821}{86249381545} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{2} + a - 2\) , \( 0\) , \( -454716 a^{3} - 376136 a^{2} + 1131604 a + 248835\) , \( -229726834 a^{3} - 190005324 a^{2} + 571750203 a + 125733493\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(-454716a^{3}-376136a^{2}+1131604a+248835\right){x}-229726834a^{3}-190005324a^{2}+571750203a+125733493$ |
| 145.2-d3 |
145.2-d |
$4$ |
$14$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5^{14} \cdot 29^{2} \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$250.7790575$ |
1.068112419 |
\( \frac{230503164291}{525625} a^{3} - \frac{277729455896}{525625} a^{2} - \frac{172985895152}{105125} a + \frac{1102426552392}{525625} \) |
\( \bigl[a^{2} - 1\) , \( a^{3} + a^{2} - 4 a - 1\) , \( a + 1\) , \( -17 a^{3} + 22 a^{2} + 64 a - 84\) , \( 67 a^{3} - 79 a^{2} - 250 a + 314\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-1\right){x}^{2}+\left(-17a^{3}+22a^{2}+64a-84\right){x}+67a^{3}-79a^{2}-250a+314$ |
| 145.2-d4 |
145.2-d |
$4$ |
$14$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5^{7} \cdot 29 \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 7 \) |
$1$ |
$1003.116230$ |
1.068112419 |
\( -\frac{46928367}{725} a^{3} - \frac{15506749}{725} a^{2} + \frac{166828287}{725} a + \frac{34453039}{725} \) |
\( \bigl[a^{2} - 1\) , \( a^{3} + a^{2} - 4 a - 1\) , \( a + 1\) , \( -2 a^{3} + 2 a^{2} + 4 a - 4\) , \( a^{3} - a^{2} - 6 a + 6\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-1\right){x}^{2}+\left(-2a^{3}+2a^{2}+4a-4\right){x}+a^{3}-a^{2}-6a+6$ |
| 145.2-e1 |
145.2-e |
$4$ |
$4$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5^{4} \cdot 29^{4} \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$10.00786948$ |
1.193508078 |
\( -\frac{837290400638977682071465035}{707281} a^{3} - \frac{283222866317043043864271452}{707281} a^{2} + \frac{14850677130045385934310775524}{3536405} a + \frac{625655434590847729165353808}{707281} \) |
\( \bigl[a^{3} - 2 a\) , \( a^{2} - a - 2\) , \( a\) , \( 143 a^{3} + 23 a^{2} - 565 a - 117\) , \( 2132 a^{3} - 97 a^{2} - 5744 a - 1177\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(143a^{3}+23a^{2}-565a-117\right){x}+2132a^{3}-97a^{2}-5744a-1177$ |
| 145.2-e2 |
145.2-e |
$4$ |
$4$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5 \cdot 29 \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$640.5036467$ |
1.193508078 |
\( \frac{1327742239202}{145} a^{3} - \frac{1605462739914}{145} a^{2} - \frac{4975467582949}{145} a + \frac{6351468223927}{145} \) |
\( \bigl[a^{3} - 2 a\) , \( a^{2} - a - 2\) , \( a\) , \( -2 a^{3} - 7 a^{2} + 10 a + 3\) , \( 5 a^{3} - 2 a^{2} - 6 a - 1\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-2a^{3}-7a^{2}+10a+3\right){x}+5a^{3}-2a^{2}-6a-1$ |
| 145.2-e3 |
145.2-e |
$4$ |
$4$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5^{2} \cdot 29^{2} \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$160.1259116$ |
1.193508078 |
\( \frac{1004538959188981}{841} a^{3} + \frac{4199027048148699}{4205} a^{2} - \frac{12403619889642577}{4205} a - \frac{2730688024090041}{4205} \) |
\( \bigl[a^{3} - 2 a\) , \( a^{2} - a - 2\) , \( a\) , \( -27 a^{3} - 82 a^{2} + 115 a + 28\) , \( 422 a^{3} - 168 a^{2} - 499 a - 93\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-27a^{3}-82a^{2}+115a+28\right){x}+422a^{3}-168a^{2}-499a-93$ |
| 145.2-e4 |
145.2-e |
$4$ |
$4$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5 \cdot 29 \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$40.03147792$ |
1.193508078 |
\( \frac{807725601322094857856829323}{145} a^{3} + \frac{668062506896781512198703964}{145} a^{2} - \frac{2010291468094612695913053076}{145} a - \frac{442082873142638373148939392}{145} \) |
\( \bigl[a^{3} - 2 a\) , \( a^{2} - a - 2\) , \( a\) , \( -597 a^{3} - 1387 a^{2} + 2475 a + 573\) , \( 25040 a^{3} - 5863 a^{2} - 32346 a - 6277\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-597a^{3}-1387a^{2}+2475a+573\right){x}+25040a^{3}-5863a^{2}-32346a-6277$ |
| 145.2-f1 |
145.2-f |
$4$ |
$4$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5^{4} \cdot 29^{4} \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$30.10557349$ |
0.897574784 |
\( -\frac{837290400638977682071465035}{707281} a^{3} - \frac{283222866317043043864271452}{707281} a^{2} + \frac{14850677130045385934310775524}{3536405} a + \frac{625655434590847729165353808}{707281} \) |
\( \bigl[a^{3} - 2 a + 1\) , \( -a^{3} + 3 a + 1\) , \( a^{2} + a - 2\) , \( 935 a^{3} + 306 a^{2} - 3343 a - 705\) , \( -17303 a^{3} - 5897 a^{2} + 61256 a + 12892\bigr] \) |
${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{3}+3a+1\right){x}^{2}+\left(935a^{3}+306a^{2}-3343a-705\right){x}-17303a^{3}-5897a^{2}+61256a+12892$ |
| 145.2-f2 |
145.2-f |
$4$ |
$4$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5^{2} \cdot 29^{2} \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$120.4222939$ |
0.897574784 |
\( \frac{1004538959188981}{841} a^{3} + \frac{4199027048148699}{4205} a^{2} - \frac{12403619889642577}{4205} a - \frac{2730688024090041}{4205} \) |
\( \bigl[a^{3} - 2 a + 1\) , \( -a^{3} + 3 a + 1\) , \( a^{2} + a - 2\) , \( 35 a^{3} + a^{2} - 148 a - 35\) , \( -338 a^{3} - 165 a^{2} + 1084 a + 222\bigr] \) |
${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{3}+3a+1\right){x}^{2}+\left(35a^{3}+a^{2}-148a-35\right){x}-338a^{3}-165a^{2}+1084a+222$ |
| 145.2-f3 |
145.2-f |
$4$ |
$4$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5 \cdot 29 \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$120.4222939$ |
0.897574784 |
\( \frac{1327742239202}{145} a^{3} - \frac{1605462739914}{145} a^{2} - \frac{4975467582949}{145} a + \frac{6351468223927}{145} \) |
\( \bigl[a^{3} - 2 a + 1\) , \( -a^{3} + 3 a + 1\) , \( a^{2} + a - 2\) , \( a^{2} - 3 a - 5\) , \( -6 a^{3} - a^{2} + 18 a - 5\bigr] \) |
${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{3}+3a+1\right){x}^{2}+\left(a^{2}-3a-5\right){x}-6a^{3}-a^{2}+18a-5$ |
| 145.2-f4 |
145.2-f |
$4$ |
$4$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
145.2 |
\( 5 \cdot 29 \) |
\( 5 \cdot 29 \) |
$5.58323$ |
$(-a-1), (a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$30.10557349$ |
0.897574784 |
\( \frac{807725601322094857856829323}{145} a^{3} + \frac{668062506896781512198703964}{145} a^{2} - \frac{2010291468094612695913053076}{145} a - \frac{442082873142638373148939392}{145} \) |
\( \bigl[a^{3} - 2 a + 1\) , \( -a^{3} + 3 a + 1\) , \( a^{2} + a - 2\) , \( -305 a^{3} - 304 a^{2} + 727 a + 155\) , \( -5961 a^{3} - 4729 a^{2} + 14976 a + 3280\bigr] \) |
${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{3}+3a+1\right){x}^{2}+\left(-305a^{3}-304a^{2}+727a+155\right){x}-5961a^{3}-4729a^{2}+14976a+3280$ |
*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.
