| 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 |
| 23716.5-a1 |
23716.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{6} \cdot 7^{6} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$0.131842497$ |
$1.105108572$ |
3.524449760 |
\( \frac{46830231}{234256} a + \frac{377324919}{234256} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 21 a - 37\) , \( 7 a - 29\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(21a-37\right){x}+7a-29$ |
| 23716.5-a2 |
23716.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{6} \cdot 7^{6} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$0.131842497$ |
$1.105108572$ |
3.524449760 |
\( -\frac{46830231}{234256} a + \frac{212077575}{117128} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -21 a - 16\) , \( -7 a - 22\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-21a-16\right){x}-7a-22$ |
| 23716.5-a3 |
23716.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{3} \cdot 7^{6} \cdot 11^{9} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.131842497$ |
$0.552554286$ |
3.524449760 |
\( \frac{56046918875913}{857435524} a + \frac{9320189138181}{214358881} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -231 a - 86\) , \( 2079 a - 764\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-231a-86\right){x}+2079a-764$ |
| 23716.5-a4 |
23716.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{3} \cdot 7^{6} \cdot 11^{9} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.131842497$ |
$0.552554286$ |
3.524449760 |
\( -\frac{56046918875913}{857435524} a + \frac{93327675428637}{857435524} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 231 a - 317\) , \( -2079 a + 1315\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(231a-317\right){x}-2079a+1315$ |
| 23716.5-a5 |
23716.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{9} \cdot 7^{6} \cdot 11^{3} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.527369991$ |
$1.105108572$ |
3.524449760 |
\( \frac{14003310699}{30976} a + \frac{5238465399}{30976} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -63 a - 58\) , \( 371 a + 62\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-63a-58\right){x}+371a+62$ |
| 23716.5-a6 |
23716.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{9} \cdot 7^{6} \cdot 11^{3} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.527369991$ |
$1.105108572$ |
3.524449760 |
\( -\frac{14003310699}{30976} a + \frac{9620888049}{15488} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 63 a - 121\) , \( -371 a + 433\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(63a-121\right){x}-371a+433$ |
| 23716.5-b1 |
23716.5-b |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{33} \cdot 7^{3} \cdot 11^{3} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.660387214$ |
0.998411621 |
\( \frac{428951306259}{507510784} a - \frac{1585065606849}{507510784} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 9 a - 122\) , \( -39 a + 666\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(9a-122\right){x}-39a+666$ |
| 23716.5-b2 |
23716.5-b |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{33} \cdot 7^{3} \cdot 11^{3} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.660387214$ |
0.998411621 |
\( -\frac{428951306259}{507510784} a - \frac{578057150295}{253755392} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -9 a - 113\) , \( 39 a + 627\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-9a-113\right){x}+39a+627$ |
| 23716.5-c1 |
23716.5-c |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{2} \cdot 7^{8} \cdot 11^{2} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1.822390698$ |
$1.879991111$ |
1.726581179 |
\( \frac{765625}{22} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -26\) , \( 46\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-26{x}+46$ |
| 23716.5-c2 |
23716.5-c |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{6} \cdot 7^{8} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$0.607463566$ |
$0.626663703$ |
1.726581179 |
\( \frac{911871625}{10648} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -271\) , \( -1718\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-271{x}-1718$ |
| 23716.5-d1 |
23716.5-d |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{6} \cdot 7^{3} \cdot 11^{3} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.094409938$ |
$3.108510495$ |
3.549531310 |
\( \frac{1682825}{1936} a - \frac{3924721}{968} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( a - 6\) , \( -2 a + 4\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a-6\right){x}-2a+4$ |
| 23716.5-d2 |
23716.5-d |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{6} \cdot 7^{3} \cdot 11^{3} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.094409938$ |
$3.108510495$ |
3.549531310 |
\( -\frac{1682825}{1936} a - \frac{6166617}{1936} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -6\) , \( 2 a + 8\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}-6{x}+2a+8$ |
| 23716.5-e1 |
23716.5-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{36} \cdot 7^{6} \cdot 11^{3} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.361596845$ |
1.093366089 |
\( \frac{31504873455125}{519691042816} a + \frac{50524809992625}{259845521408} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -129 a - 26\) , \( -294 a + 2776\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-129a-26\right){x}-294a+2776$ |
| 23716.5-e2 |
23716.5-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{36} \cdot 7^{6} \cdot 11^{3} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.361596845$ |
1.093366089 |
\( -\frac{31504873455125}{519691042816} a + \frac{132554493440375}{519691042816} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 128 a - 155\) , \( 293 a + 2482\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(128a-155\right){x}+293a+2482$ |
| 23716.5-e3 |
23716.5-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{24} \cdot 7^{6} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.361596845$ |
1.093366089 |
\( \frac{1133731711875}{959512576} a + \frac{6924008747375}{959512576} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -268 a - 236\) , \( 3000 a + 28\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-268a-236\right){x}+3000a+28$ |
| 23716.5-e4 |
23716.5-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{24} \cdot 7^{6} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.361596845$ |
1.093366089 |
\( -\frac{1133731711875}{959512576} a + \frac{4028870229625}{479756288} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 269 a - 504\) , \( -2732 a + 2524\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(269a-504\right){x}-2732a+2524$ |
| 23716.5-e5 |
23716.5-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{12} \cdot 7^{6} \cdot 11^{9} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.180798422$ |
1.093366089 |
\( \frac{915988506230265125}{54875873536} a + \frac{2123510665930979625}{54875873536} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -4188 a - 3596\) , \( 192280 a + 13020\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4188a-3596\right){x}+192280a+13020$ |
| 23716.5-e6 |
23716.5-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{12} \cdot 7^{6} \cdot 11^{9} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.180798422$ |
1.093366089 |
\( -\frac{915988506230265125}{54875873536} a + \frac{1519749586080622375}{27437936768} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 4189 a - 7784\) , \( -188092 a + 197516\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4189a-7784\right){x}-188092a+197516$ |
| 23716.5-f1 |
23716.5-f |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{18} \cdot 7^{4} \cdot 11^{2} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 1 \) |
$2.500935374$ |
$0.667368368$ |
2.523359096 |
\( \frac{551516475321}{5632} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -625\) , \( 6173\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-625{x}+6173$ |
| 23716.5-g1 |
23716.5-g |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{18} \cdot 7^{8} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{10} \) |
$0.146504834$ |
$0.357301545$ |
5.064980705 |
\( -\frac{26539759465005}{6716588032} a - \frac{31675945165289}{3358294016} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( 332 a - 529\) , \( -3964 a + 3071\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(332a-529\right){x}-3964a+3071$ |
| 23716.5-g2 |
23716.5-g |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{12} \cdot 7^{7} \cdot 11^{9} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{9} \) |
$0.073252417$ |
$0.357301545$ |
5.064980705 |
\( \frac{484480877855263}{384131114752} a - \frac{238867074550997}{192065557376} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( -269 a + 139\) , \( 1047 a - 3314\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-269a+139\right){x}+1047a-3314$ |
| 23716.5-g3 |
23716.5-g |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{33} \cdot 7^{7} \cdot 11^{3} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$0.293009668$ |
$0.357301545$ |
5.064980705 |
\( -\frac{1501567035128925}{3637837299712} a - \frac{947934887021657}{1818918649856} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -116 a + 308\) , \( 1130 a + 2194\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-116a+308\right){x}+1130a+2194$ |
| 23716.5-g4 |
23716.5-g |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{9} \cdot 7^{10} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$0.293009668$ |
$0.178650772$ |
5.064980705 |
\( \frac{17636942674068359}{183656704} a + \frac{6605911238021499}{91828352} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( 5442 a - 8579\) , \( -250518 a + 204349\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(5442a-8579\right){x}-250518a+204349$ |
| 23716.5-h1 |
23716.5-h |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{18} \cdot 7^{3} \cdot 11^{3} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 5 \) |
$0.138709702$ |
$1.166887402$ |
4.894144174 |
\( -\frac{13872889683}{123904} a - \frac{10410630165}{61952} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -28 a + 101\) , \( 228 a + 63\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-28a+101\right){x}+228a+63$ |
| 23716.5-h2 |
23716.5-h |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{24} \cdot 7^{3} \cdot 11^{3} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \cdot 5 \) |
$0.069354851$ |
$1.166887402$ |
4.894144174 |
\( -\frac{8993570211}{126877696} a + \frac{61291846233}{63438848} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -22 a + 14\) , \( 41 a + 6\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-22a+14\right){x}+41a+6$ |
| 23716.5-i1 |
23716.5-i |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{12} \cdot 7^{2} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 5 \cdot 7 \) |
$0.067658895$ |
$1.498873908$ |
5.366226761 |
\( \frac{6332299625}{20614528} a - \frac{5352102233}{10307264} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -9 a + 13\) , \( 11 a + 27\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-9a+13\right){x}+11a+27$ |
| 23716.5-j1 |
23716.5-j |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{18} \cdot 7^{8} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{10} \) |
$0.146504834$ |
$0.357301545$ |
5.064980705 |
\( \frac{26539759465005}{6716588032} a - \frac{89891649795583}{6716588032} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -333 a - 197\) , \( 3963 a - 893\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-333a-197\right){x}+3963a-893$ |
| 23716.5-j2 |
23716.5-j |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{33} \cdot 7^{7} \cdot 11^{3} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$0.293009668$ |
$0.357301545$ |
5.064980705 |
\( \frac{1501567035128925}{3637837299712} a - \frac{3397436809172239}{3637837299712} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 116 a + 192\) , \( -1130 a + 3324\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(116a+192\right){x}-1130a+3324$ |
| 23716.5-j3 |
23716.5-j |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{12} \cdot 7^{7} \cdot 11^{9} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{9} \) |
$0.073252417$ |
$0.357301545$ |
5.064980705 |
\( -\frac{484480877855263}{384131114752} a + \frac{6746728753269}{384131114752} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 269 a - 130\) , \( -1047 a - 2267\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(269a-130\right){x}-1047a-2267$ |
| 23716.5-j4 |
23716.5-j |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{9} \cdot 7^{10} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$0.293009668$ |
$0.178650772$ |
5.064980705 |
\( -\frac{17636942674068359}{183656704} a + \frac{30848765150111357}{183656704} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -5443 a - 3137\) , \( 250517 a - 46169\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-5443a-3137\right){x}+250517a-46169$ |
| 23716.5-k1 |
23716.5-k |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{18} \cdot 7^{3} \cdot 11^{3} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 5 \) |
$0.138709702$ |
$1.166887402$ |
4.894144174 |
\( \frac{13872889683}{123904} a - \frac{34694150013}{123904} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 27 a + 73\) , \( -229 a + 291\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(27a+73\right){x}-229a+291$ |
| 23716.5-k2 |
23716.5-k |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{24} \cdot 7^{3} \cdot 11^{3} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \cdot 5 \) |
$0.069354851$ |
$1.166887402$ |
4.894144174 |
\( \frac{8993570211}{126877696} a + \frac{113590122255}{126877696} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 21 a - 8\) , \( -42 a + 47\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(21a-8\right){x}-42a+47$ |
| 23716.5-l1 |
23716.5-l |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{12} \cdot 7^{2} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 5 \cdot 7 \) |
$0.067658895$ |
$1.498873908$ |
5.366226761 |
\( -\frac{6332299625}{20614528} a - \frac{4371904841}{20614528} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 9 a + 4\) , \( -11 a + 38\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(9a+4\right){x}-11a+38$ |
| 23716.5-m1 |
23716.5-m |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{30} \cdot 7^{4} \cdot 11^{2} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{3} \cdot 5^{2} \) |
$0.099026223$ |
$0.830278223$ |
9.322794253 |
\( \frac{1071912625}{360448} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -78\) , \( 139\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-78{x}+139$ |
| 23716.5-m2 |
23716.5-m |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{10} \cdot 7^{4} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \cdot 5^{2} \) |
$0.297078670$ |
$0.276759407$ |
9.322794253 |
\( \frac{413160293352625}{42592} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5678\) , \( 162315\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-5678{x}+162315$ |
| 23716.5-n1 |
23716.5-n |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{12} \cdot 7^{3} \cdot 11^{15} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1$ |
$0.195608169$ |
4.731708082 |
\( \frac{30861084894361475}{6639980697856} a + \frac{6520918061639743}{6639980697856} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -1045 a - 454\) , \( -19530 a + 10059\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-1045a-454\right){x}-19530a+10059$ |
| 23716.5-n2 |
23716.5-n |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{12} \cdot 7^{3} \cdot 11^{15} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1$ |
$0.195608169$ |
4.731708082 |
\( -\frac{30861084894361475}{6639980697856} a + \frac{18691001478000609}{3319990348928} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( 1044 a - 1498\) , \( 19529 a - 9470\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(1044a-1498\right){x}+19529a-9470$ |
| 23716.5-o1 |
23716.5-o |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{5} \cdot 7^{6} \cdot 11^{2} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.857956067$ |
5.617931086 |
\( \frac{34643161}{176} a - \frac{7276683}{176} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( 28 a - 18\) , \( -47 a - 46\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(28a-18\right){x}-47a-46$ |
| 23716.5-o2 |
23716.5-o |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{4} \cdot 7^{6} \cdot 11^{4} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$1.857956067$ |
5.617931086 |
\( \frac{704969}{484} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 13\) , \( 13\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+13{x}+13$ |
| 23716.5-o3 |
23716.5-o |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{2} \cdot 7^{6} \cdot 11^{8} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.928978033$ |
5.617931086 |
\( \frac{59776471}{29282} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -57\) , \( 41\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-57{x}+41$ |
| 23716.5-o4 |
23716.5-o |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{5} \cdot 7^{6} \cdot 11^{2} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.857956067$ |
5.617931086 |
\( -\frac{34643161}{176} a + \frac{13683239}{88} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -29 a + 10\) , \( 46 a - 93\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-29a+10\right){x}+46a-93$ |
| 23716.5-p1 |
23716.5-p |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{3} \cdot 7^{3} \cdot 11^{3} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.889152545$ |
5.879845969 |
\( \frac{133125}{484} a + \frac{753875}{484} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( a - 4\) , \( -2 a + 1\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a-4\right){x}-2a+1$ |
| 23716.5-p2 |
23716.5-p |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{3} \cdot 7^{3} \cdot 11^{3} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.889152545$ |
5.879845969 |
\( -\frac{133125}{484} a + \frac{221750}{121} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( -2 a - 2\) , \( a\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-2a-2\right){x}+a$ |
| 23716.5-q1 |
23716.5-q |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{6} \cdot 7^{4} \cdot 11^{2} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 3^{2} \) |
$0.234909178$ |
$3.241668097$ |
10.36148524 |
\( \frac{415233}{88} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -6\) , \( -3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-6{x}-3$ |
*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.
