| 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 |
| 27.2-a8 |
27.2-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{15} \) |
$0.67558$ |
$(-a), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.144817200$ |
0.690350747 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -97 a + 240\) , \( -381 a - 1012\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-97a+240\right){x}-381a-1012$ |
| 27.3-a8 |
27.3-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27.3 |
\( 3^{3} \) |
\( 3^{15} \) |
$0.67558$ |
$(-a), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.144817200$ |
0.690350747 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 70 a + 186\) , \( -573 a + 1350\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(70a+186\right){x}-573a+1350$ |
| 675.4-c8 |
675.4-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
675.4 |
\( 3^{3} \cdot 5^{2} \) |
\( 3^{15} \cdot 5^{6} \) |
$1.51064$ |
$(-a), (a-1), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.372120110$ |
$0.511977816$ |
2.297724390 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 623 a + 381\) , \( -767 a + 16084\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(623a+381\right){x}-767a+16084$ |
| 675.6-a8 |
675.6-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
675.6 |
\( 3^{3} \cdot 5^{2} \) |
\( 3^{15} \cdot 5^{6} \) |
$1.51064$ |
$(-a), (a-1), (a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.511977816$ |
1.234936958 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -527 a - 624\) , \( 9910 a + 1568\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-527a-624\right){x}+9910a+1568$ |
| 675.7-a8 |
675.7-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
675.7 |
\( 3^{3} \cdot 5^{2} \) |
\( 3^{15} \cdot 5^{6} \) |
$1.51064$ |
$(-a), (a-1), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.511977816$ |
1.234936958 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( 628 a - 996\) , \( 9778 a - 6085\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(628a-996\right){x}+9778a-6085$ |
| 675.9-c8 |
675.9-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
675.9 |
\( 3^{3} \cdot 5^{2} \) |
\( 3^{15} \cdot 5^{6} \) |
$1.51064$ |
$(-a), (a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{5} \) |
$0.465150138$ |
$0.511977816$ |
2.297724390 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -699 a + 812\) , \( 2300 a - 17944\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-699a+812\right){x}+2300a-17944$ |
| 1089.2-c8 |
1089.2-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
1089.2 |
\( 3^{2} \cdot 11^{2} \) |
\( 3^{9} \cdot 11^{6} \) |
$1.70252$ |
$(-a), (a-1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.597861284$ |
3.605239194 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -59 a + 937\) , \( 6561 a - 1591\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-59a+937\right){x}+6561a-1591$ |
| 2304.2-d8 |
2304.2-d |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2304.2 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{9} \) |
$2.05331$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.845411214$ |
$0.495720389$ |
2.527193171 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 86 a - 1365\) , \( 2183 a - 18771\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(86a-1365\right){x}+2183a-18771$ |
| 2304.2-h8 |
2304.2-h |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2304.2 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{9} \) |
$2.05331$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \) |
$4.227056070$ |
$0.495720389$ |
2.527193171 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 86 a - 1365\) , \( -2183 a + 18771\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(86a-1365\right){x}-2183a+18771$ |
| 4761.4-b8 |
4761.4-b |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
4761.4 |
\( 3^{2} \cdot 23^{2} \) |
\( 3^{9} \cdot 23^{6} \) |
$2.46184$ |
$(-a), (a-1), (a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.413459386$ |
2.493253908 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -651 a - 1251\) , \( 15607 a + 11805\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-651a-1251\right){x}+15607a+11805$ |
| 4761.6-b8 |
4761.6-b |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
4761.6 |
\( 3^{2} \cdot 23^{2} \) |
\( 3^{9} \cdot 23^{6} \) |
$2.46184$ |
$(-a), (a-1), (a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.413459386$ |
2.493253908 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( 836 a - 1733\) , \( 18267 a - 20335\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(836a-1733\right){x}+18267a-20335$ |
| 6912.2-n8 |
6912.2-n |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
6912.2 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{24} \cdot 3^{15} \) |
$2.70231$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1.486552137$ |
$0.286204300$ |
5.131211894 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -1534 a + 3837\) , \( 30465 a + 70178\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-1534a+3837\right){x}+30465a+70178$ |
| 6912.3-r8 |
6912.3-r |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{24} \cdot 3^{15} \) |
$2.70231$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{5} \) |
$7.432760689$ |
$0.286204300$ |
5.131211894 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 1109 a + 2983\) , \( 42983 a - 83742\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(1109a+2983\right){x}+42983a-83742$ |
| 8649.4-c8 |
8649.4-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
8649.4 |
\( 3^{2} \cdot 31^{2} \) |
\( 3^{9} \cdot 31^{6} \) |
$2.85809$ |
$(-a), (a-1), (-3a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \) |
$3.111678720$ |
$0.356136040$ |
5.346066004 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 1141 a + 1177\) , \( 10210 a - 52692\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(1141a+1177\right){x}+10210a-52692$ |
| 8649.6-c8 |
8649.6-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
8649.6 |
\( 3^{2} \cdot 31^{2} \) |
\( 3^{9} \cdot 31^{6} \) |
$2.85809$ |
$(-a), (a-1), (3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \cdot 5 \) |
$2.489342976$ |
$0.356136040$ |
5.346066004 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -1338 a + 1977\) , \( -332 a + 49572\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1338a+1977\right){x}-332a+49572$ |
| 9801.3-l8 |
9801.3-l |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9801.3 |
\( 3^{4} \cdot 11^{2} \) |
\( 3^{21} \cdot 11^{6} \) |
$2.94885$ |
$(-a), (a-1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.199287094$ |
0.961397118 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -528 a + 8443\) , \( -168707 a + 36088\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-528a+8443\right){x}-168707a+36088$ |
| 16875.13-bc7 |
16875.13-bc |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
16875.13 |
\( 3^{3} \cdot 5^{4} \) |
\( 3^{15} \cdot 5^{12} \) |
$3.37789$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{7} \) |
$0.779983429$ |
$0.228963440$ |
6.892315432 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( 1733 a + 4661\) , \( -87881 a + 169790\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(1733a+4661\right){x}-87881a+169790$ |
| 16875.8-ba7 |
16875.8-ba |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
16875.8 |
\( 3^{3} \cdot 5^{4} \) |
\( 3^{15} \cdot 5^{12} \) |
$3.37789$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{5} \cdot 5 \) |
$0.623986743$ |
$0.228963440$ |
6.892315432 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( -2398 a + 5997\) , \( -57103 a - 134970\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-2398a+5997\right){x}-57103a-134970$ |
| 19881.4-a7 |
19881.4-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
19881.4 |
\( 3^{2} \cdot 47^{2} \) |
\( 3^{9} \cdot 47^{6} \) |
$3.51920$ |
$(-a), (a-1), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.289233001$ |
0.348828124 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 2116 a - 2773\) , \( 56522 a - 20516\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(2116a-2773\right){x}+56522a-20516$ |
| 19881.6-b7 |
19881.6-b |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
19881.6 |
\( 3^{2} \cdot 47^{2} \) |
\( 3^{9} \cdot 47^{6} \) |
$3.51920$ |
$(-a), (a-1), (2a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.289233001$ |
0.348828124 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -1850 a - 1492\) , \( 54186 a - 6466\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-1850a-1492\right){x}+54186a-6466$ |
| 20736.3-bi7 |
20736.3-bi |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{24} \cdot 3^{21} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$4$ |
\( 2^{5} \) |
$1$ |
$0.165240129$ |
3.188593517 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 765 a - 12279\) , \( -48196 a + 521402\bigr] \) |
${y}^2={x}^{3}+\left(765a-12279\right){x}-48196a+521402$ |
| 20736.3-bl7 |
20736.3-bl |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{24} \cdot 3^{21} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$4$ |
\( 2^{5} \) |
$1$ |
$0.165240129$ |
3.188593517 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 765 a - 12279\) , \( 48196 a - 521402\bigr] \) |
${y}^2={x}^{3}+\left(765a-12279\right){x}+48196a-521402$ |
| 27225.4-f7 |
27225.4-f |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.4 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{9} \cdot 5^{6} \cdot 11^{6} \) |
$3.80695$ |
$(-a), (a-1), (-a-1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \) |
$2.844226804$ |
$0.267371694$ |
3.668624767 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 2756 a - 1351\) , \( -49535 a - 62584\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(2756a-1351\right){x}-49535a-62584$ |
| 27225.6-c7 |
27225.6-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.6 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{9} \cdot 5^{6} \cdot 11^{6} \) |
$3.80695$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \cdot 5 \) |
$0.568845360$ |
$0.267371694$ |
3.668624767 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -2699 a + 413\) , \( -63112 a + 89457\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2699a+413\right){x}-63112a+89457$ |
| 31329.4-b7 |
31329.4-b |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
31329.4 |
\( 3^{2} \cdot 59^{2} \) |
\( 3^{9} \cdot 59^{6} \) |
$3.94295$ |
$(-a), (a-1), (a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.258149190$ |
1.556698190 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -955 a - 4162\) , \( 37653 a + 97124\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-955a-4162\right){x}+37653a+97124$ |
| 31329.6-b7 |
31329.6-b |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
31329.6 |
\( 3^{2} \cdot 59^{2} \) |
\( 3^{9} \cdot 59^{6} \) |
$3.94295$ |
$(-a), (a-1), (a-8)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.258149190$ |
1.556698190 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 1523 a - 4963\) , \( 58801 a - 119051\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(1523a-4963\right){x}+58801a-119051$ |
| 36864.2-t7 |
36864.2-t |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.2 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{36} \cdot 3^{9} \) |
$4.10663$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \cdot 5 \) |
$5.598116621$ |
$0.247860194$ |
8.367242985 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 341 a - 5458\) , \( -12688 a + 156649\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(341a-5458\right){x}-12688a+156649$ |
| 36864.2-bg7 |
36864.2-bg |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.2 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{36} \cdot 3^{9} \) |
$4.10663$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \) |
$6.997645777$ |
$0.247860194$ |
8.367242985 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 341 a - 5458\) , \( 12688 a - 156649\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(341a-5458\right){x}+12688a-156649$ |
| 36963.4-a7 |
36963.4-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36963.4 |
\( 3^{3} \cdot 37^{2} \) |
\( 3^{15} \cdot 37^{6} \) |
$4.10938$ |
$(-a), (a-1), (-3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1.735952803$ |
$0.188206788$ |
3.940368569 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 5229 a + 523\) , \( 54338 a + 296805\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(5229a+523\right){x}+54338a+296805$ |
| 36963.6-a7 |
36963.6-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36963.6 |
\( 3^{3} \cdot 37^{2} \) |
\( 3^{15} \cdot 37^{6} \) |
$4.10938$ |
$(-a), (a-1), (3a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$3.683633151$ |
$0.188206788$ |
8.361328871 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -2833 a - 6524\) , \( 143616 a + 171542\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2833a-6524\right){x}+143616a+171542$ |
| 36963.7-a7 |
36963.7-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36963.7 |
\( 3^{3} \cdot 37^{2} \) |
\( 3^{15} \cdot 37^{6} \) |
$4.10938$ |
$(-a), (a-1), (-3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{5} \) |
$4.604541439$ |
$0.188206788$ |
8.361328871 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 3776 a - 8656\) , \( 184807 a - 238615\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(3776a-8656\right){x}+184807a-238615$ |
| 36963.9-a7 |
36963.9-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36963.9 |
\( 3^{3} \cdot 37^{2} \) |
\( 3^{15} \cdot 37^{6} \) |
$4.10938$ |
$(-a), (a-1), (3a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{5} \) |
$2.169941003$ |
$0.188206788$ |
3.940368569 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( -5511 a + 3995\) , \( 112100 a - 333917\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-5511a+3995\right){x}+112100a-333917$ |
| 40401.4-a7 |
40401.4-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
40401.4 |
\( 3^{2} \cdot 67^{2} \) |
\( 3^{9} \cdot 67^{6} \) |
$4.20178$ |
$(-a), (a-1), (-3a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \) |
$5.828122650$ |
$0.242247538$ |
6.811012775 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( -3129 a - 452\) , \( -95320 a + 86415\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-3129a-452\right){x}-95320a+86415$ |
| 40401.6-a7 |
40401.6-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
40401.6 |
\( 3^{2} \cdot 67^{2} \) |
\( 3^{9} \cdot 67^{6} \) |
$4.20178$ |
$(-a), (a-1), (3a-8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \cdot 5 \) |
$4.662498120$ |
$0.242247538$ |
6.811012775 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 3314 a - 2534\) , \( -83871 a - 44865\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(3314a-2534\right){x}-83871a-44865$ |
| 42849.7-c7 |
42849.7-c |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
42849.7 |
\( 3^{4} \cdot 23^{2} \) |
\( 3^{21} \cdot 23^{6} \) |
$4.26403$ |
$(-a), (a-1), (a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.137819795$ |
0.664867708 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -5855 a - 11268\) , \( -404272 a - 336280\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-5855a-11268\right){x}-404272a-336280$ |
| 42849.9-d7 |
42849.9-d |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
42849.9 |
\( 3^{4} \cdot 23^{2} \) |
\( 3^{21} \cdot 23^{6} \) |
$4.26403$ |
$(-a), (a-1), (a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.137819795$ |
0.664867708 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 7528 a - 15593\) , \( -493230 a + 549059\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(7528a-15593\right){x}-493230a+549059$ |
| 45369.4-a7 |
45369.4-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
45369.4 |
\( 3^{2} \cdot 71^{2} \) |
\( 3^{9} \cdot 71^{6} \) |
$4.32538$ |
$(-a), (a-1), (-5a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.235324746$ |
0.283812322 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -1593 a + 6071\) , \( -81345 a - 68971\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-1593a+6071\right){x}-81345a-68971$ |
| 45369.6-a7 |
45369.6-a |
$8$ |
$20$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
45369.6 |
\( 3^{2} \cdot 71^{2} \) |
\( 3^{9} \cdot 71^{6} \) |
$4.32538$ |
$(-a), (a-1), (5a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.235324746$ |
0.283812322 |
\( \frac{54238838797}{243} a + \frac{1331574640}{9} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 886 a + 5272\) , \( -99807 a + 110753\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(886a+5272\right){x}-99807a+110753$ |
*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.
