| 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 |
| 1734.1-a1 |
1734.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1734.1 |
\( 2 \cdot 3 \cdot 17^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 17^{4} \) |
$1.99752$ |
$(a+1), (a), (17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.286507785$ |
$5.588174083$ |
1.848739513 |
\( \frac{46268279}{46818} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 8\) , \( 10\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+8{x}+10$ |
| 1734.1-a2 |
1734.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1734.1 |
\( 2 \cdot 3 \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 17^{2} \) |
$1.99752$ |
$(a+1), (a), (17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.143253892$ |
$22.35269633$ |
1.848739513 |
\( \frac{1771561}{612} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -2\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-2{x}$ |
| 1734.1-b1 |
1734.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1734.1 |
\( 2 \cdot 3 \cdot 17^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 17^{16} \) |
$1.99752$ |
$(a+1), (a), (17)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.913490884$ |
$0.987006203$ |
2.180799044 |
\( -\frac{491411892194497}{125563633938} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -1644\) , \( 30942\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-1644{x}+30942$ |
| 1734.1-b2 |
1734.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1734.1 |
\( 2 \cdot 3 \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{32} \cdot 17^{2} \) |
$1.99752$ |
$(a+1), (a), (17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.826981769$ |
$0.987006203$ |
2.180799044 |
\( \frac{1276229915423}{2927177028} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 226\) , \( 2232\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+226{x}+2232$ |
| 1734.1-b3 |
1734.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1734.1 |
\( 2 \cdot 3 \cdot 17^{2} \) |
\( 2^{8} \cdot 3^{16} \cdot 17^{4} \) |
$1.99752$ |
$(a+1), (a), (17)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.913490884$ |
$3.948024812$ |
2.180799044 |
\( \frac{163936758817}{30338064} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -114\) , \( 396\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-114{x}+396$ |
| 1734.1-b4 |
1734.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1734.1 |
\( 2 \cdot 3 \cdot 17^{2} \) |
\( 2^{16} \cdot 3^{8} \cdot 17^{2} \) |
$1.99752$ |
$(a+1), (a), (17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.956745442$ |
$3.948024812$ |
2.180799044 |
\( \frac{4354703137}{352512} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -34\) , \( -68\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-34{x}-68$ |
| 1734.1-b5 |
1734.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1734.1 |
\( 2 \cdot 3 \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{8} \cdot 17^{8} \) |
$1.99752$ |
$(a+1), (a), (17)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$3.826981769$ |
$3.948024812$ |
2.180799044 |
\( \frac{576615941610337}{27060804} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -1734\) , \( 27936\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-1734{x}+27936$ |
| 1734.1-b6 |
1734.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1734.1 |
\( 2 \cdot 3 \cdot 17^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 17^{4} \) |
$1.99752$ |
$(a+1), (a), (17)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.913490884$ |
$3.948024812$ |
2.180799044 |
\( \frac{2361739090258884097}{5202} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -27744\) , \( 1781010\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-27744{x}+1781010$ |
| 1734.1-c1 |
1734.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1734.1 |
\( 2 \cdot 3 \cdot 17^{2} \) |
\( 2^{6} \cdot 3^{24} \cdot 17^{4} \) |
$1.99752$ |
$(a+1), (a), (17)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.356490835$ |
2.469840961 |
\( -\frac{1107111813625}{1228691592} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -217\) , \( -2063\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-217{x}-2063$ |
| 1734.1-c2 |
1734.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1734.1 |
\( 2 \cdot 3 \cdot 17^{2} \) |
\( 2^{18} \cdot 3^{8} \cdot 17^{12} \) |
$1.99752$ |
$(a+1), (a), (17)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2^{3} \cdot 3^{3} \) |
$1$ |
$0.356490835$ |
2.469840961 |
\( \frac{655215969476375}{1001033261568} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 1808\) , \( 37789\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+1808{x}+37789$ |
| 1734.1-c3 |
1734.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1734.1 |
\( 2 \cdot 3 \cdot 17^{2} \) |
\( 2^{36} \cdot 3^{4} \cdot 17^{6} \) |
$1.99752$ |
$(a+1), (a), (17)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{3} \) |
$1$ |
$1.425963343$ |
2.469840961 |
\( \frac{46753267515625}{11591221248} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -752\) , \( 6045\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-752{x}+6045$ |
| 1734.1-c4 |
1734.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1734.1 |
\( 2 \cdot 3 \cdot 17^{2} \) |
\( 2^{12} \cdot 3^{12} \cdot 17^{2} \) |
$1.99752$ |
$(a+1), (a), (17)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.425963343$ |
2.469840961 |
\( \frac{1845026709625}{793152} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -257\) , \( -1551\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-257{x}-1551$ |
| 1734.1-d1 |
1734.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1734.1 |
\( 2 \cdot 3 \cdot 17^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 17^{4} \) |
$1.99752$ |
$(a+1), (a), (17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.296073030$ |
$3.794149094$ |
5.188509319 |
\( \frac{46268279}{46818} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 7\) , \( -3\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+7{x}-3$ |
| 1734.1-d2 |
1734.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1734.1 |
\( 2 \cdot 3 \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 17^{2} \) |
$1.99752$ |
$(a+1), (a), (17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.148036515$ |
$15.17659637$ |
5.188509319 |
\( \frac{1771561}{612} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -3\) , \( -3\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-3{x}-3$ |
| 1734.1-e1 |
1734.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1734.1 |
\( 2 \cdot 3 \cdot 17^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 17^{16} \) |
$1.99752$ |
$(a+1), (a), (17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$4.017174891$ |
$0.136840423$ |
5.078021124 |
\( -\frac{491411892194497}{125563633938} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -1644\) , \( -30942\bigr] \) |
${y}^2+{x}{y}={x}^{3}-1644{x}-30942$ |
| 1734.1-e2 |
1734.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1734.1 |
\( 2 \cdot 3 \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{32} \cdot 17^{2} \) |
$1.99752$ |
$(a+1), (a), (17)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$2.008587445$ |
$0.547361692$ |
5.078021124 |
\( \frac{1276229915423}{2927177028} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 226\) , \( -2232\bigr] \) |
${y}^2+{x}{y}={x}^{3}+226{x}-2232$ |
| 1734.1-e3 |
1734.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1734.1 |
\( 2 \cdot 3 \cdot 17^{2} \) |
\( 2^{8} \cdot 3^{16} \cdot 17^{4} \) |
$1.99752$ |
$(a+1), (a), (17)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$1.004293722$ |
$2.189446770$ |
5.078021124 |
\( \frac{163936758817}{30338064} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -114\) , \( -396\bigr] \) |
${y}^2+{x}{y}={x}^{3}-114{x}-396$ |
| 1734.1-e4 |
1734.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1734.1 |
\( 2 \cdot 3 \cdot 17^{2} \) |
\( 2^{16} \cdot 3^{8} \cdot 17^{2} \) |
$1.99752$ |
$(a+1), (a), (17)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$0.502146861$ |
$8.757787080$ |
5.078021124 |
\( \frac{4354703137}{352512} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( 68\bigr] \) |
${y}^2+{x}{y}={x}^{3}-34{x}+68$ |
| 1734.1-e5 |
1734.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1734.1 |
\( 2 \cdot 3 \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{8} \cdot 17^{8} \) |
$1.99752$ |
$(a+1), (a), (17)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$2.008587445$ |
$0.547361692$ |
5.078021124 |
\( \frac{576615941610337}{27060804} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -1734\) , \( -27936\bigr] \) |
${y}^2+{x}{y}={x}^{3}-1734{x}-27936$ |
| 1734.1-e6 |
1734.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1734.1 |
\( 2 \cdot 3 \cdot 17^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 17^{4} \) |
$1.99752$ |
$(a+1), (a), (17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$4.017174891$ |
$0.136840423$ |
5.078021124 |
\( \frac{2361739090258884097}{5202} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -27744\) , \( -1781010\bigr] \) |
${y}^2+{x}{y}={x}^{3}-27744{x}-1781010$ |
| 1734.1-f1 |
1734.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1734.1 |
\( 2 \cdot 3 \cdot 17^{2} \) |
\( 2^{6} \cdot 3^{24} \cdot 17^{4} \) |
$1.99752$ |
$(a+1), (a), (17)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$1.940539524$ |
1.493828022 |
\( -\frac{1107111813625}{1228691592} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -216\) , \( 2062\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-216{x}+2062$ |
| 1734.1-f2 |
1734.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1734.1 |
\( 2 \cdot 3 \cdot 17^{2} \) |
\( 2^{18} \cdot 3^{8} \cdot 17^{12} \) |
$1.99752$ |
$(a+1), (a), (17)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.215615502$ |
1.493828022 |
\( \frac{655215969476375}{1001033261568} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 1809\) , \( -37790\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+1809{x}-37790$ |
| 1734.1-f3 |
1734.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1734.1 |
\( 2 \cdot 3 \cdot 17^{2} \) |
\( 2^{36} \cdot 3^{4} \cdot 17^{6} \) |
$1.99752$ |
$(a+1), (a), (17)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.862462010$ |
1.493828022 |
\( \frac{46753267515625}{11591221248} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -751\) , \( -6046\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-751{x}-6046$ |
| 1734.1-f4 |
1734.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1734.1 |
\( 2 \cdot 3 \cdot 17^{2} \) |
\( 2^{12} \cdot 3^{12} \cdot 17^{2} \) |
$1.99752$ |
$(a+1), (a), (17)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$7.762158097$ |
1.493828022 |
\( \frac{1845026709625}{793152} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -256\) , \( 1550\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-256{x}+1550$ |
*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.
