| 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 |
| 3468.1-a1 |
3468.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3468.1 |
\( 2^{2} \cdot 3 \cdot 17^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 17^{4} \) |
$1.18773$ |
$(-2a+1), (2), (17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.286507785$ |
$2.302301329$ |
1.523343895 |
\( \frac{46268279}{46818} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 8\) , \( 10\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+8{x}+10$ |
| 3468.1-a2 |
3468.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3468.1 |
\( 2^{2} \cdot 3 \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 17^{2} \) |
$1.18773$ |
$(-2a+1), (2), (17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.143253892$ |
$4.604602658$ |
1.523343895 |
\( \frac{1771561}{612} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -2\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-2{x}$ |
| 3468.1-b1 |
3468.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3468.1 |
\( 2^{2} \cdot 3 \cdot 17^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 17^{16} \) |
$1.18773$ |
$(-2a+1), (2), (17)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.183754147$ |
1.697448101 |
\( -\frac{491411892194497}{125563633938} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -1644\) , \( -30942\bigr] \) |
${y}^2+{x}{y}={x}^{3}-1644{x}-30942$ |
| 3468.1-b2 |
3468.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3468.1 |
\( 2^{2} \cdot 3 \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{32} \cdot 17^{2} \) |
$1.18773$ |
$(-2a+1), (2), (17)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.367508294$ |
1.697448101 |
\( \frac{1276229915423}{2927177028} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 226\) , \( -2232\bigr] \) |
${y}^2+{x}{y}={x}^{3}+226{x}-2232$ |
| 3468.1-b3 |
3468.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3468.1 |
\( 2^{2} \cdot 3 \cdot 17^{2} \) |
\( 2^{8} \cdot 3^{16} \cdot 17^{4} \) |
$1.18773$ |
$(-2a+1), (2), (17)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.735016588$ |
1.697448101 |
\( \frac{163936758817}{30338064} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -114\) , \( -396\bigr] \) |
${y}^2+{x}{y}={x}^{3}-114{x}-396$ |
| 3468.1-b4 |
3468.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3468.1 |
\( 2^{2} \cdot 3 \cdot 17^{2} \) |
\( 2^{16} \cdot 3^{8} \cdot 17^{2} \) |
$1.18773$ |
$(-2a+1), (2), (17)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$1.470033177$ |
1.697448101 |
\( \frac{4354703137}{352512} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( 68\bigr] \) |
${y}^2+{x}{y}={x}^{3}-34{x}+68$ |
| 3468.1-b5 |
3468.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3468.1 |
\( 2^{2} \cdot 3 \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{8} \cdot 17^{8} \) |
$1.18773$ |
$(-2a+1), (2), (17)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.367508294$ |
1.697448101 |
\( \frac{576615941610337}{27060804} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -1734\) , \( -27936\bigr] \) |
${y}^2+{x}{y}={x}^{3}-1734{x}-27936$ |
| 3468.1-b6 |
3468.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3468.1 |
\( 2^{2} \cdot 3 \cdot 17^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 17^{4} \) |
$1.18773$ |
$(-2a+1), (2), (17)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.183754147$ |
1.697448101 |
\( \frac{2361739090258884097}{5202} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -27744\) , \( -1781010\bigr] \) |
${y}^2+{x}{y}={x}^{3}-27744{x}-1781010$ |
| 3468.1-c1 |
3468.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3468.1 |
\( 2^{2} \cdot 3 \cdot 17^{2} \) |
\( 2^{6} \cdot 3^{24} \cdot 17^{4} \) |
$1.18773$ |
$(-2a+1), (2), (17)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.415867934$ |
1.920811713 |
\( -\frac{1107111813625}{1228691592} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( 215 a\) , \( 2062\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+215a{x}+2062$ |
| 3468.1-c2 |
3468.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3468.1 |
\( 2^{2} \cdot 3 \cdot 17^{2} \) |
\( 2^{18} \cdot 3^{8} \cdot 17^{12} \) |
$1.18773$ |
$(-2a+1), (2), (17)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{4} \cdot 3^{3} \) |
$1$ |
$0.138622644$ |
1.920811713 |
\( \frac{655215969476375}{1001033261568} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( -1810 a\) , \( -37790\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-1810a{x}-37790$ |
| 3468.1-c3 |
3468.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3468.1 |
\( 2^{2} \cdot 3 \cdot 17^{2} \) |
\( 2^{36} \cdot 3^{4} \cdot 17^{6} \) |
$1.18773$ |
$(-2a+1), (2), (17)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{3} \cdot 3^{3} \) |
$1$ |
$0.277245289$ |
1.920811713 |
\( \frac{46753267515625}{11591221248} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( 750 a\) , \( -6046\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+750a{x}-6046$ |
| 3468.1-c4 |
3468.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3468.1 |
\( 2^{2} \cdot 3 \cdot 17^{2} \) |
\( 2^{12} \cdot 3^{12} \cdot 17^{2} \) |
$1.18773$ |
$(-2a+1), (2), (17)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.831735869$ |
1.920811713 |
\( \frac{1845026709625}{793152} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( 255 a\) , \( 1550\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+255a{x}+1550$ |
*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.
