| 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 |
| 5202.2-a1 |
5202.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5202.2 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 17^{4} \) |
$1.51779$ |
$(a+1), (a+4), (a-4), (3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.021206807$ |
$2.302301329$ |
1.562382724 |
\( \frac{46268279}{46818} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 8\) , \( 10\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+8{x}+10$ |
| 5202.2-a2 |
5202.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5202.2 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 17^{2} \) |
$1.51779$ |
$(a+1), (a+4), (a-4), (3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.084827228$ |
$4.604602658$ |
1.562382724 |
\( \frac{1771561}{612} \) |
\( \bigl[i\) , \( -1\) , \( 0\) , \( -2\) , \( 0\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-{x}^{2}-2{x}$ |
| 5202.2-b1 |
5202.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5202.2 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2 \cdot 3^{2} \cdot 17^{7} \) |
$1.51779$ |
$(a+1), (a+4), (a-4), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.578067282$ |
$0.509184076$ |
1.766055929 |
\( -\frac{1979660058649925}{501126} a - \frac{547309863864799}{167042} \) |
\( \bigl[i\) , \( -i\) , \( 0\) , \( 1584 i + 80\) , \( 15675 i + 18965\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-i{x}^{2}+\left(1584i+80\right){x}+15675i+18965$ |
| 5202.2-b2 |
5202.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5202.2 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 17^{8} \) |
$1.51779$ |
$(a+1), (a+4), (a-4), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.289033641$ |
$1.018368152$ |
1.766055929 |
\( \frac{9390341072075}{144825414} a - \frac{6456168132412}{217238121} \) |
\( \bigl[1\) , \( i\) , \( 0\) , \( 99 i + 5\) , \( -240 i - 320\bigr] \) |
${y}^2+{x}{y}={x}^{3}+i{x}^{2}+\left(99i+5\right){x}-240i-320$ |
| 5202.2-b3 |
5202.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5202.2 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2 \cdot 3^{2} \cdot 17^{13} \) |
$1.51779$ |
$(a+1), (a+4), (a-4), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.578067282$ |
$0.509184076$ |
1.766055929 |
\( \frac{461275687224792005}{3495733423378566} a + \frac{140679328163848447}{1165244474459522} \) |
\( \bigl[1\) , \( i\) , \( 0\) , \( 54 i - 70\) , \( -141 i - 971\bigr] \) |
${y}^2+{x}{y}={x}^{3}+i{x}^{2}+\left(54i-70\right){x}-141i-971$ |
| 5202.2-b4 |
5202.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5202.2 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{8} \cdot 17^{4} \) |
$1.51779$ |
$(a+1), (a+4), (a-4), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.144516820$ |
$2.036736304$ |
1.766055929 |
\( -\frac{88739980}{132651} a + \frac{1762314767}{1591812} \) |
\( \bigl[i\) , \( -i\) , \( 0\) , \( 9 i + 5\) , \( 6 i - 4\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-i{x}^{2}+\left(9i+5\right){x}+6i-4$ |
| 5202.2-c1 |
5202.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5202.2 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{6} \cdot 3^{24} \cdot 17^{4} \) |
$1.51779$ |
$(a+1), (a+4), (a-4), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.415867934$ |
1.108981159 |
\( -\frac{1107111813625}{1228691592} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -216\) , \( 2062\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-216{x}+2062$ |
| 5202.2-c2 |
5202.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5202.2 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{18} \cdot 3^{8} \cdot 17^{12} \) |
$1.51779$ |
$(a+1), (a+4), (a-4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{5} \) |
$1$ |
$0.138622644$ |
1.108981159 |
\( \frac{655215969476375}{1001033261568} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 1809\) , \( -37790\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+1809{x}-37790$ |
| 5202.2-c3 |
5202.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5202.2 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{36} \cdot 3^{4} \cdot 17^{6} \) |
$1.51779$ |
$(a+1), (a+4), (a-4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2^{2} \) |
$1$ |
$0.277245289$ |
1.108981159 |
\( \frac{46753267515625}{11591221248} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( -750\) , \( 6046\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-750{x}+6046$ |
| 5202.2-c4 |
5202.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5202.2 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{12} \cdot 3^{12} \cdot 17^{2} \) |
$1.51779$ |
$(a+1), (a+4), (a-4), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.831735869$ |
1.108981159 |
\( \frac{1845026709625}{793152} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( -255\) , \( -1550\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-255{x}-1550$ |
| 5202.2-d1 |
5202.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5202.2 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2 \cdot 3^{2} \cdot 17^{7} \) |
$1.51779$ |
$(a+1), (a+4), (a-4), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.578067282$ |
$0.509184076$ |
1.766055929 |
\( \frac{1979660058649925}{501126} a - \frac{547309863864799}{167042} \) |
\( \bigl[i\) , \( i\) , \( 0\) , \( -1584 i + 80\) , \( -15675 i + 18965\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+i{x}^{2}+\left(-1584i+80\right){x}-15675i+18965$ |
| 5202.2-d2 |
5202.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5202.2 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 17^{8} \) |
$1.51779$ |
$(a+1), (a+4), (a-4), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.289033641$ |
$1.018368152$ |
1.766055929 |
\( -\frac{9390341072075}{144825414} a - \frac{6456168132412}{217238121} \) |
\( \bigl[1\) , \( -i\) , \( 0\) , \( -99 i + 5\) , \( 240 i - 320\bigr] \) |
${y}^2+{x}{y}={x}^{3}-i{x}^{2}+\left(-99i+5\right){x}+240i-320$ |
| 5202.2-d3 |
5202.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5202.2 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2 \cdot 3^{2} \cdot 17^{13} \) |
$1.51779$ |
$(a+1), (a+4), (a-4), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.578067282$ |
$0.509184076$ |
1.766055929 |
\( -\frac{461275687224792005}{3495733423378566} a + \frac{140679328163848447}{1165244474459522} \) |
\( \bigl[1\) , \( -i\) , \( 0\) , \( -54 i - 70\) , \( 141 i - 971\bigr] \) |
${y}^2+{x}{y}={x}^{3}-i{x}^{2}+\left(-54i-70\right){x}+141i-971$ |
| 5202.2-d4 |
5202.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5202.2 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{8} \cdot 17^{4} \) |
$1.51779$ |
$(a+1), (a+4), (a-4), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.144516820$ |
$2.036736304$ |
1.766055929 |
\( \frac{88739980}{132651} a + \frac{1762314767}{1591812} \) |
\( \bigl[i\) , \( i\) , \( 0\) , \( -9 i + 5\) , \( -6 i - 4\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+i{x}^{2}+\left(-9i+5\right){x}-6i-4$ |
| 5202.2-e1 |
5202.2-e |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5202.2 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 17^{16} \) |
$1.51779$ |
$(a+1), (a+4), (a-4), (3)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$1.913490884$ |
$0.183754147$ |
2.812895085 |
\( -\frac{491411892194497}{125563633938} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -1644\) , \( 30942\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-1644{x}+30942$ |
| 5202.2-e2 |
5202.2-e |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5202.2 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{32} \cdot 17^{2} \) |
$1.51779$ |
$(a+1), (a+4), (a-4), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.956745442$ |
$0.367508294$ |
2.812895085 |
\( \frac{1276229915423}{2927177028} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( 226\) , \( 2232\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+226{x}+2232$ |
| 5202.2-e3 |
5202.2-e |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5202.2 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 3^{16} \cdot 17^{4} \) |
$1.51779$ |
$(a+1), (a+4), (a-4), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$0.478372721$ |
$0.735016588$ |
2.812895085 |
\( \frac{163936758817}{30338064} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -114\) , \( 396\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-114{x}+396$ |
| 5202.2-e4 |
5202.2-e |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5202.2 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{16} \cdot 3^{8} \cdot 17^{2} \) |
$1.51779$ |
$(a+1), (a+4), (a-4), (3)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.956745442$ |
$1.470033177$ |
2.812895085 |
\( \frac{4354703137}{352512} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( 68\bigr] \) |
${y}^2+{x}{y}={x}^{3}-34{x}+68$ |
| 5202.2-e5 |
5202.2-e |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5202.2 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{8} \cdot 17^{8} \) |
$1.51779$ |
$(a+1), (a+4), (a-4), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$0.956745442$ |
$0.367508294$ |
2.812895085 |
\( \frac{576615941610337}{27060804} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -1734\) , \( -27936\bigr] \) |
${y}^2+{x}{y}={x}^{3}-1734{x}-27936$ |
| 5202.2-e6 |
5202.2-e |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5202.2 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 17^{4} \) |
$1.51779$ |
$(a+1), (a+4), (a-4), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1.913490884$ |
$0.183754147$ |
2.812895085 |
\( \frac{2361739090258884097}{5202} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -27744\) , \( -1781010\bigr] \) |
${y}^2+{x}{y}={x}^{3}-27744{x}-1781010$ |
*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.
