| 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 |
| 32193.5-a1 |
32193.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32193.5 |
\( 3^{2} \cdot 7^{2} \cdot 73 \) |
\( 3^{8} \cdot 7^{8} \cdot 73^{4} \) |
$2.07319$ |
$(-2a+1), (3a-2), (-9a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.264821161$ |
1.223156549 |
\( \frac{1339415391745625}{1391513809} a - \frac{6545681222547619}{4174541427} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -731 a + 2620\) , \( 46280 a - 6624\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-731a+2620\right){x}+46280a-6624$ |
| 32193.5-a2 |
32193.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32193.5 |
\( 3^{2} \cdot 7^{2} \cdot 73 \) |
\( 3^{8} \cdot 7^{8} \cdot 73 \) |
$2.07319$ |
$(-2a+1), (3a-2), (-9a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.059284644$ |
1.223156549 |
\( \frac{46553449}{3577} a - \frac{401971211}{10731} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 64 a + 25\) , \( -154 a + 315\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(64a+25\right){x}-154a+315$ |
| 32193.5-a3 |
32193.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32193.5 |
\( 3^{2} \cdot 7^{2} \cdot 73 \) |
\( 3^{14} \cdot 7^{14} \cdot 73 \) |
$2.07319$ |
$(-2a+1), (3a-2), (-9a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.264821161$ |
1.223156549 |
\( \frac{39237205025653}{11362422771} a - \frac{1344304613447}{34087268313} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -491 a - 410\) , \( 8426 a - 624\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-491a-410\right){x}+8426a-624$ |
| 32193.5-a4 |
32193.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32193.5 |
\( 3^{2} \cdot 7^{2} \cdot 73 \) |
\( 3^{7} \cdot 7^{7} \cdot 73^{8} \) |
$2.07319$ |
$(-2a+1), (3a-2), (-9a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.132410580$ |
1.223156549 |
\( \frac{18382515174811826875}{16935661929775701} a + \frac{10473186429137814628}{16935661929775701} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -1286 a + 2920\) , \( 48875 a - 26799\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1286a+2920\right){x}+48875a-26799$ |
| 32193.5-a5 |
32193.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32193.5 |
\( 3^{2} \cdot 7^{2} \cdot 73 \) |
\( 3^{10} \cdot 7^{10} \cdot 73^{2} \) |
$2.07319$ |
$(-2a+1), (3a-2), (-9a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.529642322$ |
1.223156549 |
\( -\frac{42509139235}{38384787} a + \frac{98538030496}{115154361} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -11 a + 145\) , \( 695 a + 162\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-11a+145\right){x}+695a+162$ |
| 32193.5-a6 |
32193.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32193.5 |
\( 3^{2} \cdot 7^{2} \cdot 73 \) |
\( 3^{7} \cdot 7^{7} \cdot 73^{2} \) |
$2.07319$ |
$(-2a+1), (3a-2), (-9a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$1$ |
$0.132410580$ |
1.223156549 |
\( -\frac{234281345534853355}{111909} a + \frac{171717196547780204}{111909} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -11696 a + 41920\) , \( 2956625 a - 378273\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-11696a+41920\right){x}+2956625a-378273$ |
| 32193.5-b1 |
32193.5-b |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32193.5 |
\( 3^{2} \cdot 7^{2} \cdot 73 \) |
\( 3^{6} \cdot 7^{6} \cdot 73^{3} \) |
$2.07319$ |
$(-2a+1), (3a-2), (-9a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.707535304$ |
2.450974190 |
\( \frac{60988685561}{389017} a - \frac{169775626841}{389017} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -309 a + 204\) , \( 869 a - 2009\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-309a+204\right){x}+869a-2009$ |
| 32193.5-b2 |
32193.5-b |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32193.5 |
\( 3^{2} \cdot 7^{2} \cdot 73 \) |
\( 3^{6} \cdot 7^{6} \cdot 73^{2} \) |
$2.07319$ |
$(-2a+1), (3a-2), (-9a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$1.061302956$ |
2.450974190 |
\( -\frac{927841113}{5329} a - \frac{395933743}{5329} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 81 a - 126\) , \( 497 a - 473\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(81a-126\right){x}+497a-473$ |
| 32193.5-b3 |
32193.5-b |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32193.5 |
\( 3^{2} \cdot 7^{2} \cdot 73 \) |
\( 3^{6} \cdot 7^{6} \cdot 73 \) |
$2.07319$ |
$(-2a+1), (3a-2), (-9a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$2.122605913$ |
2.450974190 |
\( \frac{9927}{73} a + \frac{20960}{73} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 6 a - 6\) , \( 8 a - 14\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(6a-6\right){x}+8a-14$ |
| 32193.5-b4 |
32193.5-b |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32193.5 |
\( 3^{2} \cdot 7^{2} \cdot 73 \) |
\( 3^{6} \cdot 7^{6} \cdot 73^{6} \) |
$2.07319$ |
$(-2a+1), (3a-2), (-9a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.353767652$ |
2.450974190 |
\( -\frac{55816089234767}{151334226289} a + \frac{107352826006104}{151334226289} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -264 a + 279\) , \( 2393 a - 2360\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-264a+279\right){x}+2393a-2360$ |
*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.
