| 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 |
| 72.1-a5 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$0.52060$ |
$(a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.635347017$ |
0.454418377 |
\( \frac{28756228}{3} \) |
\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -i + 16\) , \( -28 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-i{x}^{2}+\left(-i+16\right){x}-28i$ |
| 648.1-a5 |
648.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
648.1 |
\( 2^{3} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{14} \) |
$0.90170$ |
$(a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.211782339$ |
1.211782339 |
\( \frac{28756228}{3} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 144\) , \( -598 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+144{x}-598i$ |
| 2304.1-c5 |
2304.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{2} \) |
$1.23820$ |
$(a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.817673508$ |
1.817673508 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( 64\) , \( -220 i\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+64{x}-220i$ |
| 3600.1-c5 |
3600.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
3600.1 |
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 5^{6} \) |
$1.38434$ |
$(a+1), (-a-2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.625776610$ |
1.625776610 |
\( \frac{28756228}{3} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( -65 i - 48\) , \( 302 i + 55\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-65i-48\right){x}+302i+55$ |
| 3600.3-c5 |
3600.3-c |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
3600.3 |
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 5^{6} \) |
$1.38434$ |
$(a+1), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.625776610$ |
1.625776610 |
\( \frac{28756228}{3} \) |
\( \bigl[i + 1\) , \( -1\) , \( i + 1\) , \( 63 i - 48\) , \( -303 i + 55\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(63i-48\right){x}-303i+55$ |
| 9216.1-c5 |
9216.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
9216.1 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{26} \cdot 3^{2} \) |
$1.75107$ |
$(a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.141888207$ |
$1.285289264$ |
2.752945917 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( -128 i\) , \( -440 i + 440\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}-128i{x}-440i+440$ |
| 9216.1-j5 |
9216.1-j |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
9216.1 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{26} \cdot 3^{2} \) |
$1.75107$ |
$(a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.141888207$ |
$1.285289264$ |
2.752945917 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 128 i\) , \( 440 i + 440\bigr] \) |
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+128i{x}+440i+440$ |
| 20736.1-b5 |
20736.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
20736.1 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{20} \cdot 3^{14} \) |
$2.14462$ |
$(a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.539636932$ |
$0.605891169$ |
2.615690016 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 579\) , \( 5362 i\bigr] \) |
${y}^2={x}^{3}+579{x}+5362i$ |
| 20808.1-a5 |
20808.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
20808.1 |
\( 2^{3} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 17^{6} \) |
$2.14648$ |
$(a+1), (a+4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.881701161$ |
1.763402322 |
\( \frac{28756228}{3} \) |
\( \bigl[i + 1\) , \( -1\) , \( 0\) , \( -129 i - 241\) , \( -1164 i - 1189\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-129i-241\right){x}-1164i-1189$ |
| 20808.3-a5 |
20808.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
20808.3 |
\( 2^{3} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 17^{6} \) |
$2.14648$ |
$(a+1), (a-4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.881701161$ |
1.763402322 |
\( \frac{28756228}{3} \) |
\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( 129 i - 241\) , \( -1164 i + 1189\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(129i-241\right){x}-1164i+1189$ |
| 24336.1-a5 |
24336.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
24336.1 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 13^{6} \) |
$2.23219$ |
$(a+1), (-3a-2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.899714244$ |
$1.008263852$ |
3.628597400 |
\( \frac{28756228}{3} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( i + 1\) , \( -193 i + 80\) , \( -248 i + 1265\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-193i+80\right){x}-248i+1265$ |
| 24336.3-a5 |
24336.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
24336.3 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 13^{6} \) |
$2.23219$ |
$(a+1), (2a+3), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.899714244$ |
$1.008263852$ |
3.628597400 |
\( \frac{28756228}{3} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( 194 i + 80\) , \( 328 i + 1072\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(194i+80\right){x}+328i+1072$ |
| 32400.1-b5 |
32400.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
32400.1 |
\( 2^{4} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{14} \cdot 5^{6} \) |
$2.39775$ |
$(a+1), (-a-2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.541925536$ |
1.083851073 |
\( \frac{28756228}{3} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -580 i - 435\) , \( 7155 i + 1630\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-580i-435\right){x}+7155i+1630$ |
| 32400.3-b5 |
32400.3-b |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
32400.3 |
\( 2^{4} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{14} \cdot 5^{6} \) |
$2.39775$ |
$(a+1), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.541925536$ |
1.083851073 |
\( \frac{28756228}{3} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 579 i - 435\) , \( -7590 i + 1051\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(579i-435\right){x}-7590i+1051$ |
| 45000.3-k5 |
45000.3-k |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
45000.3 |
\( 2^{3} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{8} \cdot 3^{2} \cdot 5^{12} \) |
$2.60299$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.748483442$ |
$0.727069403$ |
4.353595283 |
\( \frac{28756228}{3} \) |
\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 402\) , \( 3036 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}+402{x}+3036i$ |
| 57600.1-d5 |
57600.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{2} \cdot 5^{6} \) |
$2.76869$ |
$(a+1), (-a-2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.062418350$ |
$0.812888305$ |
3.454509811 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( -258 i - 193\) , \( 2163 i + 247\bigr] \) |
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(-258i-193\right){x}+2163i+247$ |
| 57600.3-d5 |
57600.3-d |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
57600.3 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{2} \cdot 5^{6} \) |
$2.76869$ |
$(a+1), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.062418350$ |
$0.812888305$ |
3.454509811 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( 258 i - 193\) , \( 2163 i - 247\bigr] \) |
${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(258i-193\right){x}+2163i-247$ |
| 82944.1-g5 |
82944.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
82944.1 |
\( 2^{10} \cdot 3^{4} \) |
\( 2^{26} \cdot 3^{14} \) |
$3.03295$ |
$(a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$5.550999615$ |
$0.428429754$ |
4.756426807 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1158 i\) , \( -10724 i - 10724\bigr] \) |
${y}^2={x}^{3}+1158i{x}-10724i-10724$ |
| 82944.1-n5 |
82944.1-n |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
82944.1 |
\( 2^{10} \cdot 3^{4} \) |
\( 2^{26} \cdot 3^{14} \) |
$3.03295$ |
$(a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$5.550999615$ |
$0.428429754$ |
4.756426807 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1158 i\) , \( 10724 i - 10724\bigr] \) |
${y}^2={x}^{3}-1158i{x}+10724i-10724$ |
*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.
