| 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 |
| 512.1-a3 |
512.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
512.1 |
\( 2^{9} \) |
\( 2^{10} \) |
$0.85013$ |
$(a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$7.841522890$ |
0.980190361 |
\( 128 \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( -i\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}-i{x}$ |
| 512.1-b3 |
512.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
512.1 |
\( 2^{9} \) |
\( 2^{10} \) |
$0.85013$ |
$(a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$7.841522890$ |
0.980190361 |
\( 128 \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( i\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}+i{x}$ |
| 1024.1-a3 |
1024.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{16} \) |
$1.01098$ |
$(a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.432331164$ |
$5.544794010$ |
1.198593625 |
\( 128 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 1\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+{x}+1$ |
| 1024.1-b3 |
1024.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{16} \) |
$1.01098$ |
$(a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$5.544794010$ |
1.386198502 |
\( 128 \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( -1\) , \( -i\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}-{x}-i$ |
| 12800.1-a3 |
12800.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12800.1 |
\( 2^{9} \cdot 5^{2} \) |
\( 2^{10} \cdot 5^{6} \) |
$1.90095$ |
$(a+1), (-a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.763284993$ |
$3.506835645$ |
2.676715022 |
\( 128 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( i - 1\) , \( -2 i - 2\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(i-1\right){x}-2i-2$ |
| 12800.1-c3 |
12800.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12800.1 |
\( 2^{9} \cdot 5^{2} \) |
\( 2^{10} \cdot 5^{6} \) |
$1.90095$ |
$(a+1), (-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$3.506835645$ |
1.753417822 |
\( 128 \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( -i + 1\) , \( 2 i - 2\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+\left(-i+1\right){x}+2i-2$ |
| 12800.3-a3 |
12800.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12800.3 |
\( 2^{9} \cdot 5^{2} \) |
\( 2^{10} \cdot 5^{6} \) |
$1.90095$ |
$(a+1), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.763284993$ |
$3.506835645$ |
2.676715022 |
\( 128 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -i - 1\) , \( 2 i - 2\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-i-1\right){x}+2i-2$ |
| 12800.3-c3 |
12800.3-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12800.3 |
\( 2^{9} \cdot 5^{2} \) |
\( 2^{10} \cdot 5^{6} \) |
$1.90095$ |
$(a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$3.506835645$ |
1.753417822 |
\( 128 \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( i + 1\) , \( -2 i - 2\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+\left(i+1\right){x}-2i-2$ |
| 25600.1-c3 |
25600.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
25600.1 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{6} \) |
$2.26063$ |
$(a+1), (-a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.656314808$ |
$2.479707265$ |
3.254937196 |
\( 128 \) |
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 2 i + 2\) , \( -8 i\bigr] \) |
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(2i+2\right){x}-8i$ |
| 25600.1-l3 |
25600.1-l |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
25600.1 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{6} \) |
$2.26063$ |
$(a+1), (-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.479707265$ |
2.479707265 |
\( 128 \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( -2 i - 2\) , \( -8\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(-2i-2\right){x}-8$ |
| 25600.3-c3 |
25600.3-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
25600.3 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{6} \) |
$2.26063$ |
$(a+1), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.656314808$ |
$2.479707265$ |
3.254937196 |
\( 128 \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( -2 i + 2\) , \( 8 i\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(-2i+2\right){x}+8i$ |
| 25600.3-l3 |
25600.3-l |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
25600.3 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{6} \) |
$2.26063$ |
$(a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.479707265$ |
2.479707265 |
\( 128 \) |
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 2 i - 2\) , \( -8\bigr] \) |
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(2i-2\right){x}-8$ |
| 41472.1-c3 |
41472.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
41472.1 |
\( 2^{9} \cdot 3^{4} \) |
\( 2^{10} \cdot 3^{12} \) |
$2.55039$ |
$(a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.506155953$ |
$2.613840963$ |
3.936852128 |
\( 128 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 3 i\) , \( -5 i + 5\bigr] \) |
${y}^2={x}^{3}+3i{x}-5i+5$ |
| 41472.1-g3 |
41472.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
41472.1 |
\( 2^{9} \cdot 3^{4} \) |
\( 2^{10} \cdot 3^{12} \) |
$2.55039$ |
$(a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.506155953$ |
$2.613840963$ |
3.936852128 |
\( 128 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3 i\) , \( 5 i + 5\bigr] \) |
${y}^2={x}^{3}-3i{x}+5i+5$ |
| 82944.1-e3 |
82944.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
82944.1 |
\( 2^{10} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{12} \) |
$3.03295$ |
$(a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.848264670$ |
1.848264670 |
\( 128 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -6\) , \( 20 i\bigr] \) |
${y}^2={x}^{3}-6{x}+20i$ |
| 82944.1-q3 |
82944.1-q |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
82944.1 |
\( 2^{10} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{12} \) |
$3.03295$ |
$(a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.632943382$ |
$1.848264670$ |
6.036223124 |
\( 128 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 6\) , \( -20\bigr] \) |
${y}^2={x}^{3}+6{x}-20$ |
| 86528.1-a3 |
86528.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
86528.1 |
\( 2^{9} \cdot 13^{2} \) |
\( 2^{10} \cdot 13^{6} \) |
$3.06519$ |
$(a+1), (-3a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$2.174847142$ |
1.087423571 |
\( 128 \) |
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( i + 4\) , \( 6 i + 12\bigr] \) |
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(i+4\right){x}+6i+12$ |
| 86528.1-b3 |
86528.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
86528.1 |
\( 2^{9} \cdot 13^{2} \) |
\( 2^{10} \cdot 13^{6} \) |
$3.06519$ |
$(a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$2.903426639$ |
$2.174847142$ |
6.314509131 |
\( 128 \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( -i - 4\) , \( -12 i + 6\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(-i-4\right){x}-12i+6$ |
| 86528.3-a3 |
86528.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
86528.3 |
\( 2^{9} \cdot 13^{2} \) |
\( 2^{10} \cdot 13^{6} \) |
$3.06519$ |
$(a+1), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$2.174847142$ |
1.087423571 |
\( 128 \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( -i + 4\) , \( -6 i + 12\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(-i+4\right){x}-6i+12$ |
| 86528.3-b3 |
86528.3-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
86528.3 |
\( 2^{9} \cdot 13^{2} \) |
\( 2^{10} \cdot 13^{6} \) |
$3.06519$ |
$(a+1), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$2.903426639$ |
$2.174847142$ |
6.314509131 |
\( 128 \) |
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( i - 4\) , \( 12 i + 6\bigr] \) |
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(i-4\right){x}+12i+6$ |
*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.
