| 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 |
| 16.1-a1 |
16.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$0.61910$ |
$(a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$17.69503190$ |
0.638514464 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1\) , \( -3 a - 5\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+{x}-3a-5$ |
| 16.1-a2 |
16.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$0.61910$ |
$(a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$17.69503190$ |
0.638514464 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 1\) , \( 3 a + 5\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+{x}+3a+5$ |
| 36.1-a1 |
36.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{6} \) |
$0.75824$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$5.898343969$ |
0.851352619 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -1\bigr] \) |
${y}^2={x}^{3}-1$ |
| 36.1-a2 |
36.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{6} \) |
$0.75824$ |
$(a+1), (a)$ |
0 |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$17.69503190$ |
0.851352619 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 1\bigr] \) |
${y}^2={x}^{3}+1$ |
| 81.1-a3 |
81.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
81.1 |
\( 3^{4} \) |
\( 3^{6} \) |
$0.92865$ |
$(a)$ |
0 |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$28.08911226$ |
0.900958696 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}$ |
| 81.1-a4 |
81.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
81.1 |
\( 3^{4} \) |
\( 3^{6} \) |
$0.92865$ |
$(a)$ |
0 |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$1$ |
$9.363037422$ |
0.900958696 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( -1\bigr] \) |
${y}^2+a{y}={x}^{3}-1$ |
| 121.2-b1 |
121.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
121.2 |
\( 11^{2} \) |
\( 11^{2} \) |
$1.02666$ |
$(-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.064951758$ |
$32.62369841$ |
1.223385920 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( 1\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+{x}$ |
| 121.2-b2 |
121.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
121.2 |
\( 11^{2} \) |
\( 11^{2} \) |
$1.02666$ |
$(-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.194855274$ |
$10.87456613$ |
1.223385920 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( a\) , \( 1\) , \( -1\bigr] \) |
${y}^2+a{y}={x}^{3}+a{x}^{2}+{x}-1$ |
| 121.3-b1 |
121.3-b |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
121.3 |
\( 11^{2} \) |
\( 11^{2} \) |
$1.02666$ |
$(2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.194855274$ |
$10.87456613$ |
1.223385920 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( a\) , \( 1\) , \( -1\bigr] \) |
${y}^2+a{y}={x}^{3}-a{x}^{2}+{x}-1$ |
| 121.3-b2 |
121.3-b |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
121.3 |
\( 11^{2} \) |
\( 11^{2} \) |
$1.02666$ |
$(2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.064951758$ |
$32.62369841$ |
1.223385920 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( 1\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+{x}$ |
| 169.2-a1 |
169.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
169.2 |
\( 13^{2} \) |
\( 13^{10} \) |
$1.11609$ |
$(a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$3.313232303$ |
0.956447781 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( 1\) , \( 162 a + 279\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+{x}+162a+279$ |
| 169.2-a2 |
169.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
169.2 |
\( 13^{2} \) |
\( 13^{10} \) |
$1.11609$ |
$(a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$3.313232303$ |
0.956447781 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( a\) , \( 1\) , \( -162 a - 280\bigr] \) |
${y}^2+a{y}={x}^{3}+a{x}^{2}+{x}-162a-280$ |
| 169.3-a1 |
169.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
169.3 |
\( 13^{2} \) |
\( 13^{10} \) |
$1.11609$ |
$(a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$3.313232303$ |
0.956447781 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( a\) , \( 1\) , \( 162 a - 280\bigr] \) |
${y}^2+a{y}={x}^{3}-a{x}^{2}+{x}+162a-280$ |
| 169.3-a2 |
169.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
169.3 |
\( 13^{2} \) |
\( 13^{10} \) |
$1.11609$ |
$(a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$3.313232303$ |
0.956447781 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( 1\) , \( -162 a + 279\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+{x}-162a+279$ |
| 256.1-c1 |
256.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{8} \) |
$1.23820$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$17.69503190$ |
1.277028929 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+{x}$ |
| 256.1-c2 |
256.1-c |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{8} \) |
$1.23820$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$17.69503190$ |
1.277028929 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+{x}$ |
| 324.1-a1 |
324.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{4} \cdot 3^{6} \) |
$1.31330$ |
$(a+1), (a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$0.450320685$ |
$7.431447726$ |
1.932122672 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( -8 a - 14\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-8a-14$ |
| 324.1-a2 |
324.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{4} \cdot 3^{6} \) |
$1.31330$ |
$(a+1), (a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$0.150106895$ |
$22.29434318$ |
1.932122672 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( 7 a + 12\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+7a+12$ |
| 484.2-a1 |
484.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
484.2 |
\( 2^{2} \cdot 11^{2} \) |
\( 2^{4} \cdot 11^{10} \) |
$1.45191$ |
$(a+1), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$5.235137245$ |
1.511253948 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( a + 1\) , \( 1\) , \( 31 a + 66\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+{x}+31a+66$ |
| 484.2-a2 |
484.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
484.2 |
\( 2^{2} \cdot 11^{2} \) |
\( 2^{4} \cdot 11^{10} \) |
$1.45191$ |
$(a+1), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$1$ |
$1.745045748$ |
1.511253948 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( a + 1\) , \( 1\) , \( -32 a - 68\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+a{x}^{2}+{x}-32a-68$ |
| 484.2-c1 |
484.2-c |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
484.2 |
\( 2^{2} \cdot 11^{2} \) |
\( 2^{8} \cdot 11^{6} \) |
$1.45191$ |
$(a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$9.240929030$ |
1.333813215 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1\) , \( 43 a + 75\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+{x}+43a+75$ |
| 484.2-c2 |
484.2-c |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
484.2 |
\( 2^{2} \cdot 11^{2} \) |
\( 2^{8} \cdot 11^{6} \) |
$1.45191$ |
$(a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$3.080309676$ |
1.333813215 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 1\) , \( -43 a - 75\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+{x}-43a-75$ |
| 484.3-a1 |
484.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
484.3 |
\( 2^{2} \cdot 11^{2} \) |
\( 2^{4} \cdot 11^{10} \) |
$1.45191$ |
$(a+1), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$5.235137245$ |
1.511253948 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( a + 1\) , \( 1\) , \( -32 a + 66\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+a{x}^{2}+{x}-32a+66$ |
| 484.3-a2 |
484.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
484.3 |
\( 2^{2} \cdot 11^{2} \) |
\( 2^{4} \cdot 11^{10} \) |
$1.45191$ |
$(a+1), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$1$ |
$1.745045748$ |
1.511253948 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( a + 1\) , \( 1\) , \( 31 a - 68\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+{x}+31a-68$ |
| 484.3-c1 |
484.3-c |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
484.3 |
\( 2^{2} \cdot 11^{2} \) |
\( 2^{8} \cdot 11^{6} \) |
$1.45191$ |
$(a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$9.240929030$ |
1.333813215 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 1\) , \( -43 a + 75\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+{x}-43a+75$ |
| 484.3-c2 |
484.3-c |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
484.3 |
\( 2^{2} \cdot 11^{2} \) |
\( 2^{8} \cdot 11^{6} \) |
$1.45191$ |
$(a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$3.080309676$ |
1.333813215 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1\) , \( 43 a - 75\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+{x}+43a-75$ |
| 676.2-a1 |
676.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
676.2 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 13^{6} \) |
$1.57840$ |
$(a+1), (a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.845874701$ |
$4.907718835$ |
2.396762951 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 1\) , \( -11 a + 17\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+{x}-11a+17$ |
| 676.2-a2 |
676.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
676.2 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 13^{6} \) |
$1.57840$ |
$(a+1), (a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.281958233$ |
$4.907718835$ |
2.396762951 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1\) , \( 11 a - 17\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+{x}+11a-17$ |
| 676.2-b1 |
676.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
676.2 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 13^{2} \) |
$1.57840$ |
$(a+1), (a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.283132464$ |
$14.53909775$ |
2.376656948 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( a + 1\) , \( 1\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+a{x}^{2}+{x}-a$ |
| 676.2-b2 |
676.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
676.2 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 13^{2} \) |
$1.57840$ |
$(a+1), (a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$0.094377488$ |
$14.53909775$ |
2.376656948 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( a + 1\) , \( 1\) , \( -2\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+{x}-2$ |
| 676.3-a1 |
676.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
676.3 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 13^{6} \) |
$1.57840$ |
$(a+1), (a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.845874701$ |
$4.907718835$ |
2.396762951 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1\) , \( 11 a + 17\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+{x}+11a+17$ |
| 676.3-a2 |
676.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
676.3 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 13^{6} \) |
$1.57840$ |
$(a+1), (a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.281958233$ |
$4.907718835$ |
2.396762951 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 1\) , \( -11 a - 17\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+{x}-11a-17$ |
| 676.3-b1 |
676.3-b |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
676.3 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 13^{2} \) |
$1.57840$ |
$(a+1), (a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.283132464$ |
$14.53909775$ |
2.376656948 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( a + 1\) , \( 1\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+{x}$ |
| 676.3-b2 |
676.3-b |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
676.3 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 13^{2} \) |
$1.57840$ |
$(a+1), (a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$0.094377488$ |
$14.53909775$ |
2.376656948 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( a + 1\) , \( 1\) , \( -a - 2\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+a{x}^{2}+{x}-a-2$ |
| 729.1-a1 |
729.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
729.1 |
\( 3^{6} \) |
\( 3^{6} \) |
$1.60846$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$0.390898611$ |
$9.363037422$ |
2.113101017 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -a - 2\bigr] \) |
${y}^2+{y}={x}^{3}-a-2$ |
| 729.1-a2 |
729.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
729.1 |
\( 3^{6} \) |
\( 3^{6} \) |
$1.60846$ |
$(a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1.172695833$ |
$28.08911226$ |
2.113101017 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( a + 1\bigr] \) |
${y}^2+a{y}={x}^{3}+a+1$ |
| 729.1-b1 |
729.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
729.1 |
\( 3^{6} \) |
\( 3^{6} \) |
$1.60846$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$0.390898611$ |
$9.363037422$ |
2.113101017 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( a - 2\bigr] \) |
${y}^2+{y}={x}^{3}+a-2$ |
| 729.1-b2 |
729.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
729.1 |
\( 3^{6} \) |
\( 3^{6} \) |
$1.60846$ |
$(a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1.172695833$ |
$28.08911226$ |
2.113101017 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( -a + 1\bigr] \) |
${y}^2+a{y}={x}^{3}-a+1$ |
| 1024.1-j1 |
1024.1-j |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{14} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.429957487$ |
$21.67189957$ |
2.689873605 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1\) , \( a + 2\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+{x}+a+2$ |
| 1024.1-j2 |
1024.1-j |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{14} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.289872463$ |
$7.223966526$ |
2.689873605 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 1\) , \( -a - 2\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+{x}-a-2$ |
| 1024.1-k1 |
1024.1-k |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{14} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.289872463$ |
$7.223966526$ |
2.689873605 |
\( 0 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1\) , \( a - 2\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+{x}+a-2$ |
| 1024.1-k2 |
1024.1-k |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{14} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.429957487$ |
$21.67189957$ |
2.689873605 |
\( 0 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 1\) , \( -a + 2\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+{x}-a+2$ |
| 1089.2-c1 |
1089.2-c |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1089.2 |
\( 3^{2} \cdot 11^{2} \) |
\( 3^{6} \cdot 11^{8} \) |
$1.77822$ |
$(a), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$1.893018983$ |
1.092935019 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 399 a - 692\bigr] \) |
${y}^2+{y}={x}^{3}+399a-692$ |
| 1089.2-c2 |
1089.2-c |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1089.2 |
\( 3^{2} \cdot 11^{2} \) |
\( 3^{6} \cdot 11^{8} \) |
$1.77822$ |
$(a), (-2a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$5.679056949$ |
1.092935019 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( -399 a + 691\bigr] \) |
${y}^2+a{y}={x}^{3}-399a+691$ |
| 1089.3-c1 |
1089.3-c |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1089.3 |
\( 3^{2} \cdot 11^{2} \) |
\( 3^{6} \cdot 11^{8} \) |
$1.77822$ |
$(a), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$1.893018983$ |
1.092935019 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -399 a - 692\bigr] \) |
${y}^2+{y}={x}^{3}-399a-692$ |
| 1089.3-c2 |
1089.3-c |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1089.3 |
\( 3^{2} \cdot 11^{2} \) |
\( 3^{6} \cdot 11^{8} \) |
$1.77822$ |
$(a), (2a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$5.679056949$ |
1.092935019 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( 399 a + 691\bigr] \) |
${y}^2+a{y}={x}^{3}+399a+691$ |
| 1296.1-d1 |
1296.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1296.1 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{4} \cdot 3^{12} \) |
$1.85729$ |
$(a+1), (a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$7.431447726$ |
2.145274172 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( -2 a - 1\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-2a-1$ |
| 1296.1-d2 |
1296.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1296.1 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{4} \cdot 3^{12} \) |
$1.85729$ |
$(a+1), (a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$7.431447726$ |
2.145274172 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( a - 1\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+a-1$ |
| 1296.1-e3 |
1296.1-e |
$4$ |
$27$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1296.1 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{12} \) |
$1.85729$ |
$(a+1), (a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 1 \) |
$1$ |
$4.681518711$ |
1.351438044 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -6 a\bigr] \) |
${y}^2={x}^{3}-6a$ |
| 1296.1-e4 |
1296.1-e |
$4$ |
$27$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1296.1 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{12} \) |
$1.85729$ |
$(a+1), (a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 1 \) |
$1$ |
$4.681518711$ |
1.351438044 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 6 a\bigr] \) |
${y}^2={x}^{3}+6a$ |
*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.
