| 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 |
| 1849.1-CMa1 |
1849.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1849.1 |
\( 43^{2} \) |
\( 43^{2} \) |
$1.01492$ |
$(-7a+1)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$43$ |
43Cs.4.1 |
$1$ |
\( 1 \) |
$0.022264396$ |
$7.503489439$ |
0.771620158 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( a\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+a{x}$ |
| 1849.3-CMa1 |
1849.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1849.3 |
\( 43^{2} \) |
\( 43^{2} \) |
$1.01492$ |
$(7a-6)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$43$ |
43Cs.4.1 |
$1$ |
\( 1 \) |
$0.022264396$ |
$7.503489439$ |
0.771620158 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( a\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+a{x}$ |
| 2809.1-a1 |
2809.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2809.1 |
\( 53^{2} \) |
\( 53^{2} \) |
$1.12677$ |
$(53)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.028511600$ |
$7.221736064$ |
0.951026398 |
\( \frac{3375}{53} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}$ |
| 3181.1-a1 |
3181.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3181.1 |
\( 3181 \) |
\( 3181 \) |
$1.16236$ |
$(65a-29)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.030929611$ |
$7.018606294$ |
1.002662332 |
\( -\frac{1696788}{3181} a + \frac{4931523}{3181} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( a - 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(a-1\right){x}$ |
| 3181.2-a1 |
3181.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3181.2 |
\( 3181 \) |
\( 3181 \) |
$1.16236$ |
$(-65a+36)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.030929611$ |
$7.018606294$ |
1.002662332 |
\( \frac{1696788}{3181} a + \frac{3234735}{3181} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -2 a\) , \( -a\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}-2a{x}-a$ |
| 4051.1-a1 |
4051.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
4051.1 |
\( 4051 \) |
\( 4051 \) |
$1.23478$ |
$(66a-61)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.037714393$ |
$6.895240040$ |
1.201118563 |
\( -\frac{1976322}{4051} a + \frac{5231885}{4051} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( a - 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}$ |
| 4051.2-a1 |
4051.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
4051.2 |
\( 4051 \) |
\( 4051 \) |
$1.23478$ |
$(66a-5)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.037714393$ |
$6.895240040$ |
1.201118563 |
\( \frac{1976322}{4051} a + \frac{3255563}{4051} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -a\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}$ |
| 4219.1-a1 |
4219.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
4219.1 |
\( 4219 \) |
\( 4219 \) |
$1.24739$ |
$(-75a+38)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.038700159$ |
$6.824519363$ |
1.219871773 |
\( \frac{3578794}{4219} a - \frac{3130413}{4219} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}$ |
| 4219.2-a1 |
4219.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
4219.2 |
\( 4219 \) |
\( 4219 \) |
$1.24739$ |
$(-75a+37)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.038700159$ |
$6.824519363$ |
1.219871773 |
\( -\frac{3578794}{4219} a + \frac{448381}{4219} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( a - 1\) , \( -a + 1\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a-1\right){x}-a+1$ |
| 4225.2-a1 |
4225.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
4225.2 |
\( 5^{2} \cdot 13^{2} \) |
\( 5^{4} \cdot 13^{4} \) |
$1.24783$ |
$(-4a+1), (4a-3), (5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.038447381$ |
$3.421514516$ |
1.215190886 |
\( \frac{6967871}{4225} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 4\) , \( 1\bigr] \) |
${y}^2+{x}{y}={x}^{3}+4{x}+1$ |
| 4225.2-a2 |
4225.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
4225.2 |
\( 5^{2} \cdot 13^{2} \) |
\( 5^{2} \cdot 13^{2} \) |
$1.24783$ |
$(-4a+1), (4a-3), (5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.153789524$ |
$6.843029032$ |
1.215190886 |
\( \frac{117649}{65} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}$ |
| 4483.1-a1 |
4483.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
4483.1 |
\( 4483 \) |
\( 4483 \) |
$1.26646$ |
$(-71a+9)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.039153018$ |
$6.905139150$ |
1.248725676 |
\( -\frac{836414}{4483} a + \frac{1648647}{4483} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( a - 1\) , \( -a\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a-1\right){x}-a$ |
| 4483.2-a1 |
4483.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
4483.2 |
\( 4483 \) |
\( 4483 \) |
$1.26646$ |
$(-71a+62)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.039153018$ |
$6.905139150$ |
1.248725676 |
\( \frac{836414}{4483} a + \frac{812233}{4483} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 0\) , \( -a\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}-a$ |
| 4681.2-a1 |
4681.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
4681.2 |
\( 31 \cdot 151 \) |
\( 31 \cdot 151 \) |
$1.28022$ |
$(-6a+1), (-14a+9)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.042145681$ |
$6.726361397$ |
1.309370773 |
\( -\frac{5771264}{4681} a + \frac{1486848}{4681} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( -a + 1\) , \( -a + 1\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}+\left(-a+1\right){x}-a+1$ |
| 4681.3-a1 |
4681.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
4681.3 |
\( 31 \cdot 151 \) |
\( 31 \cdot 151 \) |
$1.28022$ |
$(6a-5), (-14a+5)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.042145681$ |
$6.726361397$ |
1.309370773 |
\( \frac{5771264}{4681} a - \frac{4284416}{4681} \) |
\( \bigl[0\) , \( 1\) , \( a + 1\) , \( a\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+{x}^{2}+a{x}$ |
| 5043.1-a1 |
5043.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
5043.1 |
\( 3 \cdot 41^{2} \) |
\( 3^{2} \cdot 41^{2} \) |
$1.30428$ |
$(-2a+1), (41)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.023757644$ |
$6.248359085$ |
1.371288116 |
\( \frac{32768}{123} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( a - 1\) , \( -1\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(a-1\right){x}-1$ |
| 5625.1-CMa1 |
5625.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
5625.1 |
\( 3^{2} \cdot 5^{4} \) |
\( 3^{6} \cdot 5^{4} \) |
$1.34039$ |
$(-2a+1), (5)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
$5$ |
5Cn.0.1 |
$1$ |
\( 2^{2} \) |
$0.017703945$ |
$4.741954575$ |
1.551017859 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 1\bigr] \) |
${y}^2+{y}={x}^{3}+1$ |
| 5776.1-CMa1 |
5776.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
5776.1 |
\( 2^{4} \cdot 19^{2} \) |
\( 2^{8} \cdot 19^{2} \) |
$1.34929$ |
$(-5a+3), (2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$19$ |
19Cs.4.1 |
$1$ |
\( 3 \) |
$0.018683933$ |
$5.416213237$ |
1.402215272 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a\) , \( a - 1\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+a{x}+a-1$ |
| 5776.3-CMa1 |
5776.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
5776.3 |
\( 2^{4} \cdot 19^{2} \) |
\( 2^{8} \cdot 19^{2} \) |
$1.34929$ |
$(-5a+2), (2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$19$ |
19Cs.4.1 |
$1$ |
\( 3 \) |
$0.018683933$ |
$5.416213237$ |
1.402215272 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a\) , \( -a\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+a{x}-a$ |
| 5929.2-a1 |
5929.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
5929.2 |
\( 7^{2} \cdot 11^{2} \) |
\( 7^{4} \cdot 11^{2} \) |
$1.35814$ |
$(-3a+1), (3a-2), (11)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.013821261$ |
$4.822573867$ |
1.231447576 |
\( \frac{884736}{539} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 2 a - 2\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}+\left(2a-2\right){x}$ |
| 6241.1-CMa1 |
6241.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
6241.1 |
\( 79^{2} \) |
\( 79^{2} \) |
$1.37567$ |
$(10a-7)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$79$ |
79Cs.8.1 |
$1$ |
\( 1 \) |
$0.043046721$ |
$6.780111505$ |
1.348050840 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( a\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+a{x}-a$ |
| 6241.3-CMa1 |
6241.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
6241.3 |
\( 79^{2} \) |
\( 79^{2} \) |
$1.37567$ |
$(10a-3)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$79$ |
79Cs.8.1 |
$1$ |
\( 1 \) |
$0.043046721$ |
$6.780111505$ |
1.348050840 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( a\) , \( a\) , \( 0\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+a{x}$ |
| 6553.1-a1 |
6553.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
6553.1 |
\( 6553 \) |
\( 6553 \) |
$1.39254$ |
$(91a-27)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.044826429$ |
$6.612324849$ |
1.369044887 |
\( -\frac{2985984}{6553} a + \frac{10063872}{6553} \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( -1\) , \( 0\bigr] \) |
${y}^2+a{y}={x}^{3}-{x}$ |
| 6553.2-a1 |
6553.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
6553.2 |
\( 6553 \) |
\( 6553 \) |
$1.39254$ |
$(91a-64)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.044826429$ |
$6.612324849$ |
1.369044887 |
\( \frac{2985984}{6553} a + \frac{7077888}{6553} \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( -1\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-{x}-a$ |
| 6561.1-CMa1 |
6561.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
6561.1 |
\( 3^{8} \) |
\( 3^{10} \) |
$1.39297$ |
$(-2a+1)$ |
$2$ |
$\Z/3\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.1[2] |
$1$ |
\( 3 \) |
$0.192305923$ |
$5.622208826$ |
1.664591759 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -1\bigr] \) |
${y}^2+{y}={x}^{3}-1$ |
| 6627.1-a1 |
6627.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
6627.1 |
\( 3 \cdot 47^{2} \) |
\( 3^{2} \cdot 47^{2} \) |
$1.39646$ |
$(-2a+1), (47)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.027690926$ |
$6.007099121$ |
1.536602889 |
\( \frac{262144}{141} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( -a + 1\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-a+1\right){x}$ |
| 6643.1-a1 |
6643.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
6643.1 |
\( 7 \cdot 13 \cdot 73 \) |
\( 7 \cdot 13^{4} \cdot 73^{2} \) |
$1.39730$ |
$(-3a+1), (-4a+1), (-9a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.070309280$ |
$2.248478401$ |
1.460362687 |
\( \frac{7637234982322}{1065410983} a - \frac{6704016696807}{1065410983} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 8 a - 15\) , \( -14 a + 19\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(8a-15\right){x}-14a+19$ |
| 6643.1-a2 |
6643.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
6643.1 |
\( 7 \cdot 13 \cdot 73 \) |
\( 7^{2} \cdot 13^{2} \cdot 73 \) |
$1.39730$ |
$(-3a+1), (-4a+1), (-9a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.070309280$ |
$4.496956803$ |
1.460362687 |
\( -\frac{275472472}{604513} a - \frac{311605715}{604513} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2 a\) , \( -2 a + 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2a{x}-2a+1$ |
| 6643.8-a1 |
6643.8-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
6643.8 |
\( 7 \cdot 13 \cdot 73 \) |
\( 7 \cdot 13^{4} \cdot 73^{2} \) |
$1.39730$ |
$(3a-2), (4a-3), (9a-8)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.070309280$ |
$2.248478401$ |
1.460362687 |
\( -\frac{7637234982322}{1065410983} a + \frac{933218285515}{1065410983} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -8 a - 7\) , \( 14 a + 5\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-8a-7\right){x}+14a+5$ |
| 6643.8-a2 |
6643.8-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
6643.8 |
\( 7 \cdot 13 \cdot 73 \) |
\( 7^{2} \cdot 13^{2} \cdot 73 \) |
$1.39730$ |
$(3a-2), (4a-3), (9a-8)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.070309280$ |
$4.496956803$ |
1.460362687 |
\( \frac{275472472}{604513} a - \frac{587078187}{604513} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 2 a - 2\) , \( 2 a - 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(2a-2\right){x}+2a-1$ |
| 6771.2-a1 |
6771.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
6771.2 |
\( 3 \cdot 37 \cdot 61 \) |
\( 3^{2} \cdot 37 \cdot 61 \) |
$1.40398$ |
$(-2a+1), (-7a+4), (-9a+4)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.113560284$ |
$6.095074814$ |
1.598471419 |
\( -\frac{188416}{2257} a - \frac{496033}{6771} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( 0\) , \( -a + 1\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}-a+1$ |
| 6771.2-a2 |
6771.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
6771.2 |
\( 3 \cdot 37 \cdot 61 \) |
\( 3 \cdot 37^{2} \cdot 61^{2} \) |
$1.40398$ |
$(-2a+1), (-7a+4), (-9a+4)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.113560284$ |
$3.047537407$ |
1.598471419 |
\( \frac{272394455278}{15282147} a - \frac{39633131711}{15282147} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( -10 a + 5\) , \( -6 a + 8\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-10a+5\right){x}-6a+8$ |
| 6771.3-a1 |
6771.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
6771.3 |
\( 3 \cdot 37 \cdot 61 \) |
\( 3^{2} \cdot 37 \cdot 61 \) |
$1.40398$ |
$(-2a+1), (-7a+3), (-9a+5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.113560284$ |
$6.095074814$ |
1.598471419 |
\( \frac{188416}{2257} a - \frac{1061281}{6771} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -a\) , \( 0\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}-a{x}$ |
| 6771.3-a2 |
6771.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
6771.3 |
\( 3 \cdot 37 \cdot 61 \) |
\( 3 \cdot 37^{2} \cdot 61^{2} \) |
$1.40398$ |
$(-2a+1), (-7a+3), (-9a+5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.113560284$ |
$3.047537407$ |
1.598471419 |
\( -\frac{272394455278}{15282147} a + \frac{232761323567}{15282147} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 9 a - 5\) , \( 5 a + 2\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(9a-5\right){x}+5a+2$ |
| 6889.1-a1 |
6889.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
6889.1 |
\( 83^{2} \) |
\( 83^{2} \) |
$1.41006$ |
$(83)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.053057089$ |
$6.604390094$ |
1.618473137 |
\( \frac{103823}{83} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+{x}$ |
| 7201.1-a1 |
7201.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7201.1 |
\( 19 \cdot 379 \) |
\( 19^{2} \cdot 379 \) |
$1.42576$ |
$(-5a+3), (22a-15)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.036632701$ |
$4.772940976$ |
1.615155603 |
\( \frac{806901587}{136819} a + \frac{195372010}{136819} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 2 a + 2\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+2\right){x}+2$ |
| 7201.4-a1 |
7201.4-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7201.4 |
\( 19 \cdot 379 \) |
\( 19^{2} \cdot 379 \) |
$1.42576$ |
$(-5a+2), (22a-7)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.036632701$ |
$4.772940976$ |
1.615155603 |
\( -\frac{806901587}{136819} a + \frac{1002273597}{136819} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 3\) , \( a - 1\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+3{x}+a-1$ |
| 7239.1-a1 |
7239.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7239.1 |
\( 3 \cdot 19 \cdot 127 \) |
\( 3^{2} \cdot 19 \cdot 127 \) |
$1.42764$ |
$(-2a+1), (-5a+3), (-13a+7)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.029682297$ |
$6.018537887$ |
1.650242899 |
\( \frac{457244}{7239} a + \frac{2081787}{2413} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -2\) , \( 0\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}-2{x}$ |
| 7239.4-a1 |
7239.4-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7239.4 |
\( 3 \cdot 19 \cdot 127 \) |
\( 3^{2} \cdot 19 \cdot 127 \) |
$1.42764$ |
$(-2a+1), (-5a+2), (-13a+6)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.029682297$ |
$6.018537887$ |
1.650242899 |
\( -\frac{457244}{7239} a + \frac{6702605}{7239} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -a - 1\) , \( -a + 1\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a-1\right){x}-a+1$ |
| 7393.1-a1 |
7393.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7393.1 |
\( 7393 \) |
\( 7393 \) |
$1.43517$ |
$(-99a+56)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.055214828$ |
$6.360941495$ |
1.622207826 |
\( \frac{19722843}{7393} a - \frac{3033835}{7393} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 2 a\) , \( -a\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+2a{x}-a$ |
| 7393.2-a1 |
7393.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7393.2 |
\( 7393 \) |
\( 7393 \) |
$1.43517$ |
$(-99a+43)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.055214828$ |
$6.360941495$ |
1.622207826 |
\( -\frac{19722843}{7393} a + \frac{16689008}{7393} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+{x}$ |
| 7732.1-a1 |
7732.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7732.1 |
\( 2^{2} \cdot 1933 \) |
\( 2^{4} \cdot 1933 \) |
$1.45135$ |
$(49a-36), (2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.030862000$ |
$5.830919463$ |
1.662342375 |
\( -\frac{5018881}{7732} a + \frac{5725525}{7732} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 2 a - 1\) , \( -a + 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a-1\right){x}-a+1$ |
| 7732.2-a1 |
7732.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7732.2 |
\( 2^{2} \cdot 1933 \) |
\( 2^{4} \cdot 1933 \) |
$1.45135$ |
$(-49a+13), (2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.030862000$ |
$5.830919463$ |
1.662342375 |
\( \frac{5018881}{7732} a + \frac{176661}{1933} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 1\) , \( 1\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+{x}+1$ |
| 7921.1-a1 |
7921.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7921.1 |
\( 89^{2} \) |
\( 89^{2} \) |
$1.46014$ |
$(89)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.057108232$ |
$6.383721620$ |
1.683844643 |
\( -\frac{117649}{89} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-{x}$ |
| 8281.3-CMb1 |
8281.3-CMb |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
8281.3 |
\( 7^{2} \cdot 13^{2} \) |
\( 7^{6} \cdot 13^{4} \) |
$1.47645$ |
$(-3a+1), (4a-3)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$7, 13$ |
7Cs.2.1, 13Cs.5.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.011943532$ |
$2.257587269$ |
1.494472576 |
\( 0 \) |
\( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( a\) , \( 11 a\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+a{x}+11a$ |
| 8281.7-CMb1 |
8281.7-CMb |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
8281.7 |
\( 7^{2} \cdot 13^{2} \) |
\( 7^{6} \cdot 13^{4} \) |
$1.47645$ |
$(3a-2), (-4a+1)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$7, 13$ |
7Cs.2.1, 13Cs.5.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.011943532$ |
$2.257587269$ |
1.494472576 |
\( 0 \) |
\( \bigl[0\) , \( -a - 1\) , \( a\) , \( a\) , \( -12 a + 12\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+a{x}-12a+12$ |
| 8464.1-a1 |
8464.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
8464.1 |
\( 2^{4} \cdot 23^{2} \) |
\( 2^{8} \cdot 23^{2} \) |
$1.48454$ |
$(2), (23)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 3 \) |
$0.022760883$ |
$5.169754595$ |
1.630458177 |
\( -\frac{6912}{23} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 1\bigr] \) |
${y}^2={x}^{3}-{x}+1$ |
| 8749.1-a1 |
8749.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
8749.1 |
\( 13 \cdot 673 \) |
\( 13^{2} \cdot 673 \) |
$1.49689$ |
$(-4a+1), (29a-8)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.034412591$ |
$4.743953637$ |
1.508054942 |
\( \frac{797257728}{113737} a - \frac{1131687936}{113737} \) |
\( \bigl[0\) , \( -a - 1\) , \( a\) , \( 4 a - 3\) , \( a + 1\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(4a-3\right){x}+a+1$ |
| 8749.4-a1 |
8749.4-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
8749.4 |
\( 13 \cdot 673 \) |
\( 13^{2} \cdot 673 \) |
$1.49689$ |
$(4a-3), (-29a+21)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.034412591$ |
$4.743953637$ |
1.508054942 |
\( -\frac{797257728}{113737} a - \frac{334430208}{113737} \) |
\( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( -2 a\) , \( -5 a + 2\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}-2a{x}-5a+2$ |
| 8773.1-a1 |
8773.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
8773.1 |
\( 31 \cdot 283 \) |
\( 31^{3} \cdot 283 \) |
$1.49791$ |
$(-6a+1), (19a-13)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.045550854$ |
$3.058960095$ |
1.930727394 |
\( \frac{301408653852}{8430853} a - \frac{229359410865}{8430853} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -4 a + 10\) , \( -10 a + 2\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-4a+10\right){x}-10a+2$ |
*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.
