| 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 |
| 1008.1-a1 |
1008.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1008.1 |
\( 2^{4} \cdot 3^{2} \cdot 7 \) |
\( 2^{16} \cdot 3^{3} \cdot 7^{2} \) |
$0.87210$ |
$(-2a+1), (-3a+1), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$2.701463321$ |
1.039793717 |
\( -\frac{452304}{49} a - \frac{118800}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 11\) , \( 8 a - 14\bigr] \) |
${y}^2={x}^{3}+\left(4a-11\right){x}+8a-14$ |
| 1008.1-a2 |
1008.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1008.1 |
\( 2^{4} \cdot 3^{2} \cdot 7 \) |
\( 2^{8} \cdot 3^{3} \cdot 7 \) |
$0.87210$ |
$(-2a+1), (-3a+1), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$5.402926643$ |
1.039793717 |
\( \frac{20736}{7} a - \frac{13824}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -a - 1\) , \( a\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}+a$ |
| 1008.1-a3 |
1008.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1008.1 |
\( 2^{4} \cdot 3^{2} \cdot 7 \) |
\( 2^{16} \cdot 3^{9} \cdot 7^{6} \) |
$0.87210$ |
$(-2a+1), (-3a+1), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.900487773$ |
1.039793717 |
\( \frac{4757232}{117649} a + \frac{223153968}{117649} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -36 a + 69\) , \( -48 a - 14\bigr] \) |
${y}^2={x}^{3}+\left(-36a+69\right){x}-48a-14$ |
| 1008.1-a4 |
1008.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1008.1 |
\( 2^{4} \cdot 3^{2} \cdot 7 \) |
\( 2^{8} \cdot 3^{9} \cdot 7^{3} \) |
$0.87210$ |
$(-2a+1), (-3a+1), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$1.800975547$ |
1.039793717 |
\( -\frac{3512064}{343} a + \frac{36883968}{343} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -21 a + 39\) , \( 57 a + 28\bigr] \) |
${y}^2={x}^{3}+\left(-21a+39\right){x}+57a+28$ |
| 1008.2-a1 |
1008.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1008.2 |
\( 2^{4} \cdot 3^{2} \cdot 7 \) |
\( 2^{16} \cdot 3^{3} \cdot 7^{2} \) |
$0.87210$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$2.701463321$ |
1.039793717 |
\( \frac{452304}{49} a - \frac{571104}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a - 7\) , \( -8 a - 6\bigr] \) |
${y}^2={x}^{3}+\left(-4a-7\right){x}-8a-6$ |
| 1008.2-a2 |
1008.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1008.2 |
\( 2^{4} \cdot 3^{2} \cdot 7 \) |
\( 2^{8} \cdot 3^{3} \cdot 7 \) |
$0.87210$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$5.402926643$ |
1.039793717 |
\( -\frac{20736}{7} a + \frac{6912}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( a - 2\) , \( -a + 1\bigr] \) |
${y}^2={x}^{3}+\left(a-2\right){x}-a+1$ |
| 1008.2-a3 |
1008.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1008.2 |
\( 2^{4} \cdot 3^{2} \cdot 7 \) |
\( 2^{16} \cdot 3^{9} \cdot 7^{6} \) |
$0.87210$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.900487773$ |
1.039793717 |
\( -\frac{4757232}{117649} a + \frac{227911200}{117649} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 36 a + 33\) , \( 48 a - 62\bigr] \) |
${y}^2={x}^{3}+\left(36a+33\right){x}+48a-62$ |
| 1008.2-a4 |
1008.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1008.2 |
\( 2^{4} \cdot 3^{2} \cdot 7 \) |
\( 2^{8} \cdot 3^{9} \cdot 7^{3} \) |
$0.87210$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$1.800975547$ |
1.039793717 |
\( \frac{3512064}{343} a + \frac{33371904}{343} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 21 a + 18\) , \( -57 a + 85\bigr] \) |
${y}^2={x}^{3}+\left(21a+18\right){x}-57a+85$ |
| 1009.1-a1 |
1009.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1009.1 |
\( 1009 \) |
\( 1009 \) |
$0.87231$ |
$(-35a+27)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$7.197922976$ |
0.923493948 |
\( \frac{7041024}{1009} a - \frac{3616768}{1009} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( -a\) , \( 0\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}-a{x}$ |
| 1009.1-a2 |
1009.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1009.1 |
\( 1009 \) |
\( 1009^{3} \) |
$0.87231$ |
$(-35a+27)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3 \) |
$1$ |
$2.399307658$ |
0.923493948 |
\( -\frac{806774616064}{1027243729} a + \frac{2748494319616}{1027243729} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( 9 a\) , \( a + 7\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}+9a{x}+a+7$ |
| 1009.2-a1 |
1009.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1009.2 |
\( 1009 \) |
\( 1009 \) |
$0.87231$ |
$(35a-8)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$7.197922976$ |
0.923493948 |
\( -\frac{7041024}{1009} a + \frac{3424256}{1009} \) |
\( \bigl[0\) , \( 1\) , \( a + 1\) , \( a - 1\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(a-1\right){x}-a$ |
| 1009.2-a2 |
1009.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1009.2 |
\( 1009 \) |
\( 1009^{3} \) |
$0.87231$ |
$(35a-8)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3 \) |
$1$ |
$2.399307658$ |
0.923493948 |
\( \frac{806774616064}{1027243729} a + \frac{1941719703552}{1027243729} \) |
\( \bigl[0\) , \( 1\) , \( a + 1\) , \( -9 a + 9\) , \( -2 a + 8\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-9a+9\right){x}-2a+8$ |
| 1024.1-a1 |
1024.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{12} \) |
$0.87554$ |
$(2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$6.875185818$ |
0.992347595 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}$ |
| 1024.1-a2 |
1024.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{24} \) |
$0.87554$ |
$(2)$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$3.437592909$ |
0.992347595 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4\) , \( 0\bigr] \) |
${y}^2={x}^{3}+4{x}$ |
| 1024.1-a3 |
1024.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$0.87554$ |
$(2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$3.437592909$ |
0.992347595 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -11\) , \( -14\bigr] \) |
${y}^2={x}^{3}-11{x}-14$ |
| 1024.1-a4 |
1024.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$0.87554$ |
$(2)$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$3.437592909$ |
0.992347595 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -11\) , \( 14\bigr] \) |
${y}^2={x}^{3}-11{x}+14$ |
| 1036.2-a1 |
1036.2-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1036.2 |
\( 2^{2} \cdot 7 \cdot 37 \) |
\( 2^{2} \cdot 7 \cdot 37 \) |
$0.87809$ |
$(-3a+1), (-7a+3), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$9$ |
\( 1 \) |
$1$ |
$0.694449686$ |
0.801881427 |
\( \frac{5629058103803395}{518} a - \frac{7384553560278229}{518} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 1133 a + 638\) , \( 14939 a - 27297\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(1133a+638\right){x}+14939a-27297$ |
| 1036.2-a2 |
1036.2-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1036.2 |
\( 2^{2} \cdot 7 \cdot 37 \) |
\( 2^{2} \cdot 7 \cdot 37 \) |
$0.87809$ |
$(-3a+1), (-7a+3), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$6.250047180$ |
0.801881427 |
\( -\frac{608823}{259} a - \frac{26628845}{518} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 4 a - 2\) , \( -2\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4a-2\right){x}-2$ |
| 1036.2-a3 |
1036.2-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1036.2 |
\( 2^{2} \cdot 7 \cdot 37 \) |
\( 2^{18} \cdot 7^{9} \cdot 37 \) |
$0.87809$ |
$(-3a+1), (-7a+3), (2)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{4} \) |
$1$ |
$0.694449686$ |
0.801881427 |
\( -\frac{7201542233586935}{382229365504} a - \frac{18769001765548989}{764458731008} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -176 a - 22\) , \( 1036 a - 352\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-176a-22\right){x}+1036a-352$ |
| 1036.2-a4 |
1036.2-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1036.2 |
\( 2^{2} \cdot 7 \cdot 37 \) |
\( 2^{6} \cdot 7^{3} \cdot 37^{3} \) |
$0.87809$ |
$(-3a+1), (-7a+3), (2)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{3} \) |
$1$ |
$2.083349060$ |
0.801881427 |
\( \frac{506445552405}{69495916} a - \frac{3543562947041}{138991832} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 9 a - 22\) , \( 16 a - 47\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(9a-22\right){x}+16a-47$ |
| 1036.2-a5 |
1036.2-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1036.2 |
\( 2^{2} \cdot 7 \cdot 37 \) |
\( 2^{2} \cdot 7 \cdot 37^{9} \) |
$0.87809$ |
$(-3a+1), (-7a+3), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{2} \) |
$1$ |
$0.694449686$ |
0.801881427 |
\( \frac{177747681234047691}{1819464357131078} a + \frac{1446247040871254777}{909732178565539} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -31 a + 108\) , \( 110 a - 69\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-31a+108\right){x}+110a-69$ |
| 1036.3-a1 |
1036.3-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1036.3 |
\( 2^{2} \cdot 7 \cdot 37 \) |
\( 2^{2} \cdot 7 \cdot 37 \) |
$0.87809$ |
$(3a-2), (-7a+4), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$9$ |
\( 1 \) |
$1$ |
$0.694449686$ |
0.801881427 |
\( -\frac{5629058103803395}{518} a - \frac{877747728237417}{259} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -1133 a + 1772\) , \( -13806 a - 14129\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1133a+1772\right){x}-13806a-14129$ |
| 1036.3-a2 |
1036.3-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1036.3 |
\( 2^{2} \cdot 7 \cdot 37 \) |
\( 2^{2} \cdot 7 \cdot 37 \) |
$0.87809$ |
$(3a-2), (-7a+4), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$6.250047180$ |
0.801881427 |
\( \frac{608823}{259} a - \frac{27846491}{518} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 2 a - 3\) , \( a\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a-3\right){x}+a$ |
| 1036.3-a3 |
1036.3-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1036.3 |
\( 2^{2} \cdot 7 \cdot 37 \) |
\( 2^{18} \cdot 7^{9} \cdot 37 \) |
$0.87809$ |
$(3a-2), (-7a+4), (2)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{4} \) |
$1$ |
$0.694449686$ |
0.801881427 |
\( \frac{7201542233586935}{382229365504} a - \frac{33172086232722859}{764458731008} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 22 a + 177\) , \( -1235 a + 706\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(22a+177\right){x}-1235a+706$ |
| 1036.3-a4 |
1036.3-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1036.3 |
\( 2^{2} \cdot 7 \cdot 37 \) |
\( 2^{6} \cdot 7^{3} \cdot 37^{3} \) |
$0.87809$ |
$(3a-2), (-7a+4), (2)$ |
0 |
$\Z/3\Z\oplus\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1[2] |
$1$ |
\( 3^{3} \) |
$1$ |
$2.083349060$ |
0.801881427 |
\( -\frac{506445552405}{69495916} a - \frac{2530671842231}{138991832} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 22 a - 8\) , \( -30 a - 9\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(22a-8\right){x}-30a-9$ |
| 1036.3-a5 |
1036.3-a |
$5$ |
$9$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1036.3 |
\( 2^{2} \cdot 7 \cdot 37 \) |
\( 2^{2} \cdot 7 \cdot 37^{9} \) |
$0.87809$ |
$(3a-2), (-7a+4), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{2} \) |
$1$ |
$0.694449686$ |
0.801881427 |
\( -\frac{177747681234047691}{1819464357131078} a + \frac{3070241762976557245}{1819464357131078} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -108 a + 32\) , \( -34 a - 67\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-108a+32\right){x}-34a-67$ |
| 1083.2-a1 |
1083.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1083.2 |
\( 3 \cdot 19^{2} \) |
\( 3^{4} \cdot 19^{2} \) |
$0.88788$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.037574592$ |
$5.328644115$ |
0.924784107 |
\( -\frac{1404928}{171} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( -2 a + 2\) , \( 2\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-2a+2\right){x}+2$ |
| 1083.2-b1 |
1083.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1083.2 |
\( 3 \cdot 19^{2} \) |
\( 3 \cdot 19^{10} \) |
$0.88788$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.816172249$ |
0.942434535 |
\( -\frac{7240152655469734}{50950689123} a + \frac{1727319988870667}{50950689123} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 130 a + 63\) , \( -464 a + 999\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(130a+63\right){x}-464a+999$ |
| 1083.2-b2 |
1083.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1083.2 |
\( 3 \cdot 19^{2} \) |
\( 3 \cdot 19^{10} \) |
$0.88788$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.816172249$ |
0.942434535 |
\( \frac{7240152655469734}{50950689123} a - \frac{5512832666599067}{50950689123} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -130 a + 193\) , \( 464 a + 535\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-130a+193\right){x}+464a+535$ |
| 1083.2-b3 |
1083.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1083.2 |
\( 3 \cdot 19^{2} \) |
\( 3^{2} \cdot 19^{8} \) |
$0.88788$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$1.632344499$ |
0.942434535 |
\( \frac{67419143}{390963} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 8\) , \( 29\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+8{x}+29$ |
| 1083.2-b4 |
1083.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1083.2 |
\( 3 \cdot 19^{2} \) |
\( 3^{2} \cdot 19^{2} \) |
$0.88788$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$6.529377996$ |
0.942434535 |
\( \frac{389017}{57} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2{x}-1$ |
| 1083.2-b5 |
1083.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1083.2 |
\( 3 \cdot 19^{2} \) |
\( 3^{4} \cdot 19^{4} \) |
$0.88788$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$3.264688998$ |
0.942434535 |
\( \frac{30664297}{3249} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -7\) , \( 5\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-7{x}+5$ |
| 1083.2-b6 |
1083.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1083.2 |
\( 3 \cdot 19^{2} \) |
\( 3^{8} \cdot 19^{2} \) |
$0.88788$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.632344499$ |
0.942434535 |
\( \frac{115714886617}{1539} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -102\) , \( 385\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-102{x}+385$ |
| 1083.2-c1 |
1083.2-c |
$2$ |
$5$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1083.2 |
\( 3 \cdot 19^{2} \) |
\( 3^{4} \cdot 19^{10} \) |
$0.88788$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.271765830$ |
1.255232601 |
\( -\frac{9358714467168256}{22284891} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( -4390 a + 4390\) , \( -113432\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-4390a+4390\right){x}-113432$ |
| 1083.2-c2 |
1083.2-c |
$2$ |
$5$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1083.2 |
\( 3 \cdot 19^{2} \) |
\( 3^{20} \cdot 19^{2} \) |
$0.88788$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$1.358829150$ |
1.255232601 |
\( \frac{841232384}{1121931} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( 20 a - 20\) , \( -32\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(20a-20\right){x}-32$ |
| 1089.1-a1 |
1089.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1089.1 |
\( 3^{2} \cdot 11^{2} \) |
\( 3^{6} \cdot 11^{2} \) |
$0.88911$ |
$(-2a+1), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.075642846$ |
$5.314975105$ |
0.928471248 |
\( \frac{19683}{11} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -2\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-2{x}$ |
| 1089.1-a2 |
1089.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1089.1 |
\( 3^{2} \cdot 11^{2} \) |
\( 3^{6} \cdot 11^{4} \) |
$0.88911$ |
$(-2a+1), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.151285692$ |
$2.657487552$ |
0.928471248 |
\( \frac{19034163}{121} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -17\) , \( 30\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-17{x}+30$ |
| 1093.1-a1 |
1093.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1093.1 |
\( 1093 \) |
\( 1093 \) |
$0.88993$ |
$(36a-29)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.050809964$ |
$7.802342922$ |
0.915531495 |
\( \frac{88373}{1093} a + \frac{28692}{1093} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}-{x}$ |
| 1093.2-a1 |
1093.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1093.2 |
\( 1093 \) |
\( 1093 \) |
$0.88993$ |
$(36a-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.050809964$ |
$7.802342922$ |
0.915531495 |
\( -\frac{88373}{1093} a + \frac{117065}{1093} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}-{x}$ |
| 1116.1-a1 |
1116.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1116.1 |
\( 2^{2} \cdot 3^{2} \cdot 31 \) |
\( 2^{2} \cdot 3^{6} \cdot 31^{3} \) |
$0.89457$ |
$(-2a+1), (-6a+1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3 \) |
$1$ |
$2.908714005$ |
1.119564542 |
\( -\frac{10618695}{29791} a - \frac{103188411}{59582} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -6 a + 1\) , \( -6 a + 5\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-6a+1\right){x}-6a+5$ |
| 1116.1-a2 |
1116.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1116.1 |
\( 2^{2} \cdot 3^{2} \cdot 31 \) |
\( 2^{6} \cdot 3^{6} \cdot 31 \) |
$0.89457$ |
$(-2a+1), (-6a+1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3 \) |
$1$ |
$2.908714005$ |
1.119564542 |
\( \frac{44272737}{124} a + \frac{10648665}{248} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 6 a - 18\) , \( 12 a - 24\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(6a-18\right){x}+12a-24$ |
| 1116.2-a1 |
1116.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1116.2 |
\( 2^{2} \cdot 3^{2} \cdot 31 \) |
\( 2^{2} \cdot 3^{6} \cdot 31^{3} \) |
$0.89457$ |
$(-2a+1), (6a-5), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3 \) |
$1$ |
$2.908714005$ |
1.119564542 |
\( \frac{10618695}{29791} a - \frac{124425801}{59582} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 6 a - 5\) , \( 6 a - 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(6a-5\right){x}+6a-1$ |
| 1116.2-a2 |
1116.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1116.2 |
\( 2^{2} \cdot 3^{2} \cdot 31 \) |
\( 2^{6} \cdot 3^{6} \cdot 31 \) |
$0.89457$ |
$(-2a+1), (6a-5), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3 \) |
$1$ |
$2.908714005$ |
1.119564542 |
\( -\frac{44272737}{124} a + \frac{99194139}{248} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -6 a - 12\) , \( -12 a - 12\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-6a-12\right){x}-12a-12$ |
| 1137.1-a1 |
1137.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1137.1 |
\( 3 \cdot 379 \) |
\( 3 \cdot 379^{5} \) |
$0.89875$ |
$(-2a+1), (22a-15)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$1.044593927$ |
1.206193170 |
\( -\frac{19572015114248192}{23459421833697} a + \frac{55499830713954304}{23459421833697} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -38 a + 50\) , \( -3 a - 58\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+\left(-38a+50\right){x}-3a-58$ |
| 1137.1-a2 |
1137.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1137.1 |
\( 3 \cdot 379 \) |
\( 3^{5} \cdot 379 \) |
$0.89875$ |
$(-2a+1), (22a-15)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5 \) |
$1$ |
$5.222969636$ |
1.206193170 |
\( \frac{7118848}{10233} a + \frac{19468288}{10233} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 2 a\) , \( a\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+2a{x}+a$ |
| 1137.2-a1 |
1137.2-a |
$2$ |
$5$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1137.2 |
\( 3 \cdot 379 \) |
\( 3 \cdot 379^{5} \) |
$0.89875$ |
$(-2a+1), (22a-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$1.044593927$ |
1.206193170 |
\( \frac{19572015114248192}{23459421833697} a + \frac{35927815599706112}{23459421833697} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 38 a + 12\) , \( 3 a - 61\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+\left(38a+12\right){x}+3a-61$ |
| 1137.2-a2 |
1137.2-a |
$2$ |
$5$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1137.2 |
\( 3 \cdot 379 \) |
\( 3^{5} \cdot 379 \) |
$0.89875$ |
$(-2a+1), (22a-7)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5 \) |
$1$ |
$5.222969636$ |
1.206193170 |
\( -\frac{7118848}{10233} a + \frac{26587136}{10233} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -2 a + 2\) , \( -a + 1\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+\left(-2a+2\right){x}-a+1$ |
| 1156.1-a1 |
1156.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1156.1 |
\( 2^{2} \cdot 17^{2} \) |
\( 2^{12} \cdot 17^{2} \) |
$0.90248$ |
$(2), (17)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2 \cdot 3 \) |
$0.562629009$ |
$4.190351719$ |
0.907445835 |
\( \frac{3048625}{1088} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -3 a + 3\) , \( 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-3a+3\right){x}+1$ |
| 1156.1-a2 |
1156.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1156.1 |
\( 2^{2} \cdot 17^{2} \) |
\( 2^{2} \cdot 17^{12} \) |
$0.90248$ |
$(2), (17)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2 \cdot 3 \) |
$3.375774058$ |
$0.698391953$ |
0.907445835 |
\( \frac{159661140625}{48275138} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -113 a + 113\) , \( -329\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-113a+113\right){x}-329$ |
| 1156.1-a3 |
1156.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1156.1 |
\( 2^{2} \cdot 17^{2} \) |
\( 2^{6} \cdot 17^{4} \) |
$0.90248$ |
$(2), (17)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2 \cdot 3 \) |
$1.125258019$ |
$2.095175859$ |
0.907445835 |
\( \frac{8805624625}{2312} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -43 a + 43\) , \( 105\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-43a+43\right){x}+105$ |
*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.
