| 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 |
| 7.1-a1 |
7.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
7.1 |
\( 7 \) |
\( 3^{12} \cdot 7^{8} \) |
$1.19858$ |
$(7,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.671083405$ |
$3.526311803$ |
0.573948268 |
\( -\frac{5467057353}{5764801} a - \frac{16785249568}{5764801} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -4 a + 32\) , \( -19 a - 172\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(-a+1\right){x}^2+\left(-4a+32\right){x}-19a-172$ |
| 7.1-a2 |
7.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
7.1 |
\( 7 \) |
\( 3^{12} \cdot 7^{4} \) |
$1.19858$ |
$(7,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.335541702$ |
$7.052623607$ |
0.573948268 |
\( \frac{382608}{2401} a - \frac{2822593}{2401} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( a - 8\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(-a+1\right){x}^2+\left(a-8\right){x}$ |
| 7.1-b1 |
7.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
7.1 |
\( 7 \) |
\( 3^{12} \cdot 7^{8} \) |
$1.19858$ |
$(7,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.526311803$ |
1.710512474 |
\( -\frac{5467057353}{5764801} a - \frac{16785249568}{5764801} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( -6 a + 28\) , \( 24 a + 142\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+a{x}^2+\left(-6a+28\right){x}+24a+142$ |
| 7.1-b2 |
7.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
7.1 |
\( 7 \) |
\( 3^{12} \cdot 7^{4} \) |
$1.19858$ |
$(7,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.052623607$ |
1.710512474 |
\( \frac{382608}{2401} a - \frac{2822593}{2401} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( -a - 12\) , \( 10\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+a{x}^2+\left(-a-12\right){x}+10$ |
| 7.2-a1 |
7.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
7.2 |
\( 7 \) |
\( 3^{12} \cdot 7^{8} \) |
$1.19858$ |
$(7,a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.671083405$ |
$3.526311803$ |
0.573948268 |
\( \frac{5467057353}{5764801} a - \frac{16785249568}{5764801} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 4 a + 32\) , \( 19 a - 172\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(a+1\right){x}^2+\left(4a+32\right){x}+19a-172$ |
| 7.2-a2 |
7.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
7.2 |
\( 7 \) |
\( 3^{12} \cdot 7^{4} \) |
$1.19858$ |
$(7,a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.335541702$ |
$7.052623607$ |
0.573948268 |
\( -\frac{382608}{2401} a - \frac{2822593}{2401} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -a - 8\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(a+1\right){x}^2+\left(-a-8\right){x}$ |
| 7.2-b1 |
7.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
7.2 |
\( 7 \) |
\( 3^{12} \cdot 7^{8} \) |
$1.19858$ |
$(7,a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.526311803$ |
1.710512474 |
\( \frac{5467057353}{5764801} a - \frac{16785249568}{5764801} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 6 a + 28\) , \( -24 a + 142\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-a{x}^2+\left(6a+28\right){x}-24a+142$ |
| 7.2-b2 |
7.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
7.2 |
\( 7 \) |
\( 3^{12} \cdot 7^{4} \) |
$1.19858$ |
$(7,a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.052623607$ |
1.710512474 |
\( -\frac{382608}{2401} a - \frac{2822593}{2401} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( a - 12\) , \( 10\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-a{x}^2+\left(a-12\right){x}+10$ |
| 8.1-a1 |
8.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \) |
$1.23927$ |
$(2,a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$10.84075801$ |
1.314635010 |
\( 2000 \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -2 a + 10\) , \( 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+{x}^2+\left(-2a+10\right){x}+4$ |
| 8.1-a2 |
8.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$1.23927$ |
$(2,a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.420379007$ |
1.314635010 |
\( 1098500 \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -2 a + 15\) , \( 2 a - 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+{x}^2+\left(-2a+15\right){x}+2a-1$ |
| 8.1-b1 |
8.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \) |
$1.23927$ |
$(2,a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$10.84075801$ |
1.314635010 |
\( 2000 \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 10\) , \( -a + 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+10{x}-a+4$ |
| 8.1-b2 |
8.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$1.23927$ |
$(2,a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.420379007$ |
1.314635010 |
\( 1098500 \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 15\) , \( -3 a - 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+15{x}-3a-1$ |
| 9.2-a1 |
9.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
9.2 |
\( 3^{2} \) |
\( 2^{12} \cdot 3^{20} \) |
$1.27630$ |
$(3,a+1), (3,a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.599650214$ |
0.775944329 |
\( -\frac{836338050625}{43046721} a - \frac{8385906271000}{43046721} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 20 a - 165\) , \( 163 a - 581\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+\left(20a-165\right){x}+163a-581$ |
| 9.2-a2 |
9.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
9.2 |
\( 3^{2} \) |
\( 2^{12} \cdot 3^{20} \) |
$1.27630$ |
$(3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.599650214$ |
0.775944329 |
\( \frac{836338050625}{43046721} a - \frac{8385906271000}{43046721} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -20 a - 165\) , \( 203 a + 939\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+\left(-20a-165\right){x}+203a+939$ |
| 9.2-a3 |
9.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
9.2 |
\( 3^{2} \) |
\( 2^{12} \cdot 3^{16} \) |
$1.27630$ |
$(3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$3.199300429$ |
0.775944329 |
\( \frac{5359375}{6561} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -5\) , \( 7 a + 19\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2-5{x}+7a+19$ |
| 9.2-a4 |
9.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
9.2 |
\( 3^{2} \) |
\( 2^{12} \cdot 3^{8} \) |
$1.27630$ |
$(3,a+1), (3,a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$6.398600858$ |
0.775944329 |
\( \frac{274625}{81} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 15\) , \( -a - 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+15{x}-a-1$ |
| 9.2-b1 |
9.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
9.2 |
\( 3^{2} \) |
\( 2^{12} \cdot 3^{20} \) |
$1.27630$ |
$(3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.599650214$ |
0.775944329 |
\( -\frac{836338050625}{43046721} a - \frac{8385906271000}{43046721} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 18 a - 165\) , \( -204 a + 939\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+{x}^2+\left(18a-165\right){x}-204a+939$ |
| 9.2-b2 |
9.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
9.2 |
\( 3^{2} \) |
\( 2^{12} \cdot 3^{20} \) |
$1.27630$ |
$(3,a+1), (3,a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.599650214$ |
0.775944329 |
\( \frac{836338050625}{43046721} a - \frac{8385906271000}{43046721} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -22 a - 165\) , \( -164 a - 581\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+{x}^2+\left(-22a-165\right){x}-164a-581$ |
| 9.2-b3 |
9.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
9.2 |
\( 3^{2} \) |
\( 2^{12} \cdot 3^{16} \) |
$1.27630$ |
$(3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$3.199300429$ |
0.775944329 |
\( \frac{5359375}{6561} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -2 a - 5\) , \( -8 a + 19\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+{x}^2+\left(-2a-5\right){x}-8a+19$ |
| 9.2-b4 |
9.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
9.2 |
\( 3^{2} \) |
\( 2^{12} \cdot 3^{8} \) |
$1.27630$ |
$(3,a+1), (3,a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$6.398600858$ |
0.775944329 |
\( \frac{274625}{81} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -2 a + 15\) , \( -1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+{x}^2+\left(-2a+15\right){x}-1$ |
| 9.2-c1 |
9.2-c |
$2$ |
$5$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
9.2 |
\( 3^{2} \) |
\( 2^{12} \cdot 3^{10} \) |
$1.27630$ |
$(3,a+1), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B |
$1$ |
\( 5 \) |
$1$ |
$2.295286137$ |
2.783443290 |
\( -\frac{13549359104}{243} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 193\) , \( 327 a\bigr] \) |
${y}^2={x}^3+a{x}^2+193{x}+327a$ |
| 9.2-c2 |
9.2-c |
$2$ |
$5$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
9.2 |
\( 3^{2} \) |
\( 2^{12} \cdot 3^{2} \) |
$1.27630$ |
$(3,a+1), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B |
$1$ |
\( 1 \) |
$1$ |
$11.47643068$ |
2.783443290 |
\( \frac{4096}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -7\) , \( -a\bigr] \) |
${y}^2={x}^3+a{x}^2-7{x}-a$ |
| 9.2-d1 |
9.2-d |
$2$ |
$5$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
9.2 |
\( 3^{2} \) |
\( 2^{12} \cdot 3^{10} \) |
$1.27630$ |
$(3,a+1), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B |
$1$ |
\( 5 \) |
$1$ |
$2.295286137$ |
2.783443290 |
\( -\frac{13549359104}{243} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 193\) , \( -327 a\bigr] \) |
${y}^2={x}^3-a{x}^2+193{x}-327a$ |
| 9.2-d2 |
9.2-d |
$2$ |
$5$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
9.2 |
\( 3^{2} \) |
\( 2^{12} \cdot 3^{2} \) |
$1.27630$ |
$(3,a+1), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B |
$1$ |
\( 1 \) |
$1$ |
$11.47643068$ |
2.783443290 |
\( \frac{4096}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -7\) , \( a\bigr] \) |
${y}^2={x}^3-a{x}^2-7{x}+a$ |
| 17.1-a1 |
17.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 17^{8} \) |
$1.49625$ |
$(a)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.545171092$ |
$2.123938699$ |
1.591930441 |
\( -\frac{35937}{83521} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 17\) , \( 14\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+17{x}+14$ |
| 17.1-a2 |
17.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$1.49625$ |
$(a)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.545171092$ |
$8.495754796$ |
1.591930441 |
\( \frac{35937}{17} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 17\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+17{x}$ |
| 17.1-a3 |
17.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 17^{4} \) |
$1.49625$ |
$(a)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.545171092$ |
$4.247877398$ |
1.591930441 |
\( \frac{20346417}{289} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 12\) , \( 14\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+12{x}+14$ |
| 17.1-a4 |
17.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$1.49625$ |
$(a)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$6.180684368$ |
$2.123938699$ |
1.591930441 |
\( \frac{82483294977}{17} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -73\) , \( 490\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2-73{x}+490$ |
| 17.1-b1 |
17.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 17^{8} \) |
$1.49625$ |
$(a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$2.123938699$ |
1.030261599 |
\( -\frac{35937}{83521} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( -14\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-{x}-14$ |
| 17.1-b2 |
17.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$1.49625$ |
$(a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$8.495754796$ |
1.030261599 |
\( \frac{35937}{17} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-{x}$ |
| 17.1-b3 |
17.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 17^{4} \) |
$1.49625$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$4.247877398$ |
1.030261599 |
\( \frac{20346417}{289} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -6\) , \( -4\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-6{x}-4$ |
| 17.1-b4 |
17.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$1.49625$ |
$(a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$2.123938699$ |
1.030261599 |
\( \frac{82483294977}{17} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -91\) , \( -310\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-91{x}-310$ |
| 18.2-a1 |
18.2-a |
$4$ |
$10$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{32} \cdot 3^{4} \) |
$1.51779$ |
$(2,a+1), (3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.660916378$ |
1.290734033 |
\( \frac{141420761}{9216} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 53\) , \( 17 a - 39\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+53{x}+17a-39$ |
| 18.2-a2 |
18.2-a |
$4$ |
$10$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{40} \) |
$1.51779$ |
$(2,a+1), (3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \cdot 5 \) |
$1$ |
$0.266091637$ |
1.290734033 |
\( \frac{211293405175481}{6973568802} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 4973\) , \( -32527 a - 4959\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+4973{x}-32527a-4959$ |
| 18.2-a3 |
18.2-a |
$4$ |
$10$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{8} \) |
$1.51779$ |
$(2,a+1), (3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.330458189$ |
1.290734033 |
\( \frac{551569744601}{2592} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 693\) , \( 1553 a - 679\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+693{x}+1553a-679$ |
| 18.2-a4 |
18.2-a |
$4$ |
$10$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{20} \) |
$1.51779$ |
$(2,a+1), (3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.532183275$ |
1.290734033 |
\( \frac{206226044828441}{236196} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 4933\) , \( -33071 a - 4919\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+4933{x}-33071a-4919$ |
| 18.2-b1 |
18.2-b |
$4$ |
$10$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{32} \cdot 3^{4} \) |
$1.51779$ |
$(2,a+1), (3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.660916378$ |
1.290734033 |
\( \frac{141420761}{9216} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -2 a + 53\) , \( -18 a - 39\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+{x}^2+\left(-2a+53\right){x}-18a-39$ |
| 18.2-b2 |
18.2-b |
$4$ |
$10$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{40} \) |
$1.51779$ |
$(2,a+1), (3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \cdot 5 \) |
$1$ |
$0.266091637$ |
1.290734033 |
\( \frac{211293405175481}{6973568802} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -2 a + 4973\) , \( 32526 a - 4959\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+{x}^2+\left(-2a+4973\right){x}+32526a-4959$ |
| 18.2-b3 |
18.2-b |
$4$ |
$10$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{8} \) |
$1.51779$ |
$(2,a+1), (3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.330458189$ |
1.290734033 |
\( \frac{551569744601}{2592} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -2 a + 693\) , \( -1554 a - 679\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+{x}^2+\left(-2a+693\right){x}-1554a-679$ |
| 18.2-b4 |
18.2-b |
$4$ |
$10$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{20} \) |
$1.51779$ |
$(2,a+1), (3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.532183275$ |
1.290734033 |
\( \frac{206226044828441}{236196} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -2 a + 4933\) , \( 33070 a - 4919\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+{x}^2+\left(-2a+4933\right){x}+33070a-4919$ |
| 21.1-a1 |
21.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{3} \cdot 7 \) |
$1.57742$ |
$(3,a+1), (7,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 1 \) |
$1$ |
$6.848611844$ |
1.661032354 |
\( \frac{3217408}{189} a - \frac{13885504}{189} \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( -4 a\) , \( -a + 16\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3+a{x}^2-4a{x}-a+16$ |
| 21.1-a2 |
21.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{15} \cdot 7^{5} \) |
$1.57742$ |
$(3,a+1), (7,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 5 \) |
$1$ |
$1.369722368$ |
1.661032354 |
\( \frac{706359389796352}{241162079949} a - \frac{1978295271552064}{241162079949} \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( -14 a + 10\) , \( 8 a + 181\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3+a{x}^2+\left(-14a+10\right){x}+8a+181$ |
| 21.1-b1 |
21.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{3} \cdot 7 \) |
$1.57742$ |
$(3,a+1), (7,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 3 \) |
$1$ |
$6.848611844$ |
4.983097062 |
\( \frac{3217408}{189} a - \frac{13885504}{189} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -5 a - 6\) , \( a + 14\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(-5a-6\right){x}+a+14$ |
| 21.1-b2 |
21.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{15} \cdot 7^{5} \) |
$1.57742$ |
$(3,a+1), (7,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 3 \cdot 5 \) |
$1$ |
$1.369722368$ |
4.983097062 |
\( \frac{706359389796352}{241162079949} a - \frac{1978295271552064}{241162079949} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -15 a + 4\) , \( 32 a - 11\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(-15a+4\right){x}+32a-11$ |
| 21.4-a1 |
21.4-a |
$2$ |
$5$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
21.4 |
\( 3 \cdot 7 \) |
\( 3^{3} \cdot 7 \) |
$1.57742$ |
$(3,a+2), (7,a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 1 \) |
$1$ |
$6.848611844$ |
1.661032354 |
\( -\frac{3217408}{189} a - \frac{13885504}{189} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -5 a - 9\) , \( a + 20\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+a{x}^2+\left(-5a-9\right){x}+a+20$ |
| 21.4-a2 |
21.4-a |
$2$ |
$5$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
21.4 |
\( 3 \cdot 7 \) |
\( 3^{15} \cdot 7^{5} \) |
$1.57742$ |
$(3,a+2), (7,a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 5 \) |
$1$ |
$1.369722368$ |
1.661032354 |
\( -\frac{706359389796352}{241162079949} a - \frac{1978295271552064}{241162079949} \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( 5 a + 1\) , \( 2 a + 15\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+a{x}^2+\left(5a+1\right){x}+2a+15$ |
| 21.4-b1 |
21.4-b |
$2$ |
$5$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
21.4 |
\( 3 \cdot 7 \) |
\( 3^{3} \cdot 7 \) |
$1.57742$ |
$(3,a+2), (7,a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 3 \) |
$1$ |
$6.848611844$ |
4.983097062 |
\( -\frac{3217408}{189} a - \frac{13885504}{189} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -6 a + 3\) , \( 2 a + 27\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3+\left(a-1\right){x}^2+\left(-6a+3\right){x}+2a+27$ |
| 21.4-b2 |
21.4-b |
$2$ |
$5$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
21.4 |
\( 3 \cdot 7 \) |
\( 3^{15} \cdot 7^{5} \) |
$1.57742$ |
$(3,a+2), (7,a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 3 \cdot 5 \) |
$1$ |
$1.369722368$ |
4.983097062 |
\( -\frac{706359389796352}{241162079949} a - \frac{1978295271552064}{241162079949} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 4 a + 13\) , \( -19 a - 168\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3+\left(a-1\right){x}^2+\left(4a+13\right){x}-19a-168$ |
| 27.2-a1 |
27.2-a |
$2$ |
$11$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 3^{30} \) |
$1.67971$ |
$(3,a+1), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$11$ |
11B |
$1$ |
\( 2 \) |
$1$ |
$2.631011483$ |
1.276228029 |
\( -\frac{44425216}{177147} a + \frac{73392128}{177147} \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 9 a - 45\) , \( -54 a - 88\bigr] \) |
${y}^2+{y}={x}^3+\left(a+1\right){x}^2+\left(9a-45\right){x}-54a-88$ |
| 27.2-a2 |
27.2-a |
$2$ |
$11$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
27.2 |
\( 3^{3} \) |
\( 2^{12} \cdot 3^{18} \) |
$1.67971$ |
$(3,a+1), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$11$ |
11B |
$1$ |
\( 2 \) |
$1$ |
$2.631011483$ |
1.276228029 |
\( \frac{44425216}{177147} a + \frac{73392128}{177147} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2 a - 28\) , \( -4 a + 34\bigr] \) |
${y}^2={x}^3+\left(a+1\right){x}^2+\left(2a-28\right){x}-4a+34$ |
*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.
