| 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 |
| 147.2-a8 |
147.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
147.2 |
\( 3 \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{4} \) |
$0.53893$ |
$(-2a+1), (-3a+1), (3a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.862076929$ |
0.497720347 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -784\) , \( -8515\bigr] \) |
${y}^2+{x}{y}={x}^{3}-784{x}-8515$ |
| 3969.1-a6 |
3969.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
3969.1 |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{14} \cdot 7^{4} \) |
$1.41853$ |
$(3), (7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$16$ |
\( 2^{3} \) |
$1$ |
$0.287358976$ |
2.298871812 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-7056{x}+229905$ |
| 567.1-a8 |
567.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( 3^{14} \cdot 7^{4} \) |
$1.15367$ |
$(-2a+1), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$10.55403529$ |
$0.287358976$ |
2.292578873 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-7056{x}+229905$ |
| 3969.3-c6 |
3969.3-c |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3969.3 |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{14} \cdot 7^{4} \) |
$2.00611$ |
$(-a-1), (a-1), (7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$1$ |
$0.287358976$ |
1.625547847 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-7056{x}+229905$ |
| 3969.3-a6 |
3969.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3969.3 |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{14} \cdot 7^{4} \) |
$2.35237$ |
$(-a), (a-1), (7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$1$ |
$0.287358976$ |
1.386271862 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-7056{x}+229905$ |
| 147.1-b6 |
147.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-15}) \) |
$2$ |
$[0, 1]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{2} \cdot 7^{4} \) |
$1.20507$ |
$(3,a+1), (7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$1$ |
$0.862076929$ |
1.780698448 |
\( \frac{53297461115137}{147} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 784 a + 2352\) , \( -25545 a + 59605\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(-a+1\right){x}^2+\left(784a+2352\right){x}-25545a+59605$ |
| 3969.2-a6 |
3969.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-19}) \) |
$2$ |
$[0, 1]$ |
3969.2 |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{14} \cdot 7^{4} \) |
$3.09162$ |
$(-a-1), (a-2), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$14.77683246$ |
$0.287358976$ |
3.896631243 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-7056{x}+229905$ |
| 147.2-b6 |
147.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
147.2 |
\( 3 \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{2} \cdot 7^{4} \) |
$1.52431$ |
$(3,a), (a+1), (a-1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$7.803842251$ |
$0.862076929$ |
2.746495423 |
\( \frac{53297461115137}{147} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -3131\) , \( -64983\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2-3131{x}-64983$ |
| 3969.2-c6 |
3969.2-c |
$6$ |
$8$ |
\(\Q(\sqrt{-31}) \) |
$2$ |
$[0, 1]$ |
3969.2 |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{14} \cdot 7^{4} \) |
$3.94902$ |
$(7,a+2), (7,a+4), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$46.51496090$ |
$0.287358976$ |
9.602771015 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-7056{x}+229905$ |
| 567.3-b6 |
567.3-b |
$6$ |
$8$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
567.3 |
\( 3^{4} \cdot 7 \) |
\( 3^{14} \cdot 7^{4} \) |
$2.57969$ |
$(3,a), (3,a+2), (7,a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$7.203395932$ |
$0.287358976$ |
2.799097454 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-7056{x}+229905$ |
| 147.1-c6 |
147.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-39}) \) |
$2$ |
$[0, 1]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{14} \cdot 7^{4} \) |
$1.94312$ |
$(3,a+1), (7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$10.68582211$ |
$0.862076929$ |
5.900402673 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-7056{x}+229905$ |
| 3969.1-a6 |
3969.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-43}) \) |
$2$ |
$[0, 1]$ |
3969.1 |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{14} \cdot 7^{4} \) |
$4.65096$ |
$(3), (7)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$41.41165303$ |
$0.287358976$ |
7.258938190 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-7056{x}+229905$ |
| 147.1-a6 |
147.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-51}) \) |
$2$ |
$[0, 1]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{14} \cdot 7^{4} \) |
$2.22205$ |
$(3,a+1), (7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$1$ |
$0.862076929$ |
0.965719324 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-7056{x}+229905$ |
| 567.3-b6 |
567.3-b |
$6$ |
$8$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
567.3 |
\( 3^{4} \cdot 7 \) |
\( 3^{14} \cdot 7^{4} \) |
$3.26308$ |
$(3,a+1), (3,a+2), (7,a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$23.79400264$ |
$0.287358976$ |
7.309509707 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-7056{x}+229905$ |
| 3969.1-a6 |
3969.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
3969.1 |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{14} \cdot 7^{4} \) |
$5.80559$ |
$(3), (7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$64$ |
\( 2^{3} \) |
$1$ |
$0.287358976$ |
2.246815135 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-7056{x}+229905$ |
| 21.1-d6 |
21.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{-21}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{14} \cdot 7^{4} \) |
$1.75321$ |
$(3,a), (7,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$64$ |
\( 2^{2} \) |
$1$ |
$0.862076929$ |
3.009929740 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-7056{x}+229905$ |
| 147.2-b6 |
147.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
147.2 |
\( 3 \cdot 7^{2} \) |
\( 3^{14} \cdot 7^{4} \) |
$2.90220$ |
$(3,a+1), (7,a+2), (7,a+4)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$18.05542860$ |
$0.862076929$ |
3.337522441 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-7056{x}+229905$ |
| 567.1-b6 |
567.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-91}) \) |
$2$ |
$[0, 1]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( 3^{14} \cdot 7^{4} \) |
$4.15963$ |
$(7,a+3), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$21.91753817$ |
$0.287358976$ |
5.281847170 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-7056{x}+229905$ |
| 147.2-b6 |
147.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-111}) \) |
$2$ |
$[0, 1]$ |
147.2 |
\( 3 \cdot 7^{2} \) |
\( 3^{14} \cdot 7^{4} \) |
$3.27815$ |
$(3,a+1), (7,a), (7,a+6)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$64$ |
\( 2^{3} \) |
$1$ |
$1.724153859$ |
5.236782148 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-7056{x}+229905$ |
| 567.3-b6 |
567.3-b |
$6$ |
$8$ |
\(\Q(\sqrt{-119}) \) |
$2$ |
$[0, 1]$ |
567.3 |
\( 3^{4} \cdot 7 \) |
\( 3^{14} \cdot 7^{4} \) |
$4.75672$ |
$(3,a), (3,a+2), (7,a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$53.60428359$ |
$0.574717953$ |
11.29641842 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-7056{x}+229905$ |
| 147.1-d6 |
147.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{14} \cdot 7^{4} \) |
$3.40846$ |
$(3,a), (7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$6.003874339$ |
$0.862076929$ |
7.559742041 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-7056{x}+229905$ |
| 3969.1-a6 |
3969.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
3969.1 |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{14} \cdot 7^{4} \) |
$9.05530$ |
$(3), (7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$64$ |
\( 2^{3} \) |
$1$ |
$0.287358976$ |
1.440492296 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-7056{x}+229905$ |
| 21.1-d6 |
21.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{-42}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{14} \cdot 7^{4} \) |
$2.47941$ |
$(3,a), (7,a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$13.74319437$ |
$0.862076929$ |
3.656276762 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-7056{x}+229905$ |
| 21.1-a6 |
21.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-231}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{14} \cdot 7^{4} \) |
$2.90736$ |
$(3,a+1), (7,a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$26.22178070$ |
$0.862076929$ |
5.949249809 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-7056{x}+229905$ |
| 21.1-d6 |
21.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{-399}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{14} \cdot 7^{4} \) |
$3.82102$ |
$(3,a+1), (7,a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$256$ |
\( 2^{2} \) |
$1$ |
$0.862076929$ |
5.524201923 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-7056{x}+229905$ |
| 21.1-f6 |
21.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{-105}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{14} \cdot 7^{4} \) |
$3.92029$ |
$(3,a), (7,a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$6.382650789$ |
$0.862076929$ |
4.295784079 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-7056{x}+229905$ |
| 21.1-a6 |
21.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-483}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{14} \cdot 7^{4} \) |
$4.20404$ |
$(3,a+1), (7,a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$11.79695750$ |
$0.862076929$ |
1.850983143 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-7056{x}+229905$ |
| 21.1-d6 |
21.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{-651}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{14} \cdot 7^{4} \) |
$4.88072$ |
$(3,a+1), (7,a+3)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$169.5761951$ |
$1.724153859$ |
11.45909740 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-7056{x}+229905$ |
| 21.1-h6 |
21.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{-210}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{14} \cdot 7^{4} \) |
$5.54413$ |
$(3,a), (7,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$256$ |
\( 2^{2} \) |
$1$ |
$1.724153859$ |
3.807293431 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-7056{x}+229905$ |
| 21.1-h6 |
21.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{-903}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{14} \cdot 7^{4} \) |
$5.74827$ |
$(3,a+1), (7,a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$256$ |
\( 2^{2} \) |
$1$ |
$1.724153859$ |
3.672079858 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-7056{x}+229905$ |
| 21.1-a6 |
21.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-987}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{14} \cdot 7^{4} \) |
$6.00969$ |
$(3,a+1), (7,a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$27.75195510$ |
$1.724153859$ |
3.046078015 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-7056{x}+229905$ |
| 3969.1-d6 |
3969.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
3969.1 |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{14} \cdot 7^{4} \) |
$1.58597$ |
$(3), (7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.945149794$ |
$4.869175922$ |
2.058121966 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-7056{x}+229905$ |
| 3969.1-b6 |
3969.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
3969.1 |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{14} \cdot 7^{4} \) |
$2.00611$ |
$(-2a+1), (2a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$4.869175922$ |
1.721513656 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-7056{x}+229905$ |
| 147.1-b7 |
147.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{4} \) |
$1.07785$ |
$(a), (7)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$2.985196834$ |
$14.60752776$ |
1.573508462 |
\( \frac{53297461115137}{147} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -784\) , \( 8515\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-784{x}+8515$ |
| 21.1-a6 |
21.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{2} \cdot 7^{4} \) |
$0.87660$ |
$(-a+2), (a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$14.60752776$ |
0.796905972 |
\( \frac{53297461115137}{147} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 3920 a - 10977\) , \( -200440 a + 559528\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(3920a-10977\right){x}-200440a+559528$ |
| 147.1-h6 |
147.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{4} \) |
$1.52431$ |
$(a+3), (7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$14.60752776$ |
2.981749119 |
\( \frac{53297461115137}{147} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 15680 a - 38419\) , \( -1670290 a + 4091357\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(15680a-38419\right){x}-1670290a+4091357$ |
| 567.1-l8 |
567.1-l |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( 3^{14} \cdot 7^{4} \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$4.869175922$ |
1.840375511 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-7056{x}+229905$ |
| 147.1-b6 |
147.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{4} \) |
$1.78741$ |
$(-2a+7), (7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$14.60752776$ |
2.542844193 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -288519 a - 684447\) , \( 142523801 a + 338106550\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-288519a-684447\right){x}+142523801a+338106550$ |
| 147.1-c6 |
147.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{4} \) |
$2.34912$ |
$(4a+13), (2a+7), (-2a+9)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$14.60752776$ |
0.967407159 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( 9470971 a - 40487615\) , \( -30838100363 a + 131830326198\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(9470971a-40487615\right){x}-30838100363a+131830326198$ |
| 147.1-a6 |
147.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{2} \cdot 7^{4} \) |
$2.41015$ |
$(3,a), (7,a+1), (7,a+6)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.889580479$ |
$14.60752776$ |
5.449239426 |
\( \frac{53297461115137}{147} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -25090 a - 97212\) , \( 4241382 a + 16426848\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-25090a-97212\right){x}+4241382a+16426848$ |
| 147.1-j6 |
147.1-j |
$6$ |
$8$ |
\(\Q(\sqrt{93}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{4} \) |
$3.00061$ |
$(a+4), (-a+6), (a+5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$14.60752776$ |
0.757365033 |
\( \frac{53297461115137}{147} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 68211 a - 363001\) , \( -21253170 a + 113105674\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(68211a-363001\right){x}-21253170a+113105674$ |
| 21.1-a6 |
21.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{105}) \) |
$2$ |
$[2, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 2^{12} \cdot 3^{2} \cdot 7^{4} \) |
$1.96014$ |
$(3,a+1), (7,a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$7.725929285$ |
$14.60752776$ |
5.506844384 |
\( \frac{53297461115137}{147} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -72917 a - 337127\) , \( 24227822 a + 112016739\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-72917a-337127\right){x}+24227822a+112016739$ |
| 21.1-b6 |
21.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{42}) \) |
$2$ |
$[2, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 2^{12} \cdot 3^{2} \cdot 7^{4} \) |
$2.47941$ |
$(3,a), (a+7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$8.753013071$ |
$14.60752776$ |
4.932302010 |
\( \frac{53297461115137}{147} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -163084 a - 1056802\) , \( 90983532 a + 589640870\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-163084a-1056802\right){x}+90983532a+589640870$ |
| 189.1-b6 |
189.1-b |
$6$ |
$8$ |
\(\Q(\zeta_{21})^+\) |
$6$ |
$[6, 0]$ |
189.1 |
\( 3^{3} \cdot 7 \) |
\( 3^{6} \cdot 7^{12} \) |
$93.16884$ |
$(a^5-6a^3+a^2+9a-4), (a^3+a^2-2a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3116.952339$ |
1.15676 |
\( \frac{53297461115137}{147} \) |
\( \bigl[a^{5} + a^{4} - 4 a^{3} - 3 a^{2} + 3 a + 1\) , \( -a^{5} - a^{4} + 4 a^{3} + 2 a^{2} - a + 3\) , \( a^{5} + a^{4} - 5 a^{3} - 2 a^{2} + 6 a - 2\) , \( 22736 a^{5} + 16464 a^{4} - 109761 a^{3} - 54880 a^{2} + 94084 a - 12540\) , \( -2875736 a^{5} - 1923843 a^{4} + 14089280 a^{3} + 6320192 a^{2} - 12636786 a + 1701779\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-4a^{3}-3a^{2}+3a+1\right){x}{y}+\left(a^{5}+a^{4}-5a^{3}-2a^{2}+6a-2\right){y}={x}^{3}+\left(-a^{5}-a^{4}+4a^{3}+2a^{2}-a+3\right){x}^{2}+\left(22736a^{5}+16464a^{4}-109761a^{3}-54880a^{2}+94084a-12540\right){x}-2875736a^{5}-1923843a^{4}+14089280a^{3}+6320192a^{2}-12636786a+1701779$ |
*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.
