| 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 |
| 6400.1-g2 |
6400.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
6400.1 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{4} \) |
$1.38434$ |
$(2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$2.996888981$ |
1.730254660 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \) |
${y}^2={x}^{3}-7{x}+6$ |
| 200.2-a6 |
200.2-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
200.2 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{4} \) |
$0.67209$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$5.993777963$ |
0.749222245 |
\( \frac{148176}{25} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i + 1\) , \( i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-i+1\right){x}+i$ |
| 6400.5-b2 |
6400.5-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6400.5 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{4} \) |
$2.11462$ |
$(a), (-a+1), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$2.996888981$ |
1.132717564 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \) |
${y}^2={x}^{3}-7{x}+6$ |
| 400.1-a2 |
400.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
400.1 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{4} \) |
$1.13031$ |
$(a), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1.444410676$ |
$5.993777963$ |
1.530440152 |
\( \frac{148176}{25} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-{x}$ |
| 6400.2-k2 |
6400.2-k |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
6400.2 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{4} \) |
$2.65082$ |
$(-a-1), (a-2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.089019562$ |
$2.996888981$ |
3.936134998 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \) |
${y}^2={x}^{3}-7{x}+6$ |
| 6400.2-z2 |
6400.2-z |
$4$ |
$4$ |
\(\Q(\sqrt{-19}) \) |
$2$ |
$[0, 1]$ |
6400.2 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{4} \) |
$3.48386$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$2.312918637$ |
$2.996888981$ |
6.360836047 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \) |
${y}^2={x}^3-7{x}+6$ |
| 40.1-b2 |
40.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$1.00501$ |
$(2,a+1), (-a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$5.993777963$ |
1.340249496 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \) |
${y}^2={x}^3-7{x}+6$ |
| 400.2-c2 |
400.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
400.2 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{4} \) |
$1.95776$ |
$(2,a), (5,a+2), (5,a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$5.993777963$ |
2.446949607 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \) |
${y}^2={x}^3-7{x}+6$ |
| 80.1-d2 |
80.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
80.1 |
\( 2^{4} \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$1.69021$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$3.096946603$ |
$5.993777963$ |
2.934974771 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \) |
${y}^2={x}^3-7{x}+6$ |
| 6400.1-a2 |
6400.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-43}) \) |
$2$ |
$[0, 1]$ |
6400.1 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{4} \) |
$5.24104$ |
$(2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$2.996888981$ |
0.457021285 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \) |
${y}^2={x}^3-7{x}+6$ |
| 200.1-b2 |
200.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{4} \) |
$2.42325$ |
$(2,a+1), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$5.993777963$ |
1.662374906 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \) |
${y}^2={x}^3-7{x}+6$ |
| 400.2-c2 |
400.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
400.2 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{4} \) |
$2.99053$ |
$(2,a), (5,a+1), (5,a+4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$5.993777963$ |
1.601904542 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \) |
${y}^2={x}^3-7{x}+6$ |
| 6400.1-a2 |
6400.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
6400.1 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{4} \) |
$6.54216$ |
$(2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$2.996888981$ |
0.366128261 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \) |
${y}^2={x}^3-7{x}+6$ |
| 200.1-c2 |
200.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{4} \) |
$2.77109$ |
$(2,a+1), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$6.070137225$ |
$5.993777963$ |
4.412093461 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \) |
${y}^2={x}^3-7{x}+6$ |
| 200.2-d2 |
200.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-21}) \) |
$2$ |
$[0, 1]$ |
200.2 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{4} \) |
$3.07989$ |
$(2,a+1), (5,a+2), (5,a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1.001736484$ |
$5.993777963$ |
5.240883262 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \) |
${y}^2={x}^3-7{x}+6$ |
| 400.1-a2 |
400.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
400.1 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{4} \) |
$3.74882$ |
$(2,a), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$2.297278241$ |
$5.993777963$ |
2.935640763 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \) |
${y}^2={x}^3-7{x}+6$ |
| 400.2-a2 |
400.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-26}) \) |
$2$ |
$[0, 1]$ |
400.2 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{4} \) |
$4.07540$ |
$(2,a), (5,a+2), (5,a+3)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$1$ |
$5.993777963$ |
4.701906276 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \) |
${y}^2={x}^3-7{x}+6$ |
| 80.1-e2 |
80.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
80.1 |
\( 2^{4} \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$2.92753$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1.700133785$ |
$5.993777963$ |
3.720943853 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \) |
${y}^2={x}^3-7{x}+6$ |
| 40.1-d2 |
40.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-65}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$3.62360$ |
$(2,a+1), (5,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$4.284375854$ |
$5.993777963$ |
3.185162070 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \) |
${y}^2={x}^3-7{x}+6$ |
| 40.1-b2 |
40.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-85}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$4.14374$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$5.993777963$ |
1.300232997 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \) |
${y}^2={x}^3-7{x}+6$ |
| 40.1-g2 |
40.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{-105}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$4.60551$ |
$(2,a+1), (5,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$2.326448801$ |
$5.993777963$ |
5.443265174 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \) |
${y}^2={x}^3-7{x}+6$ |
| 80.1-f2 |
80.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{-110}) \) |
$2$ |
$[0, 1]$ |
80.1 |
\( 2^{4} \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$5.60580$ |
$(2,a), (5,a)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
|
\( 2^{2} \) |
$1$ |
$5.993777963$ |
9.395398294 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \) |
${y}^2={x}^3-7{x}+6$ |
| 40.1-c2 |
40.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-145}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$5.41212$ |
$(2,a+1), (5,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$3.848507369$ |
$11.98755592$ |
7.662473109 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \) |
${y}^2={x}^3-7{x}+6$ |
| 40.1-e2 |
40.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$5.77332$ |
$(2,a+1), (5,a)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$3.164408531$ |
$11.98755592$ |
11.81248343 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \) |
${y}^2={x}^3-7{x}+6$ |
| 80.1-e2 |
80.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{-170}) \) |
$2$ |
$[0, 1]$ |
80.1 |
\( 2^{4} \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$6.96892$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$5.863068628$ |
$11.98755592$ |
5.390526227 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \) |
${y}^2={x}^3-7{x}+6$ |
| 40.1-d2 |
40.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$6.11321$ |
$(2,a+1), (5,a)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
|
\( 2^{3} \) |
$1$ |
$11.98755592$ |
9.951038614 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \) |
${y}^2={x}^3-7{x}+6$ |
| 40.1-e2 |
40.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{-205}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$6.43518$ |
$(2,a+1), (5,a)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$12.58239617$ |
$11.98755592$ |
10.53457625 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \) |
${y}^2={x}^3-7{x}+6$ |
| 80.1-f2 |
80.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{-230}) \) |
$2$ |
$[0, 1]$ |
80.1 |
\( 2^{4} \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$8.10597$ |
$(2,a), (5,a)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
|
\( 2^{2} \) |
$1$ |
$11.98755592$ |
7.804526344 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \) |
${y}^2={x}^3-7{x}+6$ |
| 1280.1-i4 |
1280.1-i |
$8$ |
$16$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1280.1 |
\( 2^{8} \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$1.19516$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.466696751$ |
$16.30392283$ |
1.701421401 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \) |
${y}^2={x}^{3}-7{x}+6$ |
| 400.1-b2 |
400.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
400.1 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{4} \) |
$1.13031$ |
$(a), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$32.60784567$ |
1.441076799 |
\( \frac{148176}{25} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-{x}$ |
| 200.1-b2 |
200.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{4} \) |
$1.16409$ |
$(a+1), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.341880646$ |
$32.60784567$ |
1.609073952 |
\( \frac{148176}{25} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -8 a - 12\) , \( 5 a + 8\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-8a-12\right){x}+5a+8$ |
| 400.1-d2 |
400.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
400.1 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{4} \) |
$1.95776$ |
$(-a+2), (-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1.001057188$ |
$32.60784567$ |
3.331542662 |
\( \frac{148176}{25} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -35 a - 85\) , \( 131 a + 321\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-35a-85\right){x}+131a+321$ |
| 200.1-e2 |
200.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{4} \) |
$1.77818$ |
$(a+3), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$32.60784567$ |
1.540575901 |
\( \frac{148176}{25} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -81 a - 214\) , \( 381 a + 1008\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-81a-214\right){x}+381a+1008$ |
| 80.1-c2 |
80.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
80.1 |
\( 2^{4} \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$1.69021$ |
$(2,a), (5,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$32.60784567$ |
1.288938274 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \) |
${y}^2={x}^{3}-7{x}+6$ |
| 200.1-a2 |
200.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{4} \) |
$2.22906$ |
$(a+3), (a-4), (-a-4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$32.60784567$ |
2.457908848 |
\( \frac{148176}{25} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -103 a - 343\) , \( 621 a + 2058\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-103a-343\right){x}+621a+2058$ |
| 40.1-d2 |
40.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$1.74072$ |
$(2,a+1), (5,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$32.60784567$ |
2.104827387 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \) |
${y}^2={x}^{3}-7{x}+6$ |
| 200.1-e2 |
200.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{19}) \) |
$2$ |
$[2, 0]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{4} \) |
$2.92956$ |
$(-3a+13), (2a+9), (-2a+9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$32.60784567$ |
1.870188211 |
\( \frac{148176}{25} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 23210 a - 101132\) , \( -3385427 a + 14756800\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(23210a-101132\right){x}-3385427a+14756800$ |
| 200.1-a2 |
200.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{4} \) |
$3.22322$ |
$(-a+5), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$32.60784567$ |
0.849900729 |
\( \frac{148176}{25} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -414 a - 1985\) , \( 6798 a + 32602\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-414a-1985\right){x}+6798a+32602$ |
| 320.1-h4 |
320.1-h |
$8$ |
$16$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
320.1 |
\( 2^{6} \cdot 5 \) |
\( 2^{8} \cdot 5^{8} \) |
$8.21859$ |
$(a), (a^3-a^2-3a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.116674187$ |
$1063.271599$ |
2.773984325 |
\( \frac{148176}{25} \) |
\( \bigl[a^{2} + a - 3\) , \( a^{3} - 3 a - 1\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 7 a^{3} - 22 a - 10\) , \( -17 a^{3} - 8 a^{2} + 52 a + 45\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(a^{3}-3a-1\right){x}^{2}+\left(7a^{3}-22a-10\right){x}-17a^{3}-8a^{2}+52a+45$ |
*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.
