| 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 |
| 1600.1-a1 |
1600.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{8} \) |
$0.97888$ |
$(2), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.683761292$ |
$1.498444490$ |
1.183081163 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^{3}+13{x}-34$ |
| 200.2-a3 |
200.2-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
200.2 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{8} \) |
$0.67209$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/4\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$2.996888981$ |
0.749222245 |
\( \frac{237276}{625} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( -4\) , \( -6 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}-4{x}-6i$ |
| 1600.4-a1 |
1600.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1600.4 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{8} \) |
$1.49526$ |
$(a), (-a+1), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.498444490$ |
1.132717564 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^{3}+13{x}-34$ |
| 200.1-a1 |
200.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{8} \) |
$0.95048$ |
$(a), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.996888981$ |
1.059560260 |
\( \frac{237276}{625} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 5\) , \( 3\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+5{x}+3$ |
| 1600.2-c1 |
1600.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
1600.2 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{8} \) |
$1.87441$ |
$(-a-1), (a-2), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.498444490$ |
1.807192052 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^{3}+13{x}-34$ |
| 320.4-b1 |
320.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{-15}) \) |
$2$ |
$[0, 1]$ |
320.4 |
\( 2^{6} \cdot 5 \) |
\( 2^{20} \cdot 5^{8} \) |
$1.46377$ |
$(2,a), (2,a+1), (5,a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.498444490$ |
1.547586815 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 1600.2-g1 |
1600.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{-19}) \) |
$2$ |
$[0, 1]$ |
1600.2 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{8} \) |
$2.46346$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.498444490$ |
1.375066970 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 40.1-a1 |
40.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{20} \cdot 5^{8} \) |
$1.00501$ |
$(2,a+1), (-a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.233348375$ |
$2.996888981$ |
1.250980172 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 1600.4-a1 |
1600.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
1600.4 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{8} \) |
$2.71039$ |
$(2,a), (2,a+1), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.498444490$ |
0.624894550 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 200.2-b1 |
200.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
200.2 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{8} \) |
$1.64627$ |
$(2,a), (5,a+2), (5,a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.500528594$ |
$2.996888981$ |
2.449536493 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 1600.11-c1 |
1600.11-c |
$4$ |
$4$ |
\(\Q(\sqrt{-31}) \) |
$2$ |
$[0, 1]$ |
1600.11 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{8} \) |
$3.14666$ |
$(2,a), (2,a+1), (5,a+1), (5,a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.699561828$ |
$1.498444490$ |
3.012353254 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 320.1-b1 |
320.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-35}) \) |
$2$ |
$[0, 1]$ |
320.1 |
\( 2^{6} \cdot 5 \) |
\( 2^{20} \cdot 5^{8} \) |
$2.23594$ |
$(5,a+2), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$3.156731320$ |
$1.498444490$ |
3.198189902 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 40.1-b1 |
40.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{20} \cdot 5^{8} \) |
$1.42129$ |
$(2,a), (5,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.996888981$ |
0.947699507 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 1600.1-a1 |
1600.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-43}) \) |
$2$ |
$[0, 1]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{8} \) |
$3.70598$ |
$(2), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$11.23155550$ |
$1.498444490$ |
5.133059930 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 200.1-a1 |
200.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{8} \) |
$2.42325$ |
$(2,a+1), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.602809268$ |
$2.996888981$ |
2.664469907 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 320.4-a1 |
320.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{-55}) \) |
$2$ |
$[0, 1]$ |
320.4 |
\( 2^{6} \cdot 5 \) |
\( 2^{20} \cdot 5^{8} \) |
$2.80290$ |
$(2,a), (2,a+1), (5,a+2)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.611369997$ |
$1.498444490$ |
5.209242443 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 200.2-b1 |
200.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
200.2 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{8} \) |
$2.51472$ |
$(2,a), (5,a+1), (5,a+4)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.064365342$ |
$2.996888981$ |
3.410023352 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 1600.1-a1 |
1600.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{8} \) |
$4.62600$ |
$(2), (5)$ |
$0 \le r \le 1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
|
\( 2^{3} \) |
$1$ |
$1.498444490$ |
6.161930377 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 200.1-b1 |
200.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{8} \) |
$2.77109$ |
$(2,a+1), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.804637456$ |
$2.996888981$ |
2.623409925 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 200.2-c1 |
200.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-21}) \) |
$2$ |
$[0, 1]$ |
200.2 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{8} \) |
$3.07989$ |
$(2,a+1), (5,a+2), (5,a+3)$ |
$0 \le r \le 2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$2.996888981$ |
2.615899163 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 200.1-b1 |
200.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{8} \) |
$3.15237$ |
$(2,a), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$2.996888981$ |
1.277877755 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 320.4-c1 |
320.4-c |
$4$ |
$4$ |
\(\Q(\sqrt{-95}) \) |
$2$ |
$[0, 1]$ |
320.4 |
\( 2^{6} \cdot 5 \) |
\( 2^{20} \cdot 5^{8} \) |
$3.68373$ |
$(2,a), (2,a+1), (5,a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$1$ |
$1.498444490$ |
2.459794575 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 200.2-b1 |
200.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-26}) \) |
$2$ |
$[0, 1]$ |
200.2 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{8} \) |
$3.42699$ |
$(2,a), (5,a+2), (5,a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.176669492$ |
$2.996888981$ |
2.766294836 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 320.1-b1 |
320.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-115}) \) |
$2$ |
$[0, 1]$ |
320.1 |
\( 2^{6} \cdot 5 \) |
\( 2^{20} \cdot 5^{8} \) |
$4.05298$ |
$(5,a+2), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$4.382942589$ |
$1.498444490$ |
2.449726005 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 40.1-c1 |
40.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{20} \cdot 5^{8} \) |
$2.46175$ |
$(2,a), (5,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$2.996888981$ |
2.188618263 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 1600.1-a1 |
1600.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{8} \) |
$7.21543$ |
$(2), (5)$ |
$0 \le r \le 1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
|
\( 2^{3} \) |
$1$ |
$1.498444490$ |
5.033737337 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 40.1-c1 |
40.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-65}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{20} \cdot 5^{8} \) |
$3.62360$ |
$(2,a+1), (5,a)$ |
$0 \le r \le 1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
|
\( 2^{5} \) |
$1$ |
$2.996888981$ |
5.870014372 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 40.1-c1 |
40.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-70}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{20} \cdot 5^{8} \) |
$3.76039$ |
$(2,a), (5,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$2.996888981$ |
1.432786980 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 40.1-a1 |
40.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-85}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{20} \cdot 5^{8} \) |
$4.14374$ |
$(2,a+1), (5,a)$ |
$0 \le r \le 1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
|
\( 2^{5} \) |
$1$ |
$2.996888981$ |
6.254106428 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 40.1-f1 |
40.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{-105}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{20} \cdot 5^{8} \) |
$4.60551$ |
$(2,a+1), (5,a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$4.623610654$ |
$2.996888981$ |
5.409003378 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 40.1-c1 |
40.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-110}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{20} \cdot 5^{8} \) |
$4.71389$ |
$(2,a), (5,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$2.996888981$ |
1.142968611 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 40.1-c1 |
40.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-130}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{20} \cdot 5^{8} \) |
$5.12454$ |
$(2,a), (5,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$5.993777963$ |
1.051378205 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 40.1-b1 |
40.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-145}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{20} \cdot 5^{8} \) |
$5.41212$ |
$(2,a+1), (5,a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$5.502003167$ |
$5.993777963$ |
5.477312016 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 40.1-g1 |
40.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{20} \cdot 5^{8} \) |
$5.77332$ |
$(2,a+1), (5,a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$8.225321734$ |
$5.993777963$ |
7.676116700 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 40.1-c1 |
40.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-170}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{20} \cdot 5^{8} \) |
$5.86014$ |
$(2,a), (5,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$5.993777963$ |
0.919403569 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 40.1-c1 |
40.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-185}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{20} \cdot 5^{8} \) |
$6.11321$ |
$(2,a+1), (5,a)$ |
$0 \le r \le 1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
|
\( 2^{5} \) |
$1$ |
$5.993777963$ |
2.474600764 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 40.1-d1 |
40.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-190}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{20} \cdot 5^{8} \) |
$6.19527$ |
$(2,a), (5,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$5.993777963$ |
0.869668712 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 40.1-g1 |
40.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{-205}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{20} \cdot 5^{8} \) |
$6.43518$ |
$(2,a+1), (5,a)$ |
$1 \le r \le 3$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$10.83516030$ |
$5.993777963$ |
9.071707876 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 40.1-e1 |
40.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{-210}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{20} \cdot 5^{8} \) |
$6.51318$ |
$(2,a), (5,a)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$15.16846859$ |
$5.993777963$ |
12.54765981 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 40.1-c1 |
40.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-230}) \) |
$2$ |
$[0, 1]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{20} \cdot 5^{8} \) |
$6.81628$ |
$(2,a), (5,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$5.993777963$ |
0.790436030 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^3+13{x}-34$ |
| 320.1-a3 |
320.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
320.1 |
\( 2^{6} \cdot 5 \) |
\( 2^{20} \cdot 5^{8} \) |
$0.84511$ |
$(-2a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.203480391$ |
0.985426388 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^{3}+13{x}-34$ |
| 200.1-a1 |
200.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{8} \) |
$0.95048$ |
$(a), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.722205338$ |
$4.406960782$ |
1.125265195 |
\( \frac{237276}{625} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 3\) , \( -3\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+3{x}-3$ |
| 200.1-a1 |
200.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{8} \) |
$1.16409$ |
$(a+1), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$4.406960782$ |
1.272179997 |
\( \frac{237276}{625} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 13 a + 25\) , \( -52 a - 91\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(13a+25\right){x}-52a-91$ |
| 1600.1-d1 |
1600.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{8} \) |
$2.03770$ |
$(2), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$2.203480391$ |
1.222271005 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^{3}+13{x}-34$ |
| 1600.1-h1 |
1600.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{8} \) |
$2.58987$ |
$(-a), (-a+1), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$2.003472968$ |
$2.203480391$ |
3.853390490 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^{3}+13{x}-34$ |
| 200.1-a1 |
200.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{8} \) |
$1.64627$ |
$(-a+2), (-a-1), (-a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$4.406960782$ |
1.799134205 |
\( \frac{237276}{625} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 65 a + 157\) , \( -809 a - 1983\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(65a+157\right){x}-809a-1983$ |
| 200.1-a1 |
200.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{8} \) |
$1.77818$ |
$(a+3), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$4.406960782$ |
0.832837304 |
\( \frac{237276}{625} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 158 a + 417\) , \( -2887 a - 7639\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(158a+417\right){x}-2887a-7639$ |
| 40.1-b1 |
40.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{20} \cdot 5^{8} \) |
$1.42129$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.548473301$ |
$4.406960782$ |
2.157957601 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^{3}+13{x}-34$ |
| 200.1-j1 |
200.1-j |
$4$ |
$4$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
200.1 |
\( 2^{3} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{8} \) |
$2.22906$ |
$(a+3), (a-4), (-a-4)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.544509781$ |
$4.406960782$ |
2.894066593 |
\( \frac{237276}{625} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 198 a + 658\) , \( -4566 a - 15144\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(198a+658\right){x}-4566a-15144$ |
| 1600.1-a1 |
1600.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{8} \) |
$4.11440$ |
$(2), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$2.203480391$ |
0.605342618 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^{3}+13{x}-34$ |
*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.
