| 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 |
| 37632.2-f4 |
37632.2-f |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
37632.2 |
\( 2^{8} \cdot 3 \cdot 7^{2} \) |
\( 2^{24} \cdot 3^{8} \cdot 7^{4} \) |
$2.15570$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.746299208$ |
$0.862076929$ |
2.971586411 |
\( \frac{7189057}{3969} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -64\) , \( 64\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-64{x}+64$ |
| 441.1-a3 |
441.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{8} \cdot 7^{4} \) |
$0.81899$ |
$(3), (7)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.746299208$ |
$3.448307718$ |
0.643367330 |
\( \frac{7189057}{3969} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -4\) , \( 1\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-4{x}+1$ |
| 16128.5-i3 |
16128.5-i |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{24} \cdot 3^{8} \cdot 7^{4} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$0.746299208$ |
$0.862076929$ |
3.890719903 |
\( \frac{7189057}{3969} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -64\) , \( 64\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-64{x}+64$ |
| 7056.2-a3 |
7056.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
7056.2 |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{8} \cdot 7^{4} \) |
$2.31645$ |
$(a), (-a-1), (a-1), (7)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.364000081$ |
$1.724153859$ |
3.550197289 |
\( \frac{7189057}{3969} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -16\) , \( -8\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-16{x}-8$ |
| 441.5-d3 |
441.5-d |
$6$ |
$8$ |
\(\Q(\sqrt{-5}) \) |
$2$ |
$[0, 1]$ |
441.5 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{8} \cdot 7^{4} \) |
$1.83132$ |
$(3,a+1), (3,a+2), (7,a+3), (7,a+4)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.746299208$ |
$3.448307718$ |
2.301780936 |
\( \frac{7189057}{3969} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -4\) , \( 1\bigr] \) |
${y}^2+a{x}{y}={x}^3+{x}^2-4{x}+1$ |
| 441.2-b3 |
441.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
441.2 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{8} \cdot 7^{4} \) |
$2.95291$ |
$(7,a+1), (7,a+6), (3)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.993705147$ |
$3.448307718$ |
7.627026575 |
\( \frac{7189057}{3969} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 6\) , \( 7\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+6{x}+7$ |
| 441.5-a3 |
441.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
441.5 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{8} \cdot 7^{4} \) |
$3.37678$ |
$(3,a+1), (3,a+2), (7,a+2), (7,a+5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.746299208$ |
$3.448307718$ |
1.248315980 |
\( \frac{7189057}{3969} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 8\) , \( 8\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+8{x}+8$ |
| 21.1-c3 |
21.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-21}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{8} \cdot 7^{4} \) |
$1.75321$ |
$(3,a), (7,a)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.969117046$ |
$3.448307718$ |
2.963451981 |
\( \frac{7189057}{3969} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 9\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2+9{x}$ |
| 63.2-c3 |
63.2-c |
$6$ |
$8$ |
\(\Q(\sqrt{-77}) \) |
$2$ |
$[0, 1]$ |
63.2 |
\( 3^{2} \cdot 7 \) |
\( 3^{8} \cdot 7^{4} \) |
$4.41824$ |
$(3,a+1), (3,a+2), (7,a)$ |
$1 \le r \le 2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
|
\( 2^{4} \) |
|
$3.448307718$ |
7.690167758 |
\( \frac{7189057}{3969} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 107\) , \( -200\bigr] \) |
${y}^2+a{x}{y}={x}^3+{x}^2+107{x}-200$ |
| 21.1-a3 |
21.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-105}) \) |
$2$ |
$[0, 1]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{8} \cdot 7^{4} \) |
$3.92029$ |
$(3,a), (7,a)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1.343972171$ |
$3.448307718$ |
3.618192156 |
\( \frac{7189057}{3969} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 296\) , \( -686\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+296{x}-686$ |
| 63.1-d3 |
63.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{-133}) \) |
$2$ |
$[0, 1]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{8} \cdot 7^{4} \) |
$5.80670$ |
$(7,a), (3)$ |
$1 \le r \le 3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{4} \) |
$0.746299208$ |
$6.896615437$ |
7.140738896 |
\( \frac{7189057}{3969} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 431\) , \( -1283\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+431{x}-1283$ |
| 63.2-a3 |
63.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-161}) \) |
$2$ |
$[0, 1]$ |
63.2 |
\( 3^{2} \cdot 7 \) |
\( 3^{8} \cdot 7^{4} \) |
$6.38876$ |
$(3,a+1), (3,a+2), (7,a)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$2.201015012$ |
$6.896615437$ |
2.392632911 |
\( \frac{7189057}{3969} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 590\) , \( -2146\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+590{x}-2146$ |
| 63.1-c3 |
63.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-217}) \) |
$2$ |
$[0, 1]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{8} \cdot 7^{4} \) |
$7.41709$ |
$(7,a), (3)$ |
$2 \le r \le 3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
|
\( 2^{4} \) |
|
$6.896615437$ |
14.81235184 |
\( \frac{7189057}{3969} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 977\) , \( -5840\bigr] \) |
${y}^2+a{x}{y}={x}^3+977{x}-5840$ |
| 147.1-b4 |
147.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{8} \cdot 7^{4} \) |
$1.07785$ |
$(a), (7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.746299208$ |
$14.60752776$ |
1.573508462 |
\( \frac{7189057}{3969} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -4\) , \( 1\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-4{x}+1$ |
| 63.1-b4 |
63.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{8} \cdot 7^{4} \) |
$1.33215$ |
$(-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.746299208$ |
$14.60752776$ |
1.030103091 |
\( \frac{7189057}{3969} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -5\) , \( -4\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-5{x}-4$ |
| 441.1-d3 |
441.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{8} \cdot 7^{4} \) |
$2.71628$ |
$(a+2), (a-2), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.746299208$ |
$14.60752776$ |
3.286951977 |
\( \frac{7189057}{3969} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -7\) , \( -5\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-7{x}-5$ |
| 147.1-k3 |
147.1-k |
$6$ |
$8$ |
\(\Q(\sqrt{15}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{8} \cdot 7^{4} \) |
$2.41015$ |
$(3,a), (7,a+1), (7,a+6)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.705364543$ |
$14.60752776$ |
2.660386384 |
\( \frac{7189057}{3969} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -9\) , \( -6\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-9{x}-6$ |
*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.
