| 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 |
| 39375.1-a1 |
39375.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39375.1 |
\( 3^{2} \cdot 5^{4} \cdot 7 \) |
\( 3^{12} \cdot 5^{6} \cdot 7^{4} \) |
$3.33037$ |
$(-2a+1), (3), (5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.134262002$ |
$1.093395684$ |
2.663315968 |
\( \frac{300763}{35721} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 7\) , \( 102\bigr] \) |
${y}^2+{x}{y}={x}^{3}+7{x}+102$ |
| 39375.1-a2 |
39375.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39375.1 |
\( 3^{2} \cdot 5^{4} \cdot 7 \) |
\( 3^{6} \cdot 5^{6} \cdot 7^{2} \) |
$3.33037$ |
$(-2a+1), (3), (5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.134262002$ |
$2.186791368$ |
2.663315968 |
\( \frac{5177717}{189} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -18\) , \( 27\bigr] \) |
${y}^2+{x}{y}={x}^{3}-18{x}+27$ |
| 39375.1-b1 |
39375.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39375.1 |
\( 3^{2} \cdot 5^{4} \cdot 7 \) |
\( 3^{8} \cdot 5^{14} \cdot 7^{8} \) |
$3.33037$ |
$(-2a+1), (3), (5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.472583225$ |
$0.278729474$ |
3.186340268 |
\( \frac{590589719}{972405} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 437\) , \( -4594\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+437{x}-4594$ |
| 39375.1-b2 |
39375.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39375.1 |
\( 3^{2} \cdot 5^{4} \cdot 7 \) |
\( 3^{4} \cdot 5^{16} \cdot 7^{4} \) |
$3.33037$ |
$(-2a+1), (3), (5)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.890332903$ |
$0.557458948$ |
3.186340268 |
\( \frac{47045881}{11025} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -188\) , \( -844\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-188{x}-844$ |
| 39375.1-b3 |
39375.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39375.1 |
\( 3^{2} \cdot 5^{4} \cdot 7 \) |
\( 3^{2} \cdot 5^{14} \cdot 7^{2} \) |
$3.33037$ |
$(-2a+1), (3), (5)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.890332903$ |
$1.114917897$ |
3.186340268 |
\( \frac{1771561}{105} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -63\) , \( 156\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-63{x}+156$ |
| 39375.1-b4 |
39375.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39375.1 |
\( 3^{2} \cdot 5^{4} \cdot 7 \) |
\( 3^{2} \cdot 5^{20} \cdot 7^{2} \) |
$3.33037$ |
$(-2a+1), (3), (5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.890332903$ |
$0.278729474$ |
3.186340268 |
\( \frac{157551496201}{13125} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -2813\) , \( -58594\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-2813{x}-58594$ |
| 39375.1-c1 |
39375.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39375.1 |
\( 3^{2} \cdot 5^{4} \cdot 7 \) |
\( 3^{12} \cdot 5^{18} \cdot 7^{4} \) |
$3.33037$ |
$(-2a+1), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1.254903327$ |
$0.218679136$ |
4.978629856 |
\( \frac{300763}{35721} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 175\) , \( 12750\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+175{x}+12750$ |
| 39375.1-c2 |
39375.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39375.1 |
\( 3^{2} \cdot 5^{4} \cdot 7 \) |
\( 3^{6} \cdot 5^{18} \cdot 7^{2} \) |
$3.33037$ |
$(-2a+1), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$2.509806654$ |
$0.437358273$ |
4.978629856 |
\( \frac{5177717}{189} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -450\) , \( 3375\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-450{x}+3375$ |
| 39375.1-d1 |
39375.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39375.1 |
\( 3^{2} \cdot 5^{4} \cdot 7 \) |
\( 3^{2} \cdot 5^{12} \cdot 7^{16} \) |
$3.33037$ |
$(-2a+1), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1.931482321$ |
$0.172415385$ |
8.055596601 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -850\) , \( -27125\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-850{x}-27125$ |
| 39375.1-d2 |
39375.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39375.1 |
\( 3^{2} \cdot 5^{4} \cdot 7 \) |
\( 3^{4} \cdot 5^{12} \cdot 7^{2} \) |
$3.33037$ |
$(-2a+1), (3), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$3.862964642$ |
$1.379323087$ |
8.055596601 |
\( \frac{103823}{63} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 25\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+25{x}$ |
| 39375.1-d3 |
39375.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39375.1 |
\( 3^{2} \cdot 5^{4} \cdot 7 \) |
\( 3^{8} \cdot 5^{12} \cdot 7^{4} \) |
$3.33037$ |
$(-2a+1), (3), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1.931482321$ |
$0.689661543$ |
8.055596601 |
\( \frac{7189057}{3969} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -100\) , \( -125\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-100{x}-125$ |
| 39375.1-d4 |
39375.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39375.1 |
\( 3^{2} \cdot 5^{4} \cdot 7 \) |
\( 3^{2} \cdot 5^{12} \cdot 7 \) |
$3.33037$ |
$(-2a+1), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$7.725929285$ |
$1.379323087$ |
8.055596601 |
\( \frac{2940226}{21} a + \frac{2980207}{21} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -51 a + 41\) , \( 49 a - 246\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-51a+41\right){x}+49a-246$ |
| 39375.1-d5 |
39375.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39375.1 |
\( 3^{2} \cdot 5^{4} \cdot 7 \) |
\( 3^{16} \cdot 5^{12} \cdot 7^{2} \) |
$3.33037$ |
$(-2a+1), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.965741160$ |
$0.344830771$ |
8.055596601 |
\( \frac{6570725617}{45927} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -975\) , \( 11250\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-975{x}+11250$ |
| 39375.1-d6 |
39375.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39375.1 |
\( 3^{2} \cdot 5^{4} \cdot 7 \) |
\( 3^{2} \cdot 5^{12} \cdot 7 \) |
$3.33037$ |
$(-2a+1), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$7.725929285$ |
$1.379323087$ |
8.055596601 |
\( -\frac{2940226}{21} a + \frac{5920433}{21} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 50 a - 10\) , \( -50 a - 197\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(50a-10\right){x}-50a-197$ |
| 39375.1-d7 |
39375.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39375.1 |
\( 3^{2} \cdot 5^{4} \cdot 7 \) |
\( 3^{4} \cdot 5^{12} \cdot 7^{8} \) |
$3.33037$ |
$(-2a+1), (3), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$3.862964642$ |
$0.344830771$ |
8.055596601 |
\( \frac{13027640977}{21609} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -1225\) , \( -17000\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-1225{x}-17000$ |
| 39375.1-d8 |
39375.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39375.1 |
\( 3^{2} \cdot 5^{4} \cdot 7 \) |
\( 3^{2} \cdot 5^{12} \cdot 7^{4} \) |
$3.33037$ |
$(-2a+1), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$7.725929285$ |
$0.172415385$ |
8.055596601 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -19600\) , \( -1064375\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-19600{x}-1064375$ |
*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.
