| 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 |
| 147.1-a1 |
147.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( - 3 \cdot 7^{2} \) |
$1.07785$ |
$(a), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$64$ |
\( 1 \) |
$1$ |
$0.203505108$ |
0.939949835 |
\( -\frac{796905901939896846693217}{21} a + 65727691000542993279720 \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 3395 a - 6664\) , \( 153951 a - 275173\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(3395a-6664\right){x}+153951a-275173$ |
| 147.1-a2 |
147.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{16} \) |
$1.07785$ |
$(a), (7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.814020435$ |
0.939949835 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( -217\bigr] \) |
${y}^2+{x}{y}={x}^{3}-34{x}-217$ |
| 147.1-a3 |
147.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{4} \cdot 7^{2} \) |
$1.07785$ |
$(a), (7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$13.02432697$ |
0.939949835 |
\( \frac{103823}{63} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -56 a + 97\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-56a+97\right){x}$ |
| 147.1-a4 |
147.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{8} \cdot 7^{4} \) |
$1.07785$ |
$(a), (7)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$13.02432697$ |
0.939949835 |
\( \frac{7189057}{3969} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -4\) , \( -1\bigr] \) |
${y}^2+{x}{y}={x}^{3}-4{x}-1$ |
| 147.1-a5 |
147.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{16} \cdot 7^{2} \) |
$1.07785$ |
$(a), (7)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$13.02432697$ |
0.939949835 |
\( \frac{6570725617}{45927} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -39\) , \( 90\bigr] \) |
${y}^2+{x}{y}={x}^{3}-39{x}+90$ |
| 147.1-a6 |
147.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{4} \cdot 7^{8} \) |
$1.07785$ |
$(a), (7)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$3.256081743$ |
0.939949835 |
\( \frac{13027640977}{21609} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -49\) , \( -136\bigr] \) |
${y}^2+{x}{y}={x}^{3}-49{x}-136$ |
| 147.1-a7 |
147.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{4} \) |
$1.07785$ |
$(a), (7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$1$ |
$0.814020435$ |
0.939949835 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -784\) , \( -8515\bigr] \) |
${y}^2+{x}{y}={x}^{3}-784{x}-8515$ |
| 147.1-a8 |
147.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( - 3 \cdot 7^{2} \) |
$1.07785$ |
$(a), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$64$ |
\( 1 \) |
$1$ |
$0.203505108$ |
0.939949835 |
\( \frac{796905901939896846693217}{21} a + 65727691000542993279720 \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -3395 a - 6664\) , \( -153951 a - 275173\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-3395a-6664\right){x}-153951a-275173$ |
| 147.1-b1 |
147.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( - 3 \cdot 7^{2} \) |
$1.07785$ |
$(a), (7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$5.970393669$ |
$7.303763884$ |
1.573508462 |
\( -\frac{796905901939896846693217}{21} a + 65727691000542993279720 \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 3395 a - 6664\) , \( -153951 a + 275173\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(3395a-6664\right){x}-153951a+275173$ |
| 147.1-b2 |
147.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{16} \) |
$1.07785$ |
$(a), (7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.746299208$ |
$3.651881942$ |
1.573508462 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -34\) , \( 217\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-34{x}+217$ |
| 147.1-b3 |
147.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{4} \cdot 7^{2} \) |
$1.07785$ |
$(a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.373149604$ |
$14.60752776$ |
1.573508462 |
\( \frac{103823}{63} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -54 a + 96\) , \( -55 a + 96\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-54a+96\right){x}-55a+96$ |
| 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 |
\( \frac{7189057}{3969} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -4\) , \( 1\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-4{x}+1$ |
| 147.1-b5 |
147.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{16} \cdot 7^{2} \) |
$1.07785$ |
$(a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.492598417$ |
$3.651881942$ |
1.573508462 |
\( \frac{6570725617}{45927} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -39\) , \( -90\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-39{x}-90$ |
| 147.1-b6 |
147.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( 3^{4} \cdot 7^{8} \) |
$1.07785$ |
$(a), (7)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.492598417$ |
$14.60752776$ |
1.573508462 |
\( \frac{13027640977}{21609} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -49\) , \( 136\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-49{x}+136$ |
| 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 |
\( \frac{53297461115137}{147} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -784\) , \( 8515\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-784{x}+8515$ |
| 147.1-b8 |
147.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
147.1 |
\( 3 \cdot 7^{2} \) |
\( - 3 \cdot 7^{2} \) |
$1.07785$ |
$(a), (7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$5.970393669$ |
$7.303763884$ |
1.573508462 |
\( \frac{796905901939896846693217}{21} a + 65727691000542993279720 \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -3395 a - 6664\) , \( 153951 a + 275173\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-3395a-6664\right){x}+153951a+275173$ |
*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.
