| 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 |
| 162.1-a1 |
162.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
162.1 |
\( 2 \cdot 3^{4} \) |
\( 2 \cdot 3^{46} \) |
$1.68693$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.708490014$ |
1.071136220 |
\( -\frac{22026189082216125793}{3706040377703682} a - \frac{54626740869226485845}{3706040377703682} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -60588 a + 160290\) , \( -11487731 a + 30393691\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-60588a+160290\right){x}-11487731a+30393691$ |
| 162.1-a2 |
162.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
162.1 |
\( 2 \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{20} \) |
$1.68693$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.833960059$ |
1.071136220 |
\( \frac{4913}{1296} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 153 a + 405\) , \( 35698 a + 94448\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(153a+405\right){x}+35698a+94448$ |
| 162.1-a3 |
162.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
162.1 |
\( 2 \cdot 3^{4} \) |
\( 2 \cdot 3^{46} \) |
$1.68693$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2^{3} \) |
$1$ |
$0.177122503$ |
1.071136220 |
\( \frac{22026189082216125793}{3706040377703682} a - \frac{54626740869226485845}{3706040377703682} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 60588 a + 160290\) , \( -11487731 a - 30393691\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(60588a+160290\right){x}-11487731a-30393691$ |
| 162.1-a4 |
162.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
162.1 |
\( 2 \cdot 3^{4} \) |
\( 2^{2} \cdot 3^{32} \) |
$1.68693$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$1$ |
$0.708490014$ |
1.071136220 |
\( -\frac{15840177853915205}{86093442} a + \frac{20954710660855016}{43046721} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -20457 a - 54135\) , \( -1643612 a - 4348600\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-20457a-54135\right){x}-1643612a-4348600$ |
| 162.1-a5 |
162.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
162.1 |
\( 2 \cdot 3^{4} \) |
\( 2^{4} \cdot 3^{28} \) |
$1.68693$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$2.833960059$ |
1.071136220 |
\( \frac{838561807}{26244} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -8487 a - 22455\) , \( 675418 a + 1786988\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-8487a-22455\right){x}+675418a+1786988$ |
| 162.1-a6 |
162.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
162.1 |
\( 2 \cdot 3^{4} \) |
\( 2 \cdot 3^{22} \) |
$1.68693$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2^{3} \) |
$1$ |
$0.177122503$ |
1.071136220 |
\( -\frac{2350503708439404473473}{13122} a + \frac{6218848268321376696725}{13122} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -293022 a - 775440\) , \( -140361053 a - 371361301\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-293022a-775440\right){x}-140361053a-371361301$ |
| 162.1-a7 |
162.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
162.1 |
\( 2 \cdot 3^{4} \) |
\( 2^{2} \cdot 3^{32} \) |
$1.68693$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$2.833960059$ |
1.071136220 |
\( \frac{15840177853915205}{86093442} a + \frac{20954710660855016}{43046721} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 20457 a - 54135\) , \( -1643612 a + 4348600\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(20457a-54135\right){x}-1643612a+4348600$ |
| 162.1-a8 |
162.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
162.1 |
\( 2 \cdot 3^{4} \) |
\( 2 \cdot 3^{22} \) |
$1.68693$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.833960059$ |
1.071136220 |
\( \frac{2350503708439404473473}{13122} a + \frac{6218848268321376696725}{13122} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 293022 a - 775440\) , \( -140361053 a + 371361301\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(293022a-775440\right){x}-140361053a+371361301$ |
| 162.1-b1 |
162.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
162.1 |
\( 2 \cdot 3^{4} \) |
\( 2 \cdot 3^{46} \) |
$1.68693$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2^{3} \) |
$1$ |
$0.177122503$ |
1.071136220 |
\( -\frac{22026189082216125793}{3706040377703682} a - \frac{54626740869226485845}{3706040377703682} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -60588 a + 160290\) , \( 11487731 a - 30393691\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-60588a+160290\right){x}+11487731a-30393691$ |
| 162.1-b2 |
162.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
162.1 |
\( 2 \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{20} \) |
$1.68693$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.833960059$ |
1.071136220 |
\( \frac{4913}{1296} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 153 a + 405\) , \( -35698 a - 94448\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(153a+405\right){x}-35698a-94448$ |
| 162.1-b3 |
162.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
162.1 |
\( 2 \cdot 3^{4} \) |
\( 2 \cdot 3^{46} \) |
$1.68693$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.708490014$ |
1.071136220 |
\( \frac{22026189082216125793}{3706040377703682} a - \frac{54626740869226485845}{3706040377703682} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 60588 a + 160290\) , \( 11487731 a + 30393691\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(60588a+160290\right){x}+11487731a+30393691$ |
| 162.1-b4 |
162.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
162.1 |
\( 2 \cdot 3^{4} \) |
\( 2^{2} \cdot 3^{32} \) |
$1.68693$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$2.833960059$ |
1.071136220 |
\( -\frac{15840177853915205}{86093442} a + \frac{20954710660855016}{43046721} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -20457 a - 54135\) , \( 1643612 a + 4348600\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-20457a-54135\right){x}+1643612a+4348600$ |
| 162.1-b5 |
162.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
162.1 |
\( 2 \cdot 3^{4} \) |
\( 2^{4} \cdot 3^{28} \) |
$1.68693$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$2.833960059$ |
1.071136220 |
\( \frac{838561807}{26244} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -8487 a - 22455\) , \( -675418 a - 1786988\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-8487a-22455\right){x}-675418a-1786988$ |
| 162.1-b6 |
162.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
162.1 |
\( 2 \cdot 3^{4} \) |
\( 2 \cdot 3^{22} \) |
$1.68693$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.833960059$ |
1.071136220 |
\( -\frac{2350503708439404473473}{13122} a + \frac{6218848268321376696725}{13122} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -293022 a - 775440\) , \( 140361053 a + 371361301\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-293022a-775440\right){x}+140361053a+371361301$ |
| 162.1-b7 |
162.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
162.1 |
\( 2 \cdot 3^{4} \) |
\( 2^{2} \cdot 3^{32} \) |
$1.68693$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$1$ |
$0.708490014$ |
1.071136220 |
\( \frac{15840177853915205}{86093442} a + \frac{20954710660855016}{43046721} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 20457 a - 54135\) , \( 1643612 a - 4348600\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(20457a-54135\right){x}+1643612a-4348600$ |
| 162.1-b8 |
162.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
162.1 |
\( 2 \cdot 3^{4} \) |
\( 2 \cdot 3^{22} \) |
$1.68693$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2^{3} \) |
$1$ |
$0.177122503$ |
1.071136220 |
\( \frac{2350503708439404473473}{13122} a + \frac{6218848268321376696725}{13122} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 293022 a - 775440\) , \( 140361053 a - 371361301\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(293022a-775440\right){x}+140361053a-371361301$ |
*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.
