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 |
1.1-a1 |
1.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{106}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$1.84002$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$33.67140610$ |
1.635228035 |
\( 25777 a + 264235 \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( -262494 a - 2702508\) , \( -235431668 a - 2423917415\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-262494a-2702508\right){x}-235431668a-2423917415$ |
1.1-b1 |
1.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{106}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$1.84002$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$33.67140610$ |
1.635228035 |
\( -25777 a + 264235 \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 262494 a - 2702508\) , \( 235431668 a - 2423917415\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(262494a-2702508\right){x}+235431668a-2423917415$ |
1.1-c1 |
1.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{106}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( - 2^{12} \) |
$1.84002$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$33.67140610$ |
1.635228035 |
\( -25777 a + 264235 \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 1049995 a - 10809937\) , \( 1882093082 a - 19377332290\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(1049995a-10809937\right){x}+1882093082a-19377332290$ |
1.1-d1 |
1.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{106}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( - 2^{12} \) |
$1.84002$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$33.67140610$ |
1.635228035 |
\( 25777 a + 264235 \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -1049995 a - 10809937\) , \( -1882093082 a - 19377332290\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1049995a-10809937\right){x}-1882093082a-19377332290$ |
3.1-a1 |
3.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{106}) \) |
$2$ |
$[2, 0]$ |
3.1 |
\( 3 \) |
\( 3^{12} \) |
$2.42160$ |
$(3,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$7.279780841$ |
0.707074821 |
\( \frac{917674496}{531441} a - \frac{12306610112}{531441} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -301050 a - 3099043\) , \( 329963957 a + 3397188706\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-301050a-3099043\right){x}+329963957a+3397188706$ |
3.1-b1 |
3.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{106}) \) |
$2$ |
$[2, 0]$ |
3.1 |
\( 3 \) |
\( 2^{12} \cdot 3^{4} \) |
$2.42160$ |
$(3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$1.056683201$ |
$12.28540203$ |
5.043606958 |
\( \frac{78884}{81} a - \frac{804137}{81} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 19 a + 241\) , \( 100 a + 1190\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(19a+241\right){x}+100a+1190$ |
3.1-c1 |
3.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{106}) \) |
$2$ |
$[2, 0]$ |
3.1 |
\( 3 \) |
\( 3^{4} \) |
$2.42160$ |
$(3,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$12.28540203$ |
1.193263731 |
\( \frac{78884}{81} a - \frac{804137}{81} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 37\) , \( -4 a + 2\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+37{x}-4a+2$ |
3.1-d1 |
3.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{106}) \) |
$2$ |
$[2, 0]$ |
3.1 |
\( 3 \) |
\( 2^{12} \cdot 3^{12} \) |
$2.42160$ |
$(3,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \cdot 3 \) |
$0.879054255$ |
$7.279780841$ |
7.458685570 |
\( \frac{917674496}{531441} a - \frac{12306610112}{531441} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 2738701812 a - 28196660894\) , \( 255545025319958 a - 2630997065063416\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(2738701812a-28196660894\right){x}+255545025319958a-2630997065063416$ |
3.2-a1 |
3.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{106}) \) |
$2$ |
$[2, 0]$ |
3.2 |
\( 3 \) |
\( 3^{12} \) |
$2.42160$ |
$(3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$7.279780841$ |
0.707074821 |
\( -\frac{917674496}{531441} a - \frac{12306610112}{531441} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( 301049 a - 3099043\) , \( -329963957 a + 3397188706\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(301049a-3099043\right){x}-329963957a+3397188706$ |
3.2-b1 |
3.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{106}) \) |
$2$ |
$[2, 0]$ |
3.2 |
\( 3 \) |
\( 2^{12} \cdot 3^{4} \) |
$2.42160$ |
$(3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$1.056683201$ |
$12.28540203$ |
5.043606958 |
\( -\frac{78884}{81} a - \frac{804137}{81} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -19 a + 241\) , \( -100 a + 1190\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-19a+241\right){x}-100a+1190$ |
3.2-c1 |
3.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{106}) \) |
$2$ |
$[2, 0]$ |
3.2 |
\( 3 \) |
\( 3^{4} \) |
$2.42160$ |
$(3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$12.28540203$ |
1.193263731 |
\( -\frac{78884}{81} a - \frac{804137}{81} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 37\) , \( 4 a + 2\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+37{x}+4a+2$ |
3.2-d1 |
3.2-d |
$1$ |
$1$ |
\(\Q(\sqrt{106}) \) |
$2$ |
$[2, 0]$ |
3.2 |
\( 3 \) |
\( 2^{12} \cdot 3^{12} \) |
$2.42160$ |
$(3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \cdot 3 \) |
$0.879054255$ |
$7.279780841$ |
7.458685570 |
\( -\frac{917674496}{531441} a - \frac{12306610112}{531441} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -2738701812 a - 28196660894\) , \( -255545025319958 a - 2630997065063416\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2738701812a-28196660894\right){x}-255545025319958a-2630997065063416$ |
*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.