| 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 |
| 1600.1-a1 |
1600.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{8} \) |
$4.11440$ |
$(2), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$2.203480391$ |
0.605342618 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^{3}+13{x}-34$ |
| 1600.1-a2 |
1600.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{4} \) |
$4.11440$ |
$(2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$8.813921565$ |
0.605342618 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( -6\bigr] \) |
${y}^2={x}^{3}-7{x}-6$ |
| 1600.1-a3 |
1600.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{2} \) |
$4.11440$ |
$(2), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$35.25568626$ |
0.605342618 |
\( \frac{55296}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( 1\bigr] \) |
${y}^2={x}^{3}-2{x}+1$ |
| 1600.1-a4 |
1600.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{2} \) |
$4.11440$ |
$(2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$2.203480391$ |
0.605342618 |
\( \frac{132304644}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -107\) , \( -426\bigr] \) |
${y}^2={x}^{3}-107{x}-426$ |
| 1600.1-b1 |
1600.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{8} \) |
$4.11440$ |
$(2), (5)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$1.270433879$ |
$3.205725375$ |
8.950770658 |
\( -\frac{821390690371892}{625} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -137660 a - 432640\) , \( 52928900 a + 166203100\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-137660a-432640\right){x}+52928900a+166203100$ |
| 1600.1-c1 |
1600.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( - 2^{22} \cdot 5^{4} \) |
$4.11440$ |
$(2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$6.044745514$ |
$7.846500256$ |
6.515024903 |
\( -\frac{29851898}{25} a + \frac{123619346}{25} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 32 a + 96\) , \( 160 a + 512\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(32a+96\right){x}+160a+512$ |
| 1600.1-c2 |
1600.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{2} \) |
$4.11440$ |
$(2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$3.022372757$ |
$15.69300051$ |
6.515024903 |
\( -\frac{948}{5} a + \frac{15832}{5} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -8 a - 24\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-8a-24\right){x}$ |
| 1600.1-d1 |
1600.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{2} \) |
$4.11440$ |
$(2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$3.022372757$ |
$15.69300051$ |
6.515024903 |
\( \frac{948}{5} a + \frac{14884}{5} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 10 a - 33\) , \( -9 a + 33\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(10a-33\right){x}-9a+33$ |
| 1600.1-d2 |
1600.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( - 2^{22} \cdot 5^{4} \) |
$4.11440$ |
$(2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$6.044745514$ |
$7.846500256$ |
6.515024903 |
\( \frac{29851898}{25} a + \frac{93767448}{25} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -30 a + 127\) , \( -129 a + 545\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-30a+127\right){x}-129a+545$ |
| 1600.1-e1 |
1600.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( - 2^{20} \cdot 5^{12} \) |
$4.11440$ |
$(2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$11.62616602$ |
$1.960782111$ |
6.262646773 |
\( -\frac{6616468}{15625} a + \frac{47886672}{15625} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 314 a - 1289\) , \( 4695 a - 19447\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(314a-1289\right){x}+4695a-19447$ |
| 1600.1-e2 |
1600.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{6} \) |
$4.11440$ |
$(2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$5.813083010$ |
$3.921564222$ |
6.262646773 |
\( -\frac{221751024}{125} a + \frac{918342928}{125} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -225 a - 707\) , \( -1767 a - 5549\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-225a-707\right){x}-1767a-5549$ |
| 1600.1-f1 |
1600.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{8} \) |
$4.11440$ |
$(2), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{3} \) |
$6.871930383$ |
$0.520550584$ |
7.861831607 |
\( -\frac{23929792539828}{625} a - \frac{75140863388804}{625} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -119 a - 360\) , \( -1547 a - 2900\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-119a-360\right){x}-1547a-2900$ |
| 1600.1-g1 |
1600.1-g |
$1$ |
$1$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{8} \) |
$4.11440$ |
$(2), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{3} \) |
$6.871930383$ |
$0.520550584$ |
7.861831607 |
\( \frac{23929792539828}{625} a - \frac{99070655928632}{625} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 119 a - 479\) , \( 1547 a - 4447\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(119a-479\right){x}+1547a-4447$ |
| 1600.1-h1 |
1600.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( - 2^{20} \cdot 5^{12} \) |
$4.11440$ |
$(2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$11.62616602$ |
$1.960782111$ |
6.262646773 |
\( \frac{6616468}{15625} a + \frac{41270204}{15625} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -312 a - 976\) , \( -5008 a - 15728\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-312a-976\right){x}-5008a-15728$ |
| 1600.1-h2 |
1600.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{53}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{6} \) |
$4.11440$ |
$(2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$5.813083010$ |
$3.921564222$ |
6.262646773 |
\( \frac{221751024}{125} a + \frac{696591904}{125} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 225 a - 932\) , \( 1767 a - 7316\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(225a-932\right){x}+1767a-7316$ |
*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.
