| 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 |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( - 2^{6} \cdot 5^{2} \) |
$1.59850$ |
$(a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$14.94486967$ |
1.320952336 |
\( -\frac{77940121832}{5} a + \frac{110223977912}{5} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 12 a - 15\) , \( -34 a + 42\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(12a-15\right){x}-34a+42$ |
| 1600.1-a2 |
1600.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( - 2^{6} \cdot 5^{8} \) |
$1.59850$ |
$(a), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$14.94486967$ |
1.320952336 |
\( \frac{1263688}{625} a + \frac{1755832}{625} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -3 a - 4\) , \( a + 4\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a-4\right){x}+a+4$ |
| 1600.1-a3 |
1600.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{4} \) |
$1.59850$ |
$(a), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$14.94486967$ |
1.320952336 |
\( -\frac{1759488}{25} a + \frac{2779712}{25} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -8\) , \( -4 a + 2\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-8{x}-4a+2$ |
| 1600.1-a4 |
1600.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{2} \) |
$1.59850$ |
$(a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$7.472434838$ |
1.320952336 |
\( \frac{209816832}{5} a + \frac{296734528}{5} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -12 a - 20\) , \( -44 a - 62\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-12a-20\right){x}-44a-62$ |
| 1600.1-b1 |
1600.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( - 2^{6} \cdot 5^{8} \) |
$1.59850$ |
$(a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.668326260$ |
2.004055968 |
\( -\frac{1263688}{625} a + \frac{1755832}{625} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 3 a - 4\) , \( a - 4\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(3a-4\right){x}+a-4$ |
| 1600.1-b2 |
1600.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{2} \) |
$1.59850$ |
$(a), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$22.67330504$ |
2.004055968 |
\( -\frac{209816832}{5} a + \frac{296734528}{5} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 12 a - 20\) , \( -44 a + 62\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(12a-20\right){x}-44a+62$ |
| 1600.1-b3 |
1600.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{4} \) |
$1.59850$ |
$(a), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$11.33665252$ |
2.004055968 |
\( \frac{1759488}{25} a + \frac{2779712}{25} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -8\) , \( -4 a - 2\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}-8{x}-4a-2$ |
| 1600.1-b4 |
1600.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( - 2^{6} \cdot 5^{2} \) |
$1.59850$ |
$(a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$5.668326260$ |
2.004055968 |
\( \frac{77940121832}{5} a + \frac{110223977912}{5} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -12 a - 15\) , \( -34 a - 43\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-12a-15\right){x}-34a-43$ |
| 1600.1-c1 |
1600.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( - 2^{6} \cdot 5^{8} \) |
$1.59850$ |
$(a), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$14.94486967$ |
1.320952336 |
\( -\frac{1263688}{625} a + \frac{1755832}{625} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 3 a - 4\) , \( -a + 4\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(3a-4\right){x}-a+4$ |
| 1600.1-c2 |
1600.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{2} \) |
$1.59850$ |
$(a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$7.472434838$ |
1.320952336 |
\( -\frac{209816832}{5} a + \frac{296734528}{5} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 12 a - 20\) , \( 44 a - 62\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(12a-20\right){x}+44a-62$ |
| 1600.1-c3 |
1600.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{4} \) |
$1.59850$ |
$(a), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$14.94486967$ |
1.320952336 |
\( \frac{1759488}{25} a + \frac{2779712}{25} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -8\) , \( 4 a + 2\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}-8{x}+4a+2$ |
| 1600.1-c4 |
1600.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( - 2^{6} \cdot 5^{2} \) |
$1.59850$ |
$(a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$14.94486967$ |
1.320952336 |
\( \frac{77940121832}{5} a + \frac{110223977912}{5} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -12 a - 15\) , \( 34 a + 42\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-12a-15\right){x}+34a+42$ |
| 1600.1-d1 |
1600.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( - 2^{6} \cdot 5^{2} \) |
$1.59850$ |
$(a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$5.668326260$ |
2.004055968 |
\( -\frac{77940121832}{5} a + \frac{110223977912}{5} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 12 a - 15\) , \( 34 a - 43\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(12a-15\right){x}+34a-43$ |
| 1600.1-d2 |
1600.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( - 2^{6} \cdot 5^{8} \) |
$1.59850$ |
$(a), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.668326260$ |
2.004055968 |
\( \frac{1263688}{625} a + \frac{1755832}{625} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -3 a - 4\) , \( -a - 4\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-3a-4\right){x}-a-4$ |
| 1600.1-d3 |
1600.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{4} \) |
$1.59850$ |
$(a), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$11.33665252$ |
2.004055968 |
\( -\frac{1759488}{25} a + \frac{2779712}{25} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -8\) , \( 4 a - 2\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-8{x}+4a-2$ |
| 1600.1-d4 |
1600.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1600.1 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{2} \) |
$1.59850$ |
$(a), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$22.67330504$ |
2.004055968 |
\( \frac{209816832}{5} a + \frac{296734528}{5} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -12 a - 20\) , \( 44 a + 62\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-12a-20\right){x}+44a+62$ |
*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.
