| 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 |
| 98.1-a1 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{36} \cdot 7^{2} \) |
$0.79523$ |
$(a), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$0.875417135$ |
0.309506696 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-171{x}-874$ |
| 784.1-c1 |
784.1-c |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{48} \cdot 7^{2} \) |
$1.33740$ |
$(a), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{2} \) |
$1$ |
$0.437708567$ |
2.785560266 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -682\) , \( -6990\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-682{x}-6990$ |
| 4802.1-a1 |
4802.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
4802.1 |
\( 2 \cdot 7^{4} \) |
\( 2^{36} \cdot 7^{14} \) |
$2.10397$ |
$(a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$12.63051067$ |
$0.125059590$ |
4.467688722 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -8355\) , \( 291341\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-8355{x}+291341$ |
| 7938.3-d1 |
7938.3-d |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
7938.3 |
\( 2 \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{36} \cdot 3^{12} \cdot 7^{2} \) |
$2.38568$ |
$(a), (-a-1), (a-1), (7)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$3.324049150$ |
$0.291805711$ |
5.487015846 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1535\) , \( 23591\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-1535{x}+23591$ |
| 28322.1-a1 |
28322.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
28322.1 |
\( 2 \cdot 7^{2} \cdot 17^{2} \) |
\( 2^{36} \cdot 7^{2} \cdot 17^{6} \) |
$3.27880$ |
$(a), (-2a+3), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.212319842$ |
2.702390401 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 2045 a - 170\) , \( 33202 a + 39319\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2045a-170\right){x}+33202a+39319$ |
| 28322.3-a1 |
28322.3-a |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
28322.3 |
\( 2 \cdot 7^{2} \cdot 17^{2} \) |
\( 2^{36} \cdot 7^{2} \cdot 17^{6} \) |
$3.27880$ |
$(a), (2a+3), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.212319842$ |
2.702390401 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -2047 a - 170\) , \( -33203 a + 39319\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-2047a-170\right){x}-33203a+39319$ |
| 38416.1-b1 |
38416.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
38416.1 |
\( 2^{4} \cdot 7^{4} \) |
\( 2^{48} \cdot 7^{14} \) |
$3.53844$ |
$(a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$3.507207167$ |
$0.062529795$ |
1.240576118 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -33421\) , \( 2364150\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-33421{x}+2364150$ |
*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.
