| 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 |
| 3364.1-b2 |
3364.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3364.1 |
\( 2^{2} \cdot 29^{2} \) |
\( 2^{20} \cdot 29^{2} \) |
$1.17873$ |
$(2), (29)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2 \cdot 5 \) |
$0.650453053$ |
$2.497049844$ |
1.500384344 |
\( \frac{13651919}{29696} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 5\) , \( 9\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+5{x}+9$ |
| 1682.2-b2 |
1682.2-b |
$2$ |
$5$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1682.2 |
\( 2 \cdot 29^{2} \) |
\( 2^{20} \cdot 29^{2} \) |
$1.14452$ |
$(a+1), (-2a+5), (2a+5)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$2.497049844$ |
1.997639875 |
\( \frac{13651919}{29696} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( 6\) , \( -9\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}+6{x}-9$ |
| 3364.5-b2 |
3364.5-b |
$2$ |
$5$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3364.5 |
\( 2^{2} \cdot 29^{2} \) |
\( 2^{20} \cdot 29^{2} \) |
$1.80054$ |
$(a), (-a+1), (-4a+1), (4a-3)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2^{2} \cdot 5^{2} \) |
$0.344312215$ |
$2.497049844$ |
5.199368580 |
\( \frac{13651919}{29696} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 5\) , \( 9\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+5{x}+9$ |
| 1682.1-b2 |
1682.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1682.1 |
\( 2 \cdot 29^{2} \) |
\( 2^{20} \cdot 29^{2} \) |
$1.61860$ |
$(a), (29)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.897754698$ |
$2.497049844$ |
2.536237287 |
\( \frac{13651919}{29696} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 5\) , \( 9\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+5{x}+9$ |
| 3364.1-b2 |
3364.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3364.1 |
\( 2^{2} \cdot 29^{2} \) |
\( 2^{20} \cdot 29^{2} \) |
$2.25709$ |
$(2), (29)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2 \cdot 5 \) |
$2.344523689$ |
$2.497049844$ |
2.824265213 |
\( \frac{13651919}{29696} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 5\) , \( 9\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+5{x}+9$ |
| 3364.1-b2 |
3364.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{-19}) \) |
$2$ |
$[0, 1]$ |
3364.1 |
\( 2^{2} \cdot 29^{2} \) |
\( 2^{20} \cdot 29^{2} \) |
$2.96640$ |
$(2), (29)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$4$ |
\( 2 \cdot 5 \) |
$1.204103555$ |
$2.497049844$ |
4.414629123 |
\( \frac{13651919}{29696} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 5\) , \( 9\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2+5{x}+9$ |
| 3364.2-d2 |
3364.2-d |
$2$ |
$5$ |
\(\Q(\sqrt{-31}) \) |
$2$ |
$[0, 1]$ |
3364.2 |
\( 2^{2} \cdot 29^{2} \) |
\( 2^{20} \cdot 29^{2} \) |
$3.78908$ |
$(2,a), (2,a+1), (29)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2^{2} \cdot 5^{2} \) |
$1$ |
$2.497049844$ |
3.587867132 |
\( \frac{13651919}{29696} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 5\) , \( 9\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2+5{x}+9$ |
| 3364.1-a2 |
3364.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{-43}) \) |
$2$ |
$[0, 1]$ |
3364.1 |
\( 2^{2} \cdot 29^{2} \) |
\( 2^{20} \cdot 29^{2} \) |
$4.46259$ |
$(2), (29)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2 \cdot 5 \) |
$9.091057537$ |
$2.497049844$ |
5.538949082 |
\( \frac{13651919}{29696} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 5\) , \( 9\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2+5{x}+9$ |
| 3364.2-c2 |
3364.2-c |
$2$ |
$5$ |
\(\Q(\sqrt{-67}) \) |
$2$ |
$[0, 1]$ |
3364.2 |
\( 2^{2} \cdot 29^{2} \) |
\( 2^{20} \cdot 29^{2} \) |
$5.57045$ |
$(a+3), (a-4), (2)$ |
$0 \le r \le 2$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$16$ |
\( 2 \cdot 5 \) |
$1$ |
$2.497049844$ |
3.904808858 |
\( \frac{13651919}{29696} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 5\) , \( 9\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2+5{x}+9$ |
| 116.2-c2 |
116.2-c |
$2$ |
$5$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
116.2 |
\( 2^{2} \cdot 29 \) |
\( 2^{20} \cdot 29^{2} \) |
$2.73535$ |
$(2,a), (2,a+1), (29,a+14)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2^{3} \cdot 5^{2} \) |
$0.752629878$ |
$2.497049844$ |
6.447613839 |
\( \frac{13651919}{29696} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 5\) , \( 9\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2+5{x}+9$ |
| 3364.1-a2 |
3364.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{-163}) \) |
$2$ |
$[0, 1]$ |
3364.1 |
\( 2^{2} \cdot 29^{2} \) |
\( 2^{20} \cdot 29^{2} \) |
$8.68853$ |
$(2), (29)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2 \cdot 5 \) |
$17.91883843$ |
$2.497049844$ |
5.607422058 |
\( \frac{13651919}{29696} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 5\) , \( 9\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2+5{x}+9$ |
| 58.1-b2 |
58.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{-58}) \) |
$2$ |
$[0, 1]$ |
58.1 |
\( 2 \cdot 29 \) |
\( 2^{20} \cdot 29^{2} \) |
$3.75612$ |
$(2,a), (29,a)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$4$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$2.497049844$ |
2.098423729 |
\( \frac{13651919}{29696} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 5\) , \( 9\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2+5{x}+9$ |
| 58.1-g2 |
58.1-g |
$2$ |
$5$ |
\(\Q(\sqrt{-145}) \) |
$2$ |
$[0, 1]$ |
58.1 |
\( 2 \cdot 29 \) |
\( 2^{20} \cdot 29^{2} \) |
$5.93895$ |
$(2,a+1), (29,a)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$9$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$4.994099689$ |
2.986109317 |
\( \frac{13651919}{29696} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 5\) , \( 9\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2+5{x}+9$ |
| 58.1-f2 |
58.1-f |
$2$ |
$5$ |
\(\Q(\sqrt{-174}) \) |
$2$ |
$[0, 1]$ |
58.1 |
\( 2 \cdot 29 \) |
\( 2^{20} \cdot 29^{2} \) |
$6.50579$ |
$(2,a), (29,a)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$9$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$4.994099689$ |
2.725932386 |
\( \frac{13651919}{29696} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 5\) , \( 9\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2+5{x}+9$ |
| 3364.1-f2 |
3364.1-f |
$2$ |
$5$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
3364.1 |
\( 2^{2} \cdot 29^{2} \) |
\( 2^{20} \cdot 29^{2} \) |
$1.52173$ |
$(a+5), (a-6), (2)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1[2] |
$1$ |
\( 2 \cdot 5 \) |
$1.044923648$ |
$6.671985983$ |
2.494276920 |
\( \frac{13651919}{29696} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 5\) , \( 9\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+5{x}+9$ |
| 1682.1-a2 |
1682.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1682.1 |
\( 2 \cdot 29^{2} \) |
\( 2^{20} \cdot 29^{2} \) |
$1.61860$ |
$(a), (29)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$6.671985983$ |
1.887122613 |
\( \frac{13651919}{29696} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 5\) , \( 9\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+5{x}+9$ |
| 1682.1-g2 |
1682.1-g |
$2$ |
$5$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1682.1 |
\( 2 \cdot 29^{2} \) |
\( 2^{20} \cdot 29^{2} \) |
$1.98237$ |
$(a+1), (29)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$6.671985983$ |
1.540829161 |
\( \frac{13651919}{29696} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 5\) , \( 9\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+5{x}+9$ |
| 116.1-a2 |
116.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
116.1 |
\( 2^{2} \cdot 29 \) |
\( 2^{20} \cdot 29^{2} \) |
$1.57925$ |
$(-2a+1), (2)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1.304023053$ |
$6.671985983$ |
2.585004945 |
\( \frac{13651919}{29696} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 5\) , \( 9\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+5{x}+9$ |
*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.
