| 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 |
| 4.1-a2 |
4.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{40} \) |
$0.68054$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$1.952394749$ |
0.725101206 |
\( \frac{237176659}{1048576} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -64 a + 209\) , \( 1147 a - 3660\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-64a+209\right){x}+1147a-3660$ |
| 100.2-e2 |
100.2-e |
$2$ |
$5$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{40} \cdot 5^{6} \) |
$1.52173$ |
$(-a-1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.361675224$ |
$0.873137475$ |
2.345645522 |
\( \frac{237176659}{1048576} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( 37 a + 102\) , \( -628 a - 1433\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(37a+102\right){x}-628a-1433$ |
| 100.3-e2 |
100.3-e |
$2$ |
$5$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
100.3 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{40} \cdot 5^{6} \) |
$1.52173$ |
$(-a+2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.361675224$ |
$0.873137475$ |
2.345645522 |
\( \frac{237176659}{1048576} \) |
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( -39 a + 140\) , \( 627 a - 2060\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-39a+140\right){x}+627a-2060$ |
| 196.2-b2 |
196.2-b |
$2$ |
$5$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
196.2 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{40} \cdot 7^{6} \) |
$1.80054$ |
$(-a), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2^{2} \) |
$1.674513155$ |
$1.045763740$ |
2.601435912 |
\( \frac{237176659}{1048576} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -310 a + 993\) , \( 12459 a - 39768\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-310a+993\right){x}+12459a-39768$ |
| 196.3-b2 |
196.3-b |
$2$ |
$5$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
196.3 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{40} \cdot 7^{6} \) |
$1.80054$ |
$(a-1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2^{2} \) |
$1.674513155$ |
$1.045763740$ |
2.601435912 |
\( \frac{237176659}{1048576} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( 309 a + 684\) , \( -12460 a - 27308\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(309a+684\right){x}-12460a-27308$ |
| 256.1-a2 |
256.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{64} \) |
$1.92485$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.2 |
$4$ |
\( 2^{2} \) |
$1$ |
$0.980251637$ |
2.912450549 |
\( \frac{237176659}{1048576} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 1032 a + 2272\) , \( 77520 a + 169984\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(1032a+2272\right){x}+77520a+169984$ |
| 256.1-f2 |
256.1-f |
$2$ |
$5$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{64} \) |
$1.92485$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \) |
$6.339118722$ |
$0.691707696$ |
3.256960458 |
\( \frac{237176659}{1048576} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 209\) , \( 1161 a - 476\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+209\right){x}+1161a-476$ |
| 256.1-m2 |
256.1-m |
$2$ |
$5$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{64} \) |
$1.92485$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \) |
$6.339118722$ |
$0.691707696$ |
3.256960458 |
\( \frac{237176659}{1048576} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 209\) , \( -1161 a + 476\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+209\right){x}-1161a+476$ |
| 324.1-a2 |
324.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{40} \cdot 3^{12} \) |
$2.04161$ |
$(2), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \) |
$1$ |
$1.307002183$ |
0.485408424 |
\( \frac{237176659}{1048576} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -581 a + 1855\) , \( -32704 a + 104414\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-581a+1855\right){x}-32704a+104414$ |
| 676.2-k2 |
676.2-k |
$2$ |
$5$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
676.2 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{40} \cdot 13^{6} \) |
$2.45372$ |
$(a-5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.571944656$ |
$1.087491551$ |
4.619988463 |
\( \frac{237176659}{1048576} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 207 a + 480\) , \( 7342 a + 16211\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(207a+480\right){x}+7342a+16211$ |
| 676.3-k2 |
676.3-k |
$2$ |
$5$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
676.3 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{40} \cdot 13^{6} \) |
$2.45372$ |
$(a+4), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.571944656$ |
$1.087491551$ |
4.619988463 |
\( \frac{237176659}{1048576} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -206 a + 686\) , \( -7136 a + 22867\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-206a+686\right){x}-7136a+22867$ |
*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.
