| 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-a1 |
4.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$0.68054$ |
$(2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$48.80986873$ |
0.725101206 |
\( -\frac{1030301}{16} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 11 a - 31\) , \( -23 a + 75\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(11a-31\right){x}-23a+75$ |
| 100.2-e1 |
100.2-e |
$2$ |
$5$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$1.52173$ |
$(-a-1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{2} \) |
$0.072335044$ |
$21.82843689$ |
2.345645522 |
\( -\frac{1030301}{16} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -8 a - 18\) , \( 17 a + 37\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-8a-18\right){x}+17a+37$ |
| 100.3-e1 |
100.3-e |
$2$ |
$5$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
100.3 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$1.52173$ |
$(-a+2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{2} \) |
$0.072335044$ |
$21.82843689$ |
2.345645522 |
\( -\frac{1030301}{16} \) |
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( 6 a - 25\) , \( -18 a + 55\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(6a-25\right){x}-18a+55$ |
| 196.2-b1 |
196.2-b |
$2$ |
$5$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
196.2 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{6} \) |
$1.80054$ |
$(-a), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{2} \) |
$0.334902631$ |
$5.228818701$ |
2.601435912 |
\( -\frac{1030301}{16} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 50 a - 162\) , \( -306 a + 972\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(50a-162\right){x}-306a+972$ |
| 196.3-b1 |
196.3-b |
$2$ |
$5$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
196.3 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{6} \) |
$1.80054$ |
$(a-1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{2} \) |
$0.334902631$ |
$5.228818701$ |
2.601435912 |
\( -\frac{1030301}{16} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( -51 a - 111\) , \( 305 a + 667\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-51a-111\right){x}+305a+667$ |
| 256.1-a1 |
256.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{32} \) |
$1.92485$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.1 |
$4$ |
\( 2^{2} \) |
$1$ |
$0.980251637$ |
2.912450549 |
\( -\frac{1030301}{16} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -168 a - 368\) , \( -2160 a - 4736\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-168a-368\right){x}-2160a-4736$ |
| 256.1-f1 |
256.1-f |
$2$ |
$5$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{32} \) |
$1.92485$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$1.267823744$ |
$3.458538483$ |
3.256960458 |
\( -\frac{1030301}{16} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a - 31\) , \( -39 a + 4\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a-31\right){x}-39a+4$ |
| 256.1-m1 |
256.1-m |
$2$ |
$5$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{32} \) |
$1.92485$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$1.267823744$ |
$3.458538483$ |
3.256960458 |
\( -\frac{1030301}{16} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a - 31\) , \( 39 a - 4\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a-31\right){x}+39a-4$ |
| 324.1-a1 |
324.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{12} \) |
$2.04161$ |
$(2), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$1.307002183$ |
0.485408424 |
\( -\frac{1030301}{16} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 94 a - 305\) , \( 911 a - 2911\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(94a-305\right){x}+911a-2911$ |
| 676.2-k1 |
676.2-k |
$2$ |
$5$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
676.2 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 13^{6} \) |
$2.45372$ |
$(a-5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{2} \) |
$2.859723283$ |
$1.087491551$ |
4.619988463 |
\( -\frac{1030301}{16} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -33 a - 75\) , \( -233 a - 514\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-33a-75\right){x}-233a-514$ |
| 676.3-k1 |
676.3-k |
$2$ |
$5$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
676.3 |
\( 2^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 13^{6} \) |
$2.45372$ |
$(a+4), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{2} \) |
$2.859723283$ |
$1.087491551$ |
4.619988463 |
\( -\frac{1030301}{16} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 34 a - 109\) , \( 199 a - 638\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(34a-109\right){x}+199a-638$ |
*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.
