| 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 |
| 1.1-a1 |
1.1-a |
$4$ |
$15$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.48121$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$3, 5$ |
3B.1.2, 5B |
$1$ |
\( 1 \) |
$1$ |
$2.044974771$ |
0.379742281 |
\( -1407628760845 a - 3086342051803 \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -23 a - 53\) , \( -169 a - 372\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-23a-53\right){x}-169a-372$ |
| 1.1-a2 |
1.1-a |
$4$ |
$15$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.48121$ |
$\textsf{none}$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$3, 5$ |
3B.1.1, 5B |
$1$ |
\( 1 \) |
$1$ |
$18.40477294$ |
0.379742281 |
\( -3515 a - 7688 \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 2 a + 2\) , \( a + 1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+2\right){x}+a+1$ |
| 1.1-a3 |
1.1-a |
$4$ |
$15$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.48121$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$3, 5$ |
3B.1.2, 5B |
$1$ |
\( 1 \) |
$1$ |
$2.044974771$ |
0.379742281 |
\( 1407628760845 a - 4493970812648 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 27 a - 74\) , \( 92 a - 284\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(27a-74\right){x}+92a-284$ |
| 1.1-a4 |
1.1-a |
$4$ |
$15$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.48121$ |
$\textsf{none}$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$3, 5$ |
3B.1.1, 5B |
$1$ |
\( 1 \) |
$1$ |
$18.40477294$ |
0.379742281 |
\( 3515 a - 11203 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 2 a + 6\) , \( 2 a + 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2a+6\right){x}+2a+4$ |
| 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 |
\( -\frac{1030301}{16} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 11 a - 31\) , \( -23 a + 75\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(11a-31\right){x}-23a+75$ |
| 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 |
\( \frac{237176659}{1048576} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -64 a + 209\) , \( 1147 a - 3660\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-64a+209\right){x}+1147a-3660$ |
| 7.1-a1 |
7.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( -7 \) |
$0.78273$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 1 \) |
$1$ |
$20.28981932$ |
0.941931215 |
\( -\frac{94831363}{7} a + \frac{268859728}{7} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 7 a - 18\) , \( 12 a - 37\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(7a-18\right){x}+12a-37$ |
| 7.1-a2 |
7.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{5} \) |
$0.78273$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 1 \) |
$1$ |
$20.28981932$ |
0.941931215 |
\( -\frac{173650213}{16807} a + \frac{583264453}{16807} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( a + 2\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+2\right){x}$ |
| 7.1-a3 |
7.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{10} \) |
$0.78273$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \) |
$1$ |
$10.14490966$ |
0.941931215 |
\( \frac{91176666325}{282475249} a + \frac{199910878122}{282475249} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -4 a - 8\) , \( -a - 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a-8\right){x}-a-1$ |
| 7.1-a4 |
7.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{2} \) |
$0.78273$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \) |
$1$ |
$10.14490966$ |
0.941931215 |
\( \frac{213433415640625}{49} a + \frac{467970351097797}{49} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 2 a - 28\) , \( 16 a - 33\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a-28\right){x}+16a-33$ |
| 7.2-a1 |
7.2-a |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{2} \) |
$0.78273$ |
$(a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \) |
$1$ |
$10.14490966$ |
0.941931215 |
\( -\frac{213433415640625}{49} a + \frac{97343395248346}{7} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -27\) , \( -15 a + 10\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}-27{x}-15a+10$ |
| 7.2-a2 |
7.2-a |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{10} \) |
$0.78273$ |
$(a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \) |
$1$ |
$10.14490966$ |
0.941931215 |
\( -\frac{91176666325}{282475249} a + \frac{41583934921}{40353607} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 4 a - 12\) , \( a - 2\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(4a-12\right){x}+a-2$ |
| 7.2-a3 |
7.2-a |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{5} \) |
$0.78273$ |
$(a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 1 \) |
$1$ |
$20.28981932$ |
0.941931215 |
\( \frac{173650213}{16807} a + \frac{58516320}{2401} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -a + 3\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-a+3\right){x}$ |
| 7.2-a4 |
7.2-a |
$4$ |
$10$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
7.2 |
\( 7 \) |
\( -7 \) |
$0.78273$ |
$(a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 1 \) |
$1$ |
$20.28981932$ |
0.941931215 |
\( \frac{94831363}{7} a + 24861195 \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -5 a - 12\) , \( -6 a - 13\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-5a-12\right){x}-6a-13$ |
| 13.1-a1 |
13.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
13.1 |
\( 13 \) |
\( - 13^{5} \) |
$0.91374$ |
$(a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 5 \) |
$0.029002274$ |
$18.79911555$ |
1.012442762 |
\( \frac{14025781931}{371293} a + \frac{30870795619}{371293} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( -4 a - 7\) , \( 4 a + 9\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-4a-7\right){x}+4a+9$ |
| 13.1-a2 |
13.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
13.1 |
\( 13 \) |
\( -13 \) |
$0.91374$ |
$(a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 1 \) |
$0.145011373$ |
$18.79911555$ |
1.012442762 |
\( \frac{6367743011}{13} a - \frac{20195061566}{13} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -75 a - 165\) , \( -492 a - 1079\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-75a-165\right){x}-492a-1079$ |
| 13.2-a1 |
13.2-a |
$2$ |
$5$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
13.2 |
\( 13 \) |
\( -13 \) |
$0.91374$ |
$(a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 1 \) |
$0.145011373$ |
$18.79911555$ |
1.012442762 |
\( -\frac{6367743011}{13} a - \frac{13827318555}{13} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 77 a - 240\) , \( 568 a - 1811\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(77a-240\right){x}+568a-1811$ |
| 13.2-a2 |
13.2-a |
$2$ |
$5$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
13.2 |
\( 13 \) |
\( - 13^{5} \) |
$0.91374$ |
$(a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 5 \) |
$0.029002274$ |
$18.79911555$ |
1.012442762 |
\( -\frac{14025781931}{371293} a + \frac{44896577550}{371293} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 3 a - 11\) , \( -4 a + 13\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(3a-11\right){x}-4a+13$ |
| 16.1-a1 |
16.1-a |
$2$ |
$7$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$0.96243$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$7$ |
7B |
$1$ |
\( 1 \) |
$1$ |
$6.065863468$ |
1.126402568 |
\( -58240 a - 127696 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -2 a - 1\) , \( -3 a - 7\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a-1\right){x}-3a-7$ |
| 16.1-a2 |
16.1-a |
$2$ |
$7$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$0.96243$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$7$ |
7B |
$1$ |
\( 1 \) |
$1$ |
$6.065863468$ |
1.126402568 |
\( 58240 a - 185936 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 2 a - 3\) , \( 3 a - 10\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(2a-3\right){x}+3a-10$ |
| 20.1-a1 |
20.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{18} \cdot 5 \) |
$1.01764$ |
$(-a-1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3^{2} \) |
$1$ |
$0.902214666$ |
1.507833519 |
\( \frac{19984640951}{640} a - \frac{255780138153}{2560} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -142 a - 307\) , \( -1521 a - 3336\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-142a-307\right){x}-1521a-3336$ |
| 20.1-a2 |
20.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{6} \cdot 5^{3} \) |
$1.01764$ |
$(-a-1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$8.119932001$ |
1.507833519 |
\( \frac{124021}{1000} a + \frac{43187}{250} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( a - 4\) , \( 12 a - 43\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(a-4\right){x}+12a-43$ |
| 20.1-b1 |
20.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{2} \cdot 5^{7} \) |
$1.01764$ |
$(-a-1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$5.994874057$ |
1.113220165 |
\( -\frac{119629571}{156250} a + \frac{805426}{78125} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -2 a + 3\) , \( -a + 2\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-2a+3\right){x}-a+2$ |
| 20.2-a1 |
20.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( 2^{18} \cdot 5 \) |
$1.01764$ |
$(-a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3^{2} \) |
$1$ |
$0.902214666$ |
1.507833519 |
\( -\frac{19984640951}{640} a - \frac{175841574349}{2560} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 142 a - 449\) , \( 1521 a - 4857\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(142a-449\right){x}+1521a-4857$ |
| 20.2-a2 |
20.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( 2^{6} \cdot 5^{3} \) |
$1.01764$ |
$(-a+2), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$8.119932001$ |
1.507833519 |
\( -\frac{124021}{1000} a + \frac{296769}{1000} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( -2 a - 2\) , \( -13 a - 30\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-2a-2\right){x}-13a-30$ |
| 20.2-b1 |
20.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( 2^{2} \cdot 5^{7} \) |
$1.01764$ |
$(-a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$5.994874057$ |
1.113220165 |
\( \frac{119629571}{156250} a - \frac{118018719}{156250} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( a + 1\) , \( a + 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(a+1\right){x}+a+1$ |
| 25.1-a1 |
25.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{12} \) |
$1.07603$ |
$(-a-1), (-a+2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.829376951$ |
$13.22753554$ |
1.358127807 |
\( -\frac{22083041}{3125} a + \frac{350257206}{15625} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -9 a - 20\) , \( 68 a + 148\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-9a-20\right){x}+68a+148$ |
| 25.1-a2 |
25.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{20} \) |
$1.07603$ |
$(-a-1), (-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$2.488130854$ |
$1.469726171$ |
1.358127807 |
\( -\frac{55158051500782997}{3814697265625} a + \frac{176615422907709839}{3814697265625} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( 71 a + 145\) , \( -1764 a - 3893\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(71a+145\right){x}-1764a-3893$ |
| 25.1-a3 |
25.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{10} \) |
$1.07603$ |
$(-a-1), (-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$4.976261708$ |
$2.939452343$ |
1.358127807 |
\( -\frac{2164654005908433}{1953125} a + \frac{6910857099301696}{1953125} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -59 a - 140\) , \( -398 a - 898\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-59a-140\right){x}-398a-898$ |
| 25.1-a4 |
25.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$1.07603$ |
$(-a-1), (-a+2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1.658753902$ |
$26.45507109$ |
1.358127807 |
\( \frac{9011529}{125} a + \frac{20092663}{125} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -14 a - 30\) , \( 35 a + 76\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-14a-30\right){x}+35a+76$ |
| 25.1-b1 |
25.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$1.07603$ |
$(-a-1), (-a+2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1.658753902$ |
$26.45507109$ |
1.358127807 |
\( -\frac{9011529}{125} a + \frac{29104192}{125} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 12 a - 43\) , \( -36 a + 111\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(12a-43\right){x}-36a+111$ |
| 25.1-b2 |
25.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{12} \) |
$1.07603$ |
$(-a-1), (-a+2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.829376951$ |
$13.22753554$ |
1.358127807 |
\( \frac{22083041}{3125} a + \frac{239842001}{15625} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 7 a - 28\) , \( -69 a + 216\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(7a-28\right){x}-69a+216$ |
| 25.1-b3 |
25.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{20} \) |
$1.07603$ |
$(-a-1), (-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$2.488130854$ |
$1.469726171$ |
1.358127807 |
\( \frac{55158051500782997}{3814697265625} a + \frac{121457371406926842}{3814697265625} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -73 a + 217\) , \( 1763 a - 5657\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-73a+217\right){x}+1763a-5657$ |
| 25.1-b4 |
25.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{10} \) |
$1.07603$ |
$(-a-1), (-a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$4.976261708$ |
$2.939452343$ |
1.358127807 |
\( \frac{2164654005908433}{1953125} a + \frac{4746203093393263}{1953125} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 57 a - 198\) , \( 397 a - 1296\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(57a-198\right){x}+397a-1296$ |
| 25.2-a1 |
25.2-a |
$4$ |
$15$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{6} \) |
$1.07603$ |
$(-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3B, 5B |
$9$ |
\( 1 \) |
$1$ |
$0.914540520$ |
1.528433200 |
\( -1407628760845 a - 3086342051803 \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -16 a - 38\) , \( -64 a - 195\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-16a-38\right){x}-64a-195$ |
| 25.2-a2 |
25.2-a |
$4$ |
$15$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{6} \) |
$1.07603$ |
$(-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3B, 5B |
$1$ |
\( 1 \) |
$1$ |
$8.230864683$ |
1.528433200 |
\( -3515 a - 7688 \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -a + 2\) , \( -a - 2\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a+2\right){x}-a-2$ |
| 25.2-a3 |
25.2-a |
$4$ |
$15$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{6} \) |
$1.07603$ |
$(-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3B, 5B |
$9$ |
\( 1 \) |
$1$ |
$0.914540520$ |
1.528433200 |
\( 1407628760845 a - 4493970812648 \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -15 a - 40\) , \( -481 a - 1066\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-15a-40\right){x}-481a-1066$ |
| 25.2-a4 |
25.2-a |
$4$ |
$15$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{6} \) |
$1.07603$ |
$(-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3B, 5B |
$1$ |
\( 1 \) |
$1$ |
$8.230864683$ |
1.528433200 |
\( 3515 a - 11203 \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 0\) , \( 17 a + 37\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+17a+37$ |
| 25.3-a1 |
25.3-a |
$4$ |
$15$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{6} \) |
$1.07603$ |
$(-a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3B, 5B |
$9$ |
\( 1 \) |
$1$ |
$0.914540520$ |
1.528433200 |
\( -1407628760845 a - 3086342051803 \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 13 a - 53\) , \( 480 a - 1546\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(13a-53\right){x}+480a-1546$ |
| 25.3-a2 |
25.3-a |
$4$ |
$15$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{6} \) |
$1.07603$ |
$(-a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3B, 5B |
$1$ |
\( 1 \) |
$1$ |
$8.230864683$ |
1.528433200 |
\( -3515 a - 7688 \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -2 a + 2\) , \( -18 a + 55\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-2a+2\right){x}-18a+55$ |
| 25.3-a3 |
25.3-a |
$4$ |
$15$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{6} \) |
$1.07603$ |
$(-a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3B, 5B |
$9$ |
\( 1 \) |
$1$ |
$0.914540520$ |
1.528433200 |
\( 1407628760845 a - 4493970812648 \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( 15 a - 53\) , \( 63 a - 258\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(15a-53\right){x}+63a-258$ |
| 25.3-a4 |
25.3-a |
$4$ |
$15$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{6} \) |
$1.07603$ |
$(-a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3B, 5B |
$1$ |
\( 1 \) |
$1$ |
$8.230864683$ |
1.528433200 |
\( 3515 a - 11203 \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( 2\) , \( -2\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+2{x}-2$ |
| 28.1-a1 |
28.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( - 2^{4} \cdot 7^{3} \) |
$1.10695$ |
$(-a), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$15.03985749$ |
1.396415711 |
\( -\frac{116300}{343} a + \frac{1485191}{1372} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 2\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+2{x}$ |
| 28.1-a2 |
28.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{2} \cdot 7^{6} \) |
$1.10695$ |
$(-a), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$15.03985749$ |
1.396415711 |
\( -\frac{12890615364}{117649} a + \frac{94554608905}{235298} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -8\) , \( -8 a + 6\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}-8{x}-8a+6$ |
| 28.1-b1 |
28.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{12} \cdot 7^{4} \) |
$1.10695$ |
$(-a), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \cdot 3 \) |
$0.059060672$ |
$5.519552377$ |
1.452828972 |
\( \frac{198387025}{153664} a - \frac{79186783}{19208} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 3 a + 5\) , \( 22 a + 47\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3a+5\right){x}+22a+47$ |
| 28.2-a1 |
28.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( - 2^{4} \cdot 7^{3} \) |
$1.10695$ |
$(a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$15.03985749$ |
1.396415711 |
\( \frac{116300}{343} a + \frac{145713}{196} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 2\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+2{x}$ |
| 28.2-a2 |
28.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{2} \cdot 7^{6} \) |
$1.10695$ |
$(a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$15.03985749$ |
1.396415711 |
\( \frac{12890615364}{117649} a + \frac{9824768311}{33614} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -8\) , \( 8 a - 2\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}-8{x}+8a-2$ |
| 28.2-b1 |
28.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{12} \cdot 7^{4} \) |
$1.10695$ |
$(a-1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \cdot 3 \) |
$0.059060672$ |
$5.519552377$ |
1.452828972 |
\( -\frac{198387025}{153664} a - \frac{62158177}{21952} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 2 a - 1\) , \( -19 a + 64\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(2a-1\right){x}-19a+64$ |
| 35.1-a1 |
35.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( - 5^{8} \cdot 7^{2} \) |
$1.17045$ |
$(-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$9.170464641$ |
1.702912532 |
\( -\frac{34387992882}{19140625} a + \frac{16001575137}{2734375} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 2 a + 3\) , \( -15 a - 34\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a+3\right){x}-15a-34$ |
| 35.1-a2 |
35.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{29}) \) |
$2$ |
$[2, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( - 5^{4} \cdot 7 \) |
$1.17045$ |
$(-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$18.34092928$ |
1.702912532 |
\( \frac{9208728}{4375} a + \frac{2984877}{625} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -3 a - 7\) , \( -2 a - 5\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3a-7\right){x}-2a-5$ |
*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.
