| 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 |
$2$ |
$5$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.91129$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$3, 5$ |
3Nn, 5B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$0.736148266$ |
0.649667488 |
\( -23788477376 \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 595 a - 3050\) , \( 20142 a - 102714\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(595a-3050\right){x}+20142a-102714$ |
| 1.1-a2 |
1.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.91129$ |
$\textsf{none}$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$3, 5$ |
3Nn, 5B.1.1 |
$9$ |
\( 1 \) |
$1$ |
$18.40370665$ |
0.649667488 |
\( 64 \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -5 a + 10\) , \( -3 a + 6\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-5a+10\right){x}-3a+6$ |
| 1.1-b1 |
1.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 2^{12} \) |
$0.91129$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$3, 5$ |
3Nn, 5B.4.2 |
$25$ |
\( 1 \) |
$1$ |
$0.736148266$ |
1.804631911 |
\( -23788477376 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 2396 a - 12214\) , \( 139366 a - 710632\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(2396a-12214\right){x}+139366a-710632$ |
| 1.1-b2 |
1.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 2^{12} \) |
$0.91129$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$3, 5$ |
3Nn, 5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$18.40370665$ |
1.804631911 |
\( 64 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -4 a + 26\) , \( 46 a - 232\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a+26\right){x}+46a-232$ |
| 8.1-a1 |
8.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{20} \) |
$1.53260$ |
$(2,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$8.909190355$ |
1.747235979 |
\( -23504 a - 119652 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2 a + 22\) , \( -10 a + 58\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a+22\right){x}-10a+58$ |
| 8.1-b1 |
8.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$1.53260$ |
$(2,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.309407382$ |
$8.909190355$ |
2.162430844 |
\( 23504 a - 119652 \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 5 a + 26\) , \( 10 a + 51\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(5a+26\right){x}+10a+51$ |
| 8.1-c1 |
8.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{20} \) |
$1.53260$ |
$(2,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$8.909190355$ |
1.747235979 |
\( 23504 a - 119652 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2 a + 22\) , \( 10 a + 58\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a+22\right){x}+10a+58$ |
| 8.1-d1 |
8.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$1.53260$ |
$(2,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.309407382$ |
$8.909190355$ |
2.162430844 |
\( -23504 a - 119652 \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -5 a + 26\) , \( -10 a + 51\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-5a+26\right){x}-10a+51$ |
| 9.1-a1 |
9.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{12} \) |
$1.57840$ |
$(3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$4$ |
\( 2 \) |
$1$ |
$21.40949540$ |
4.198747493 |
\( -\frac{778688}{729} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 15 a - 92\) , \( -104 a + 521\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(15a-92\right){x}-104a+521$ |
| 9.1-a2 |
9.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.57840$ |
$(3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$4$ |
\( 1 \) |
$1$ |
$42.81899080$ |
4.198747493 |
\( \frac{78402752}{27} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 356 a - 1810\) , \( -7554 a + 38516\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(356a-1810\right){x}-7554a+38516$ |
| 9.1-b1 |
9.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 2^{12} \cdot 3^{12} \) |
$1.57840$ |
$(3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \) |
$0.327721564$ |
$21.40949540$ |
1.376020096 |
\( -\frac{778688}{729} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 76 a - 382\) , \( -1490 a + 7600\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(76a-382\right){x}-1490a+7600$ |
| 9.1-b2 |
9.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$1.57840$ |
$(3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 1 \) |
$0.327721564$ |
$42.81899080$ |
1.376020096 |
\( \frac{78402752}{27} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( 93 a - 445\) , \( -988 a + 5086\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(93a-445\right){x}-988a+5086$ |
| 10.1-a1 |
10.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{17} \cdot 5^{5} \) |
$1.62052$ |
$(2,a), (5,a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$17.05624564$ |
1.672502487 |
\( -\frac{37617129}{25000} a + \frac{44393049}{6250} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 5 a - 8\) , \( 26 a - 119\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(5a-8\right){x}+26a-119$ |
| 10.1-a2 |
10.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{13} \cdot 5 \) |
$1.62052$ |
$(2,a), (5,a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$25$ |
\( 1 \) |
$1$ |
$0.682249825$ |
1.672502487 |
\( -\frac{530618171482888843761}{10} a + \frac{1352816205329086378722}{5} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 3145 a - 16048\) , \( 224946 a - 1147199\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(3145a-16048\right){x}+224946a-1147199$ |
| 10.1-b1 |
10.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{25} \cdot 5 \) |
$1.62052$ |
$(2,a), (5,a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.536698983$ |
$17.17500600$ |
1.807760930 |
\( -\frac{391019}{640} a + \frac{357337}{80} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 1479 a - 7517\) , \( -61002 a + 311088\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(1479a-7517\right){x}-61002a+311088$ |
| 10.1-c1 |
10.1-c |
$2$ |
$5$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{5} \cdot 5^{5} \) |
$1.62052$ |
$(2,a), (5,a+4)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5^{2} \) |
$1$ |
$17.05624564$ |
1.672502487 |
\( -\frac{37617129}{25000} a + \frac{44393049}{6250} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 8 a + 28\) , \( 12 a + 48\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(8a+28\right){x}+12a+48$ |
| 10.1-c2 |
10.1-c |
$2$ |
$5$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5 \) |
$1.62052$ |
$(2,a), (5,a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 1 \) |
$1$ |
$0.682249825$ |
1.672502487 |
\( -\frac{530618171482888843761}{10} a + \frac{1352816205329086378722}{5} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 793 a - 3982\) , \( 26907 a - 137142\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(793a-3982\right){x}+26907a-137142$ |
| 10.1-d1 |
10.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{13} \cdot 5 \) |
$1.62052$ |
$(2,a), (5,a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 13 \) |
$0.080526241$ |
$17.17500600$ |
3.526070609 |
\( -\frac{391019}{640} a + \frac{357337}{80} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 368 a - 1872\) , \( -6871 a + 35033\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(368a-1872\right){x}-6871a+35033$ |
| 10.2-a1 |
10.2-a |
$2$ |
$5$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{17} \cdot 5^{5} \) |
$1.62052$ |
$(2,a), (5,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$17.05624564$ |
1.672502487 |
\( \frac{37617129}{25000} a + \frac{44393049}{6250} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -5 a - 8\) , \( -26 a - 119\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-5a-8\right){x}-26a-119$ |
| 10.2-a2 |
10.2-a |
$2$ |
$5$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{13} \cdot 5 \) |
$1.62052$ |
$(2,a), (5,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$25$ |
\( 1 \) |
$1$ |
$0.682249825$ |
1.672502487 |
\( \frac{530618171482888843761}{10} a + \frac{1352816205329086378722}{5} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -3145 a - 16048\) , \( -224946 a - 1147199\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-3145a-16048\right){x}-224946a-1147199$ |
| 10.2-b1 |
10.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{25} \cdot 5 \) |
$1.62052$ |
$(2,a), (5,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.536698983$ |
$17.17500600$ |
1.807760930 |
\( \frac{391019}{640} a + \frac{357337}{80} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -8 a + 27\) , \( -15 a + 70\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-8a+27\right){x}-15a+70$ |
| 10.2-c1 |
10.2-c |
$2$ |
$5$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{5} \cdot 5^{5} \) |
$1.62052$ |
$(2,a), (5,a+1)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5^{2} \) |
$1$ |
$17.05624564$ |
1.672502487 |
\( \frac{37617129}{25000} a + \frac{44393049}{6250} \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( 5 a + 15\) , \( 3 a + 9\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(5a+15\right){x}+3a+9$ |
| 10.2-c2 |
10.2-c |
$2$ |
$5$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5 \) |
$1.62052$ |
$(2,a), (5,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 1 \) |
$1$ |
$0.682249825$ |
1.672502487 |
\( \frac{530618171482888843761}{10} a + \frac{1352816205329086378722}{5} \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( -780 a - 3995\) , \( -30902 a - 157591\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-780a-3995\right){x}-30902a-157591$ |
| 10.2-d1 |
10.2-d |
$1$ |
$1$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{13} \cdot 5 \) |
$1.62052$ |
$(2,a), (5,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 13 \) |
$0.080526241$ |
$17.17500600$ |
3.526070609 |
\( \frac{391019}{640} a + \frac{357337}{80} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -368 a - 1872\) , \( 6871 a + 35033\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-368a-1872\right){x}+6871a+35033$ |
| 13.1-a1 |
13.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
13.1 |
\( 13 \) |
\( 13^{4} \) |
$1.73038$ |
$(13,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.629188872$ |
$3.908720549$ |
1.929252060 |
\( \frac{2292144}{169} a - \frac{11688353}{169} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 20 a - 26\) , \( 70 a - 222\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(20a-26\right){x}+70a-222$ |
| 13.1-b1 |
13.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
13.1 |
\( 13 \) |
\( 13^{4} \) |
$1.73038$ |
$(13,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.629188872$ |
$3.908720549$ |
1.929252060 |
\( -\frac{2292144}{169} a - \frac{11688353}{169} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -6 a - 39\) , \( -109 a - 560\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-6a-39\right){x}-109a-560$ |
| 13.1-c1 |
13.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
13.1 |
\( 13 \) |
\( 2^{12} \cdot 13^{4} \) |
$1.73038$ |
$(13,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$3.908720549$ |
0.766563167 |
\( -\frac{2292144}{169} a - \frac{11688353}{169} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -51 a - 259\) , \( -561 a - 2857\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-51a-259\right){x}-561a-2857$ |
| 13.1-d1 |
13.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
13.1 |
\( 13 \) |
\( 2^{12} \cdot 13^{4} \) |
$1.73038$ |
$(13,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$3.908720549$ |
0.766563167 |
\( \frac{2292144}{169} a - \frac{11688353}{169} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 51 a - 259\) , \( 561 a - 2857\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(51a-259\right){x}+561a-2857$ |
| 16.1-a1 |
16.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{20} \) |
$1.82257$ |
$(2,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.326166095$ |
$24.54409375$ |
3.139996309 |
\( -23504 a - 119652 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -2 a + 22\) , \( 10 a - 58\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a+22\right){x}+10a-58$ |
| 16.1-b1 |
16.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{24} \) |
$1.82257$ |
$(2,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Nn, 5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$21.28911211$ |
2.087569194 |
\( -23788477376 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 9586 a - 48883\) , \( -1173397 a + 5983175\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(9586a-48883\right){x}-1173397a+5983175$ |
| 16.1-b2 |
16.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{24} \) |
$1.82257$ |
$(2,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Nn, 5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$21.28911211$ |
2.087569194 |
\( 64 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -14 a + 77\) , \( -277 a + 1415\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-14a+77\right){x}-277a+1415$ |
| 16.1-c1 |
16.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{20} \) |
$1.82257$ |
$(2,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.326166095$ |
$24.54409375$ |
3.139996309 |
\( 23504 a - 119652 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 2 a + 22\) , \( -10 a - 58\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(2a+22\right){x}-10a-58$ |
| 16.1-d1 |
16.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$1.82257$ |
$(2,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.269173633$ |
$24.54409375$ |
2.591330699 |
\( 23504 a - 119652 \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -3 a + 22\) , \( -6 a + 13\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3a+22\right){x}-6a+13$ |
| 16.1-e1 |
16.1-e |
$2$ |
$5$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$1.82257$ |
$(2,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Nn, 5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$21.28911211$ |
2.087569194 |
\( -23788477376 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2396 a - 12214\) , \( -139366 a + 710632\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(2396a-12214\right){x}-139366a+710632$ |
| 16.1-e2 |
16.1-e |
$2$ |
$5$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$1.82257$ |
$(2,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3Nn, 5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$21.28911211$ |
2.087569194 |
\( 64 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -4 a + 26\) , \( -46 a + 232\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a+26\right){x}-46a+232$ |
| 16.1-f1 |
16.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$1.82257$ |
$(2,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.269173633$ |
$24.54409375$ |
2.591330699 |
\( -23504 a - 119652 \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 3 a + 22\) , \( 6 a + 13\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(3a+22\right){x}+6a+13$ |
| 17.1-a1 |
17.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
17.1 |
\( 17 \) |
\( - 2^{12} \cdot 17^{6} \) |
$1.85041$ |
$(a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$4$ |
\( 2 \) |
$1$ |
$8.036318802$ |
1.576051784 |
\( -\frac{516632309525}{24137569} a + \frac{2632534734107}{24137569} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 26 a - 103\) , \( -111 a + 602\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(26a-103\right){x}-111a+602$ |
| 17.1-a2 |
17.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
17.1 |
\( 17 \) |
\( 2^{12} \cdot 17^{3} \) |
$1.85041$ |
$(a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$4$ |
\( 1 \) |
$1$ |
$16.07263760$ |
1.576051784 |
\( \frac{123207298}{4913} a + \frac{636786691}{4913} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 6 a - 3\) , \( 5 a + 6\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(6a-3\right){x}+5a+6$ |
| 17.1-b1 |
17.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
17.1 |
\( 17 \) |
\( - 17^{6} \) |
$1.85041$ |
$(a+3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \) |
$2.202689616$ |
$8.036318802$ |
3.471552899 |
\( -\frac{516632309525}{24137569} a + \frac{2632534734107}{24137569} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 8 a - 6\) , \( -3 a + 53\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(8a-6\right){x}-3a+53$ |
| 17.1-b2 |
17.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
17.1 |
\( 17 \) |
\( 17^{3} \) |
$1.85041$ |
$(a+3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 1 \) |
$2.202689616$ |
$16.07263760$ |
3.471552899 |
\( \frac{123207298}{4913} a + \frac{636786691}{4913} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 3 a + 19\) , \( 4 a + 16\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(3a+19\right){x}+4a+16$ |
| 17.2-a1 |
17.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
17.2 |
\( 17 \) |
\( 2^{12} \cdot 17^{3} \) |
$1.85041$ |
$(a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$4$ |
\( 1 \) |
$1$ |
$16.07263760$ |
1.576051784 |
\( -\frac{123207298}{4913} a + \frac{636786691}{4913} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -6 a - 3\) , \( -5 a + 6\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-6a-3\right){x}-5a+6$ |
| 17.2-a2 |
17.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
17.2 |
\( 17 \) |
\( - 2^{12} \cdot 17^{6} \) |
$1.85041$ |
$(a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$4$ |
\( 2 \) |
$1$ |
$8.036318802$ |
1.576051784 |
\( \frac{516632309525}{24137569} a + \frac{2632534734107}{24137569} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -26 a - 103\) , \( 111 a + 602\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-26a-103\right){x}+111a+602$ |
| 17.2-b1 |
17.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
17.2 |
\( 17 \) |
\( 17^{3} \) |
$1.85041$ |
$(a-3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 1 \) |
$2.202689616$ |
$16.07263760$ |
3.471552899 |
\( -\frac{123207298}{4913} a + \frac{636786691}{4913} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -3 a + 19\) , \( -4 a + 16\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a+19\right){x}-4a+16$ |
| 17.2-b2 |
17.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
17.2 |
\( 17 \) |
\( - 17^{6} \) |
$1.85041$ |
$(a-3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \) |
$2.202689616$ |
$8.036318802$ |
3.471552899 |
\( \frac{516632309525}{24137569} a + \frac{2632534734107}{24137569} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -8 a - 6\) , \( 3 a + 53\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-8a-6\right){x}+3a+53$ |
| 20.1-a1 |
20.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{8} \cdot 5^{2} \) |
$1.92714$ |
$(2,a), (5,a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$9.101597095$ |
$14.39552905$ |
3.211948519 |
\( -\frac{449312768164}{25} a + \frac{2291054610364}{25} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 223 a - 1105\) , \( -3866 a + 19765\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(223a-1105\right){x}-3866a+19765$ |
| 20.1-a2 |
20.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{4} \) |
$1.92714$ |
$(2,a), (5,a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$4.550798547$ |
$28.79105811$ |
3.211948519 |
\( -\frac{26162592}{625} a + \frac{134634992}{625} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 18 a - 60\) , \( -50 a + 306\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(18a-60\right){x}-50a+306$ |
| 20.1-a3 |
20.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{8} \cdot 5^{8} \) |
$1.92714$ |
$(2,a), (5,a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.275399273$ |
$14.39552905$ |
3.211948519 |
\( \frac{3507883972}{390625} a + \frac{17822712628}{390625} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 13 a - 35\) , \( -98 a + 549\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(13a-35\right){x}-98a+549$ |
| 20.1-a4 |
20.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{20} \cdot 5^{2} \) |
$1.92714$ |
$(2,a), (5,a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.275399273$ |
$14.39552905$ |
3.211948519 |
\( \frac{2494464}{25} a + \frac{12763136}{25} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 18 a - 87\) , \( -49 a + 251\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(18a-87\right){x}-49a+251$ |
| 20.1-b1 |
20.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{20} \cdot 5^{2} \) |
$1.92714$ |
$(2,a), (5,a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$14.39552905$ |
2.117396641 |
\( -\frac{449312768164}{25} a + \frac{2291054610364}{25} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 962 a + 4910\) , \( -11906 a - 60710\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(962a+4910\right){x}-11906a-60710$ |
| 20.1-b2 |
20.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{26}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{16} \cdot 5^{4} \) |
$1.92714$ |
$(2,a), (5,a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$28.79105811$ |
2.117396641 |
\( -\frac{26162592}{625} a + \frac{134634992}{625} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -258 a - 1310\) , \( -2318 a - 11822\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-258a-1310\right){x}-2318a-11822$ |
*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.
