| 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 |
| 8.1-a1 |
8.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$1.44147$ |
$(-a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.290517010$ |
$17.55912210$ |
2.127357326 |
\( 256 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -80 a + 384\) , \( 2072 a - 9937\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-80a+384\right){x}+2072a-9937$ |
| 8.1-b1 |
8.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$1.44147$ |
$(-a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.290517010$ |
$17.55912210$ |
2.127357326 |
\( 256 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -80 a + 384\) , \( -2072 a + 9937\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-80a+384\right){x}-2072a+9937$ |
| 9.1-a1 |
9.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$1.48454$ |
$(3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.671003177$ |
$11.01298155$ |
1.533399817 |
\( -\frac{2924207}{81} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 715 a - 3429\) , \( -23270 a + 111599\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(715a-3429\right){x}-23270a+111599$ |
| 9.1-a2 |
9.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{2} \) |
$1.48454$ |
$(3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$10.68401271$ |
$11.01298155$ |
1.533399817 |
\( -\frac{576110079740793605}{3} a + 920975627106405096 \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -11590 a - 55573\) , \( -1475005 a - 7073869\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-11590a-55573\right){x}-1475005a-7073869$ |
| 9.1-a3 |
9.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$1.48454$ |
$(3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$5.342006355$ |
$11.01298155$ |
1.533399817 |
\( \frac{12214672127}{9} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 11515 a - 55224\) , \( -1472000 a + 7059464\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(11515a-55224\right){x}-1472000a+7059464$ |
| 9.1-a4 |
9.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{2} \) |
$1.48454$ |
$(3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$10.68401271$ |
$2.753245389$ |
1.533399817 |
\( \frac{576110079740793605}{3} a + 920975627106405096 \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 11590 a - 55584\) , \( -1451825 a + 6962708\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(11590a-55584\right){x}-1451825a+6962708$ |
| 9.1-b1 |
9.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$1.48454$ |
$(3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.671003177$ |
$11.01298155$ |
1.533399817 |
\( -\frac{2924207}{81} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 715 a - 3418\) , \( 24700 a - 118450\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(715a-3418\right){x}+24700a-118450$ |
| 9.1-b2 |
9.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{2} \) |
$1.48454$ |
$(3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$10.68401271$ |
$2.753245389$ |
1.533399817 |
\( -\frac{576110079740793605}{3} a + 920975627106405096 \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -11590 a - 55584\) , \( 1451825 a + 6962708\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-11590a-55584\right){x}+1451825a+6962708$ |
| 9.1-b3 |
9.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$1.48454$ |
$(3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$5.342006355$ |
$11.01298155$ |
1.533399817 |
\( \frac{12214672127}{9} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 11515 a - 55213\) , \( 1495030 a - 7169905\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(11515a-55213\right){x}+1495030a-7169905$ |
| 9.1-b4 |
9.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{2} \) |
$1.48454$ |
$(3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$10.68401271$ |
$11.01298155$ |
1.533399817 |
\( \frac{576110079740793605}{3} a + 920975627106405096 \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 11590 a - 55573\) , \( 1475005 a - 7073869\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(11590a-55573\right){x}+1475005a-7073869$ |
| 11.1-a1 |
11.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{3} \) |
$1.56092$ |
$(-2a+9)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 1 \) |
$1$ |
$13.63633641$ |
1.421686348 |
\( \frac{8066560}{1331} a + \frac{40525632}{1331} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 6 a + 24\) , \( 11 a + 45\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6a+24\right){x}+11a+45$ |
| 11.1-b1 |
11.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{3} \) |
$1.56092$ |
$(-2a+9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$0.114283851$ |
$26.97262573$ |
1.928259279 |
\( \frac{8066560}{1331} a + \frac{40525632}{1331} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 4 a + 16\) , \( 7 a + 26\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(4a+16\right){x}+7a+26$ |
| 11.2-a1 |
11.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
11.2 |
\( 11 \) |
\( - 11^{3} \) |
$1.56092$ |
$(2a+9)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 1 \) |
$1$ |
$13.63633641$ |
1.421686348 |
\( -\frac{8066560}{1331} a + \frac{40525632}{1331} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 7 a + 35\) , \( 13 a + 62\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(7a+35\right){x}+13a+62$ |
| 11.2-b1 |
11.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
11.2 |
\( 11 \) |
\( - 11^{3} \) |
$1.56092$ |
$(2a+9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$0.114283851$ |
$26.97262573$ |
1.928259279 |
\( -\frac{8066560}{1331} a + \frac{40525632}{1331} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 5 a + 27\) , \( 9 a + 43\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(5a+27\right){x}+9a+43$ |
| 16.1-a1 |
16.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$1.71420$ |
$(-a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.463514535$ |
$25.95485587$ |
2.508522851 |
\( -12800 a - 60672 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 11\) , \( -a - 2\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+11{x}-a-2$ |
| 16.1-b1 |
16.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$1.71420$ |
$(-a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1.547762297$ |
$8.850540007$ |
2.856341401 |
\( 12800 a - 60672 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 11\) , \( -a + 2\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+11{x}-a+2$ |
| 16.1-c1 |
16.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$1.71420$ |
$(-a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.463514535$ |
$25.95485587$ |
2.508522851 |
\( 12800 a - 60672 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 11\) , \( a - 2\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+11{x}+a-2$ |
| 16.1-d1 |
16.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$1.71420$ |
$(-a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1.547762297$ |
$8.850540007$ |
2.856341401 |
\( -12800 a - 60672 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 11\) , \( a + 2\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+11{x}+a+2$ |
| 22.1-a1 |
22.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( - 2^{6} \cdot 11^{3} \) |
$1.85626$ |
$(-a+5), (-2a+9)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$2.546132399$ |
0.530905305 |
\( \frac{888928020465}{10648} a - \frac{2131508856307}{5324} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( 272 a - 1296\) , \( 5885 a - 28217\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(272a-1296\right){x}+5885a-28217$ |
| 22.1-a2 |
22.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( - 2^{2} \cdot 11 \) |
$1.85626$ |
$(-a+5), (-2a+9)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$22.91519159$ |
0.530905305 |
\( \frac{723699}{22} a + \frac{1731269}{11} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( 2 a - 1\) , \( 16 a - 70\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(2a-1\right){x}+16a-70$ |
| 22.1-b1 |
22.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( - 2^{6} \cdot 11^{3} \) |
$1.85626$ |
$(-a+5), (-2a+9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$0.065464909$ |
$24.74161214$ |
2.026394031 |
\( \frac{888928020465}{10648} a - \frac{2131508856307}{5324} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( 272 a - 1307\) , \( -5340 a + 25604\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(272a-1307\right){x}-5340a+25604$ |
| 22.1-b2 |
22.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( - 2^{2} \cdot 11 \) |
$1.85626$ |
$(-a+5), (-2a+9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.196394727$ |
$24.74161214$ |
2.026394031 |
\( \frac{723699}{22} a + \frac{1731269}{11} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( 2 a - 12\) , \( -11 a + 47\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(2a-12\right){x}-11a+47$ |
| 22.2-a1 |
22.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
22.2 |
\( 2 \cdot 11 \) |
\( - 2^{6} \cdot 11^{3} \) |
$1.85626$ |
$(-a+5), (2a+9)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$2.546132399$ |
0.530905305 |
\( -\frac{888928020465}{10648} a - \frac{2131508856307}{5324} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( -273 a - 1296\) , \( -5885 a - 28217\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-273a-1296\right){x}-5885a-28217$ |
| 22.2-a2 |
22.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
22.2 |
\( 2 \cdot 11 \) |
\( - 2^{2} \cdot 11 \) |
$1.85626$ |
$(-a+5), (2a+9)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$22.91519159$ |
0.530905305 |
\( -\frac{723699}{22} a + \frac{1731269}{11} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( -3 a - 1\) , \( -16 a - 70\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-3a-1\right){x}-16a-70$ |
| 22.2-b1 |
22.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
22.2 |
\( 2 \cdot 11 \) |
\( - 2^{6} \cdot 11^{3} \) |
$1.85626$ |
$(-a+5), (2a+9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$0.065464909$ |
$24.74161214$ |
2.026394031 |
\( -\frac{888928020465}{10648} a - \frac{2131508856307}{5324} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( -273 a - 1307\) , \( 5340 a + 25604\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-273a-1307\right){x}+5340a+25604$ |
| 22.2-b2 |
22.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
22.2 |
\( 2 \cdot 11 \) |
\( - 2^{2} \cdot 11 \) |
$1.85626$ |
$(-a+5), (2a+9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.196394727$ |
$24.74161214$ |
2.026394031 |
\( -\frac{723699}{22} a + \frac{1731269}{11} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( -3 a - 12\) , \( 11 a + 47\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-3a-12\right){x}+11a+47$ |
| 25.1-a1 |
25.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$1.91654$ |
$(5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 1 \) |
$1$ |
$12.39496478$ |
1.292264409 |
\( -\frac{32768}{125} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -160 a - 767\) , \( -6594 a - 31624\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}+\left(-160a-767\right){x}-6594a-31624$ |
| 25.1-b1 |
25.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$1.91654$ |
$(5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 1 \) |
$1$ |
$12.39496478$ |
1.292264409 |
\( -\frac{32768}{125} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( -160 a - 767\) , \( 6594 a + 31618\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}+\left(-160a-767\right){x}+6594a+31618$ |
| 26.1-a1 |
26.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{4} \cdot 13^{2} \) |
$1.93542$ |
$(-a+5), (a-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$18.25262699$ |
3.805935822 |
\( \frac{74750337}{169} a - \frac{1433958043}{676} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( a + 12\) , \( -31 a - 150\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+12\right){x}-31a-150$ |
| 26.1-a2 |
26.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{2} \cdot 13 \) |
$1.93542$ |
$(-a+5), (a-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$18.25262699$ |
3.805935822 |
\( -\frac{24402922831899}{13} a + \frac{234064614018301}{26} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -59 a - 278\) , \( -421 a - 2022\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-59a-278\right){x}-421a-2022$ |
| 26.1-b1 |
26.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{9} \cdot 13^{3} \) |
$1.93542$ |
$(-a+5), (a-6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3^{2} \) |
$0.101360370$ |
$22.55344511$ |
4.290023491 |
\( \frac{1169733145}{70304} a - \frac{5737718647}{70304} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 25 a - 109\) , \( -102 a + 496\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(25a-109\right){x}-102a+496$ |
| 26.1-c1 |
26.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{9} \cdot 13^{3} \) |
$1.93542$ |
$(-a+5), (a-6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3^{2} \) |
$0.968415518$ |
$2.373126329$ |
4.312818575 |
\( \frac{1169733145}{70304} a - \frac{5737718647}{70304} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 25 a - 120\) , \( 152 a - 729\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(25a-120\right){x}+152a-729$ |
| 26.1-d1 |
26.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{4} \cdot 13^{2} \) |
$1.93542$ |
$(-a+5), (a-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$6.211018668$ |
1.295086918 |
\( \frac{74750337}{169} a - \frac{1433958043}{676} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 5 a + 16\) , \( 37 a + 174\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(5a+16\right){x}+37a+174$ |
| 26.1-d2 |
26.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{2} \cdot 13 \) |
$1.93542$ |
$(-a+5), (a-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$6.211018668$ |
1.295086918 |
\( -\frac{24402922831899}{13} a + \frac{234064614018301}{26} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( -55 a - 274\) , \( 307 a + 1466\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-55a-274\right){x}+307a+1466$ |
| 26.2-a1 |
26.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
26.2 |
\( 2 \cdot 13 \) |
\( 2^{4} \cdot 13^{2} \) |
$1.93542$ |
$(-a+5), (a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$18.25262699$ |
3.805935822 |
\( -\frac{74750337}{169} a - \frac{1433958043}{676} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -2 a + 12\) , \( 30 a - 150\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a+12\right){x}+30a-150$ |
| 26.2-a2 |
26.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
26.2 |
\( 2 \cdot 13 \) |
\( 2^{2} \cdot 13 \) |
$1.93542$ |
$(-a+5), (a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$18.25262699$ |
3.805935822 |
\( \frac{24402922831899}{13} a + \frac{234064614018301}{26} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 58 a - 278\) , \( 420 a - 2022\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(58a-278\right){x}+420a-2022$ |
| 26.2-b1 |
26.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
26.2 |
\( 2 \cdot 13 \) |
\( 2^{9} \cdot 13^{3} \) |
$1.93542$ |
$(-a+5), (a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3^{2} \) |
$0.101360370$ |
$22.55344511$ |
4.290023491 |
\( -\frac{1169733145}{70304} a - \frac{5737718647}{70304} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -25 a - 109\) , \( 102 a + 496\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-25a-109\right){x}+102a+496$ |
| 26.2-c1 |
26.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
26.2 |
\( 2 \cdot 13 \) |
\( 2^{9} \cdot 13^{3} \) |
$1.93542$ |
$(-a+5), (a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3^{2} \) |
$0.968415518$ |
$2.373126329$ |
4.312818575 |
\( -\frac{1169733145}{70304} a - \frac{5737718647}{70304} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -25 a - 120\) , \( -152 a - 729\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-25a-120\right){x}-152a-729$ |
| 26.2-d1 |
26.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
26.2 |
\( 2 \cdot 13 \) |
\( 2^{4} \cdot 13^{2} \) |
$1.93542$ |
$(-a+5), (a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$6.211018668$ |
1.295086918 |
\( -\frac{74750337}{169} a - \frac{1433958043}{676} \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -6 a + 16\) , \( -38 a + 174\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6a+16\right){x}-38a+174$ |
| 26.2-d2 |
26.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
26.2 |
\( 2 \cdot 13 \) |
\( 2^{2} \cdot 13 \) |
$1.93542$ |
$(-a+5), (a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$6.211018668$ |
1.295086918 |
\( \frac{24402922831899}{13} a + \frac{234064614018301}{26} \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 54 a - 274\) , \( -308 a + 1466\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(54a-274\right){x}-308a+1466$ |
| 28.1-a1 |
28.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( - 2^{4} \cdot 7 \) |
$1.97161$ |
$(-a+5), (-a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 3 \) |
$1$ |
$29.39740986$ |
2.298668884 |
\( \frac{1472}{7} a + \frac{8464}{7} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 5 a + 24\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(5a+24\right){x}$ |
| 28.1-a2 |
28.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7^{2} \) |
$1.97161$ |
$(-a+5), (-a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$14.69870493$ |
2.298668884 |
\( \frac{8732868}{49} a + \frac{42307568}{49} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -20 a - 96\) , \( -284 a - 1362\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-20a-96\right){x}-284a-1362$ |
| 28.1-b1 |
28.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( - 2^{4} \cdot 7 \) |
$1.97161$ |
$(-a+5), (-a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.760351911$ |
$23.50334847$ |
2.794742034 |
\( \frac{1472}{7} a + \frac{8464}{7} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 2 a + 4\) , \( -4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2a+4\right){x}-4$ |
| 28.1-b2 |
28.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7^{2} \) |
$1.97161$ |
$(-a+5), (-a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.380175955$ |
$23.50334847$ |
2.794742034 |
\( \frac{8732868}{49} a + \frac{42307568}{49} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -23 a - 116\) , \( 64 a + 303\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-23a-116\right){x}+64a+303$ |
| 28.2-a1 |
28.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( - 2^{4} \cdot 7 \) |
$1.97161$ |
$(-a+5), (-a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 3 \) |
$1$ |
$29.39740986$ |
2.298668884 |
\( -\frac{1472}{7} a + \frac{8464}{7} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 8 a + 12\) , \( 12 a + 40\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(8a+12\right){x}+12a+40$ |
| 28.2-a2 |
28.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7^{2} \) |
$1.97161$ |
$(-a+5), (-a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$14.69870493$ |
2.298668884 |
\( -\frac{8732868}{49} a + \frac{42307568}{49} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 33 a - 108\) , \( 176 a - 747\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(33a-108\right){x}+176a-747$ |
| 28.2-b1 |
28.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( - 2^{4} \cdot 7 \) |
$1.97161$ |
$(-a+5), (-a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.760351911$ |
$23.50334847$ |
2.794742034 |
\( -\frac{1472}{7} a + \frac{8464}{7} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 7 a + 16\) , \( 4 a + 48\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(7a+16\right){x}+4a+48$ |
| 28.2-b2 |
28.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{8} \cdot 7^{2} \) |
$1.97161$ |
$(-a+5), (-a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.380175955$ |
$23.50334847$ |
2.794742034 |
\( -\frac{8732868}{49} a + \frac{42307568}{49} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 32 a - 104\) , \( -180 a + 930\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(32a-104\right){x}-180a+930$ |
| 46.1-a1 |
46.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
46.1 |
\( 2 \cdot 23 \) |
\( 2^{20} \cdot 23^{2} \) |
$2.23214$ |
$(-a+5), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$4.101081815$ |
$1.747176977$ |
1.494071611 |
\( -\frac{116930169}{23552} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -10\) , \( -12\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-10{x}-12$ |
| 46.1-a2 |
46.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{23}) \) |
$2$ |
$[2, 0]$ |
46.1 |
\( 2 \cdot 23 \) |
\( 2^{10} \cdot 23^{4} \) |
$2.23214$ |
$(-a+5), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.050540907$ |
$1.747176977$ |
1.494071611 |
\( \frac{545138290809}{16928} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -170\) , \( -812\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-170{x}-812$ |
*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.
