| 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 |
| 24336.2-a1 |
24336.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 13^{4} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.996842954$ |
$3.067520634$ |
2.162216804 |
\( -\frac{256000}{507} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -3\) , \( 6\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-3{x}+6$ |
| 24336.2-a2 |
24336.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 13^{2} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.498421477$ |
$3.067520634$ |
2.162216804 |
\( \frac{137842000}{117} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -17\) , \( -30\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-17{x}-30$ |
| 24336.2-b1 |
24336.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{16} \cdot 13^{2} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.290412728$ |
1.824919182 |
\( -\frac{34153369600}{62178597} a - \frac{43076829184}{62178597} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 10 a + 19\) , \( -40 a + 38\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(10a+19\right){x}-40a+38$ |
| 24336.2-b2 |
24336.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{8} \cdot 13^{4} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$1.290412728$ |
1.824919182 |
\( \frac{582894288160}{369603} a + \frac{400569131728}{369603} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 40 a + 91\) , \( 209 a - 301\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(40a+91\right){x}+209a-301$ |
| 24336.2-c1 |
24336.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 13^{2} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.492709306$ |
$1.882955324$ |
5.248144329 |
\( \frac{16384000}{9477} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -13\) , \( 4\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-13{x}+4$ |
| 24336.2-c2 |
24336.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 13^{12} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1.970837224$ |
$0.627651774$ |
5.248144329 |
\( \frac{181037698000}{14480427} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -186\) , \( -945\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-186{x}-945$ |
| 24336.2-c3 |
24336.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 13^{4} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1.970837224$ |
$1.882955324$ |
5.248144329 |
\( \frac{1409938000}{4563} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -36\) , \( 81\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-36{x}+81$ |
| 24336.2-c4 |
24336.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 13^{6} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.492709306$ |
$0.627651774$ |
5.248144329 |
\( \frac{2725888000000}{19773} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -733\) , \( 7888\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-733{x}+7888$ |
| 24336.2-d1 |
24336.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 13^{8} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.911822885$ |
$1.332286356$ |
3.685205968 |
\( \frac{48668}{85683} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 2\) , \( -56\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+2{x}-56$ |
| 24336.2-d2 |
24336.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 13^{2} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.977955721$ |
$2.664572713$ |
3.685205968 |
\( \frac{2725888}{1053} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -7\) , \( -2\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-7{x}-2$ |
| 24336.2-d3 |
24336.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 13^{4} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.955911442$ |
$2.664572713$ |
3.685205968 |
\( \frac{61918288}{1521} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -13\) , \( -20\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-13{x}-20$ |
| 24336.2-d4 |
24336.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 13^{2} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$3.911822885$ |
$1.332286356$ |
3.685205968 |
\( \frac{62275269892}{39} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -208\) , \( -1190\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-208{x}-1190$ |
| 24336.2-e1 |
24336.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 13^{4} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.987391756$ |
$2.159942461$ |
3.035363226 |
\( \frac{702464}{4563} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 5\) , \( -14\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+5{x}-14$ |
| 24336.2-e2 |
24336.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 13^{2} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.993695878$ |
$2.159942461$ |
3.035363226 |
\( \frac{94875856}{9477} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -15\) , \( 18\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-15{x}+18$ |
| 24336.2-f1 |
24336.2-f |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{16} \cdot 13^{2} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.290412728$ |
1.824919182 |
\( \frac{34153369600}{62178597} a - \frac{43076829184}{62178597} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -10 a + 19\) , \( 40 a + 38\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-10a+19\right){x}+40a+38$ |
| 24336.2-f2 |
24336.2-f |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{8} \cdot 13^{4} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$1.290412728$ |
1.824919182 |
\( -\frac{582894288160}{369603} a + \frac{400569131728}{369603} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -40 a + 91\) , \( -209 a - 301\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-40a+91\right){x}-209a-301$ |
| 24336.2-g1 |
24336.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{19} \cdot 13^{2} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$3.855633616$ |
$0.643404292$ |
5.262425598 |
\( -\frac{253048096475372}{559607373} a - \frac{218119524144004}{559607373} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -75 a - 347\) , \( 720 a + 2642\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-75a-347\right){x}+720a+2642$ |
| 24336.2-g2 |
24336.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{7} \cdot 13^{8} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.963908404$ |
$0.643404292$ |
5.262425598 |
\( \frac{141982147868}{2313441} a - \frac{41954607644}{2313441} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -145 a - 157\) , \( -1088 a - 134\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-145a-157\right){x}-1088a-134$ |
| 24336.2-g3 |
24336.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{14} \cdot 13^{4} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1.927816808$ |
$1.286808584$ |
5.262425598 |
\( -\frac{417240032}{1108809} a + \frac{1399915568}{1108809} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -10 a - 22\) , \( -8 a + 55\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-10a-22\right){x}-8a+55$ |
| 24336.2-g4 |
24336.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{16} \cdot 13^{2} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.963908404$ |
$1.286808584$ |
5.262425598 |
\( \frac{3919376384}{6908733} a + \frac{14220271616}{6908733} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 14 a + 22\) , \( 10 a - 49\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(14a+22\right){x}+10a-49$ |
| 24336.2-h1 |
24336.2-h |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 13^{4} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.891832161$ |
2.675454701 |
\( -\frac{1952763232}{13689} a - \frac{2882870192}{13689} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 23 a - 12\) , \( 42 a + 11\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(23a-12\right){x}+42a+11$ |
| 24336.2-h2 |
24336.2-h |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 13^{2} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.891832161$ |
2.675454701 |
\( -\frac{6957056}{85293} a + \frac{87197696}{85293} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 6 a - 8\) , \( -6 a - 15\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(6a-8\right){x}-6a-15$ |
| 24336.2-i1 |
24336.2-i |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 13^{4} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.891832161$ |
2.675454701 |
\( \frac{1952763232}{13689} a - \frac{2882870192}{13689} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -23 a - 12\) , \( -42 a + 11\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-23a-12\right){x}-42a+11$ |
| 24336.2-i2 |
24336.2-i |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 13^{2} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.891832161$ |
2.675454701 |
\( \frac{6957056}{85293} a + \frac{87197696}{85293} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -6 a - 8\) , \( 6 a - 15\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-6a-8\right){x}+6a-15$ |
| 24336.2-j1 |
24336.2-j |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{19} \cdot 13^{2} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$3.855633616$ |
$0.643404292$ |
5.262425598 |
\( \frac{253048096475372}{559607373} a - \frac{218119524144004}{559607373} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 75 a - 347\) , \( -720 a + 2642\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(75a-347\right){x}-720a+2642$ |
| 24336.2-j2 |
24336.2-j |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{7} \cdot 13^{8} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.963908404$ |
$0.643404292$ |
5.262425598 |
\( -\frac{141982147868}{2313441} a - \frac{41954607644}{2313441} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 145 a - 157\) , \( 1088 a - 134\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(145a-157\right){x}+1088a-134$ |
| 24336.2-j3 |
24336.2-j |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{14} \cdot 13^{4} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1.927816808$ |
$1.286808584$ |
5.262425598 |
\( \frac{417240032}{1108809} a + \frac{1399915568}{1108809} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 10 a - 22\) , \( 8 a + 55\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(10a-22\right){x}+8a+55$ |
| 24336.2-j4 |
24336.2-j |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{16} \cdot 13^{2} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.963908404$ |
$1.286808584$ |
5.262425598 |
\( -\frac{3919376384}{6908733} a + \frac{14220271616}{6908733} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -14 a + 22\) , \( -10 a - 49\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-14a+22\right){x}-10a-49$ |
| 24336.2-k1 |
24336.2-k |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{2} \cdot 13^{2} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.780590085$ |
2.673280886 |
\( \frac{12167}{39} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 3\) , \( -2\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+3{x}-2$ |
| 24336.2-k2 |
24336.2-k |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 13^{4} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.890295042$ |
2.673280886 |
\( \frac{10218313}{1521} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -17\) , \( -22\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-17{x}-22$ |
| 24336.2-k3 |
24336.2-k |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{2} \cdot 13^{8} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.945147521$ |
2.673280886 |
\( \frac{822656953}{85683} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -77\) , \( 254\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-77{x}+254$ |
| 24336.2-k4 |
24336.2-k |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{12} \cdot 3^{8} \cdot 13^{2} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.945147521$ |
2.673280886 |
\( \frac{37159393753}{1053} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -277\) , \( -1738\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-277{x}-1738$ |
| 24336.2-l1 |
24336.2-l |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 13^{8} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$2.220408588$ |
$1.091420708$ |
6.854410053 |
\( \frac{269676572}{257049} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 35\) , \( 56\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+35{x}+56$ |
| 24336.2-l2 |
24336.2-l |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{8} \cdot 13^{4} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.110204294$ |
$2.182841417$ |
6.854410053 |
\( \frac{37642192}{13689} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -10\) , \( 11\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-10{x}+11$ |
| 24336.2-l3 |
24336.2-l |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{16} \cdot 13^{2} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$0.555102147$ |
$1.091420708$ |
6.854410053 |
\( \frac{3044193988}{85293} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -75\) , \( -236\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-75{x}-236$ |
| 24336.2-l4 |
24336.2-l |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 13^{2} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.220408588$ |
$2.182841417$ |
6.854410053 |
\( \frac{420616192}{117} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -39\) , \( -108\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-39{x}-108$ |
| 24336.2-m1 |
24336.2-m |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 13^{4} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.675228376$ |
$3.874235061$ |
7.328782477 |
\( \frac{686000}{507} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 4\) , \( -1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+4{x}-1$ |
| 24336.2-m2 |
24336.2-m |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 13^{2} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.337614188$ |
$3.874235061$ |
7.328782477 |
\( \frac{256000}{117} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-3{x}$ |
| 24336.2-n1 |
24336.2-n |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{10} \cdot 13^{12} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \cdot 5^{2} \) |
$0.406751427$ |
$0.342059320$ |
7.378647798 |
\( \frac{77366117936}{1172914587} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 142\) , \( 3209\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+142{x}+3209$ |
| 24336.2-n2 |
24336.2-n |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{20} \cdot 13^{6} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
$0.203375713$ |
$0.342059320$ |
7.378647798 |
\( \frac{1909913257984}{129730653} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -651\) , \( -6228\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-651{x}-6228$ |
| 24336.2-o1 |
24336.2-o |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 13^{4} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$3.590171887$ |
5.077269774 |
\( \frac{3631696}{507} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -5\) , \( -3\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-5{x}-3$ |
| 24336.2-o2 |
24336.2-o |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 13^{2} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.590171887$ |
5.077269774 |
\( \frac{1048576}{117} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -5\) , \( -6\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-5{x}-6$ |
| 24336.2-p1 |
24336.2-p |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{44} \cdot 3^{10} \cdot 13^{2} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5^{2} \) |
$1$ |
$0.288515022$ |
5.100273218 |
\( -\frac{822656953}{207028224} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -77\) , \( 5558\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-77{x}+5558$ |
| 24336.2-p2 |
24336.2-p |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{20} \cdot 3^{40} \cdot 13^{2} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \cdot 5^{2} \) |
$1$ |
$0.072128755$ |
5.100273218 |
\( \frac{1416134368422073}{725251155408} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -9357\) , \( -116618\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-9357{x}-116618$ |
| 24336.2-p3 |
24336.2-p |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{28} \cdot 3^{20} \cdot 13^{4} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \cdot 5^{2} \) |
$1$ |
$0.144257511$ |
5.100273218 |
\( \frac{242702053576633}{2554695936} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -5197\) , \( 143798\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-5197{x}+143798$ |
| 24336.2-p4 |
24336.2-p |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
24336.2 |
\( 2^{4} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{20} \cdot 3^{10} \cdot 13^{8} \) |
$3.15679$ |
$(a), (-a-1), (a-1), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 5^{2} \) |
$1$ |
$0.072128755$ |
5.100273218 |
\( \frac{986551739719628473}{111045168} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -82957\) , \( 9210614\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-82957{x}+9210614$ |
*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.
