| 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 |
| 72.1-a1 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( - 2^{10} \cdot 3^{18} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.795372951$ |
2.012152092 |
\( -\frac{1497379111186634}{43046721} a + \frac{4734706974798626}{43046721} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 262 a - 852\) , \( 4628 a - 14672\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(262a-852\right){x}+4628a-14672$ |
| 72.1-a2 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{18} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$3.181491805$ |
2.012152092 |
\( -\frac{3004990072}{43046721} a + \frac{14707981316}{43046721} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -8 a + 28\) , \( -40 a + 122\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-8a+28\right){x}-40a+122$ |
| 72.1-a3 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{6} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$25.45193444$ |
2.012152092 |
\( -\frac{176918528}{81} a + \frac{559937536}{81} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 48 a - 154\) , \( -278 a + 888\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(48a-154\right){x}-278a+888$ |
| 72.1-a4 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{12} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$12.72596722$ |
2.012152092 |
\( \frac{7017920}{6561} a + \frac{51821648}{6561} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 2 a - 7\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a-7\right){x}$ |
| 72.1-a5 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{12} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$3.181491805$ |
2.012152092 |
\( \frac{114749397880}{6561} a + \frac{362971739468}{6561} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 12 a - 62\) , \( 84 a - 300\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(12a-62\right){x}+84a-300$ |
| 72.1-a6 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( - 2^{10} \cdot 3^{6} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.795372951$ |
2.012152092 |
\( \frac{156744508474885994}{81} a + \frac{495669657504209806}{81} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -78 a - 152\) , \( -204 a - 2208\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-78a-152\right){x}-204a-2208$ |
| 72.1-b1 |
72.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( - 2^{22} \cdot 3^{18} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$4.662222227$ |
$0.795372951$ |
2.345275052 |
\( -\frac{1497379111186634}{43046721} a + \frac{4734706974798626}{43046721} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 1052 a - 3421\) , \( 32553 a - 103446\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(1052a-3421\right){x}+32553a-103446$ |
| 72.1-b2 |
72.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{18} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.582777778$ |
$3.181491805$ |
2.345275052 |
\( -\frac{3004990072}{43046721} a + \frac{14707981316}{43046721} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -28 a + 99\) , \( -191 a + 586\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-28a+99\right){x}-191a+586$ |
| 72.1-b3 |
72.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{6} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.582777778$ |
$25.45193444$ |
2.345275052 |
\( -\frac{176918528}{81} a + \frac{559937536}{81} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 12 a - 36\) , \( -54 a + 171\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(12a-36\right){x}-54a+171$ |
| 72.1-b4 |
72.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{12} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.165555556$ |
$12.72596722$ |
2.345275052 |
\( \frac{7017920}{6561} a + \frac{51821648}{6561} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 12 a - 41\) , \( -51 a + 150\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(12a-41\right){x}-51a+150$ |
| 72.1-b5 |
72.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{12} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$2.331111113$ |
$3.181491805$ |
2.345275052 |
\( \frac{114749397880}{6561} a + \frac{362971739468}{6561} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 52 a - 261\) , \( 361 a - 1630\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(52a-261\right){x}+361a-1630$ |
| 72.1-b6 |
72.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( - 2^{22} \cdot 3^{6} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$4.662222227$ |
$0.795372951$ |
2.345275052 |
\( \frac{156744508474885994}{81} a + \frac{495669657504209806}{81} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -308 a - 621\) , \( -1943 a - 20134\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-308a-621\right){x}-1943a-20134$ |
| 72.1-c1 |
72.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( - 2^{10} \cdot 3^{6} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.795372951$ |
2.012152092 |
\( -\frac{156744508474885994}{81} a + \frac{495669657504209806}{81} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 78 a - 152\) , \( 204 a - 2208\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(78a-152\right){x}+204a-2208$ |
| 72.1-c2 |
72.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{18} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$3.181491805$ |
2.012152092 |
\( \frac{3004990072}{43046721} a + \frac{14707981316}{43046721} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 8 a + 28\) , \( 40 a + 122\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(8a+28\right){x}+40a+122$ |
| 72.1-c3 |
72.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{12} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$12.72596722$ |
2.012152092 |
\( -\frac{7017920}{6561} a + \frac{51821648}{6561} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -2 a - 7\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a-7\right){x}$ |
| 72.1-c4 |
72.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{12} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$3.181491805$ |
2.012152092 |
\( -\frac{114749397880}{6561} a + \frac{362971739468}{6561} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -12 a - 62\) , \( -84 a - 300\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-12a-62\right){x}-84a-300$ |
| 72.1-c5 |
72.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{6} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$25.45193444$ |
2.012152092 |
\( \frac{176918528}{81} a + \frac{559937536}{81} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -48 a - 154\) , \( 278 a + 888\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-48a-154\right){x}+278a+888$ |
| 72.1-c6 |
72.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( - 2^{10} \cdot 3^{18} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.795372951$ |
2.012152092 |
\( \frac{1497379111186634}{43046721} a + \frac{4734706974798626}{43046721} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -262 a - 852\) , \( -4628 a - 14672\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-262a-852\right){x}-4628a-14672$ |
| 72.1-d1 |
72.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( - 2^{22} \cdot 3^{6} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$4.662222227$ |
$0.795372951$ |
2.345275052 |
\( -\frac{156744508474885994}{81} a + \frac{495669657504209806}{81} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 308 a - 621\) , \( 1943 a - 20134\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(308a-621\right){x}+1943a-20134$ |
| 72.1-d2 |
72.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{18} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.582777778$ |
$3.181491805$ |
2.345275052 |
\( \frac{3004990072}{43046721} a + \frac{14707981316}{43046721} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 28 a + 99\) , \( 191 a + 586\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(28a+99\right){x}+191a+586$ |
| 72.1-d3 |
72.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{12} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.165555556$ |
$12.72596722$ |
2.345275052 |
\( -\frac{7017920}{6561} a + \frac{51821648}{6561} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -12 a - 41\) , \( 51 a + 150\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-12a-41\right){x}+51a+150$ |
| 72.1-d4 |
72.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{12} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$2.331111113$ |
$3.181491805$ |
2.345275052 |
\( -\frac{114749397880}{6561} a + \frac{362971739468}{6561} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -52 a - 261\) , \( -361 a - 1630\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-52a-261\right){x}-361a-1630$ |
| 72.1-d5 |
72.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{6} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.582777778$ |
$25.45193444$ |
2.345275052 |
\( \frac{176918528}{81} a + \frac{559937536}{81} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -12 a - 36\) , \( 54 a + 171\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-12a-36\right){x}+54a+171$ |
| 72.1-d6 |
72.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( - 2^{22} \cdot 3^{18} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$4.662222227$ |
$0.795372951$ |
2.345275052 |
\( \frac{1497379111186634}{43046721} a + \frac{4734706974798626}{43046721} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -1052 a - 3421\) , \( -32553 a - 103446\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-1052a-3421\right){x}-32553a-103446$ |
| 72.1-e1 |
72.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{16} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1$ |
$2.325279868$ |
2.941272233 |
\( \frac{207646}{6561} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 6\) , \( -18\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+6{x}-18$ |
| 72.1-e2 |
72.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{2} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$18.60223895$ |
2.941272233 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 3\) , \( 3\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+3{x}+3$ |
| 72.1-e3 |
72.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{4} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$37.20447790$ |
2.941272233 |
\( \frac{35152}{9} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}$ |
| 72.1-e4 |
72.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$9.301119475$ |
2.941272233 |
\( \frac{1556068}{81} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -4\) , \( -10\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-4{x}-10$ |
| 72.1-e5 |
72.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$37.20447790$ |
2.941272233 |
\( \frac{28756228}{3} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -14\) , \( 12\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-14{x}+12$ |
| 72.1-e6 |
72.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{4} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$2.325279868$ |
2.941272233 |
\( \frac{3065617154}{9} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -94\) , \( -442\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-94{x}-442$ |
| 72.1-f1 |
72.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{16} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.124911523$ |
$2.325279868$ |
1.654335513 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 16\) , \( -180\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+16{x}-180$ |
| 72.1-f2 |
72.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.249823046$ |
$18.60223895$ |
1.654335513 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+{x}$ |
| 72.1-f3 |
72.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{4} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.124911523$ |
$37.20447790$ |
1.654335513 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -4\) , \( 4\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-4{x}+4$ |
| 72.1-f4 |
72.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{8} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.562455761$ |
$9.301119475$ |
1.654335513 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -24\) , \( -36\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-24{x}-36$ |
| 72.1-f5 |
72.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{2} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.562455761$ |
$37.20447790$ |
1.654335513 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -64\) , \( 220\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-64{x}+220$ |
| 72.1-f6 |
72.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{4} \) |
$1.64627$ |
$(2,a), (3,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.124911523$ |
$2.325279868$ |
1.654335513 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -384\) , \( -2772\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-384{x}-2772$ |
*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.
