| 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 |
| 9.1-CMa1 |
9.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$0.43777$ |
$(-a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \) |
$1$ |
$7.326567372$ |
0.287814748 |
\( 8000 \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}-{x}$ |
| 9.3-CMa1 |
9.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9.3 |
\( 3^{2} \) |
\( 3^{6} \) |
$0.43777$ |
$(a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{yes}$ |
$-8$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \) |
$1$ |
$7.326567372$ |
0.287814748 |
\( 8000 \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( -a - 1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-a-1\right){x}$ |
| 32.1-a1 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$0.60113$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$6.875185818$ |
0.607686314 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}$ |
| 32.1-a2 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$0.60113$ |
$(a)$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$6.875185818$ |
0.607686314 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}$ |
| 32.1-a3 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$0.60113$ |
$(a)$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$6.875185818$ |
0.607686314 |
\( 287496 \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -2\) , \( 3\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-2{x}+3$ |
| 32.1-a4 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$0.60113$ |
$(a)$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$6.875185818$ |
0.607686314 |
\( 287496 \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-{x}$ |
| 51.1-a1 |
51.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
51.1 |
\( 3 \cdot 17 \) |
\( 3^{2} \cdot 17^{2} \) |
$0.67542$ |
$(-a-1), (-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.032029606$ |
$7.122411322$ |
0.322621752 |
\( -\frac{1437952}{2601} a - \frac{95168}{2601} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -a\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}-a{x}$ |
| 51.1-a2 |
51.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
51.1 |
\( 3 \cdot 17 \) |
\( 3^{4} \cdot 17 \) |
$0.67542$ |
$(-a-1), (-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.064059212$ |
$7.122411322$ |
0.322621752 |
\( \frac{4268288}{1377} a + \frac{2027584}{1377} \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -2 a + 2\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a+2\right){x}$ |
| 51.4-a1 |
51.4-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
51.4 |
\( 3 \cdot 17 \) |
\( 3^{2} \cdot 17^{2} \) |
$0.67542$ |
$(a-1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.032029606$ |
$7.122411322$ |
0.322621752 |
\( \frac{1437952}{2601} a - \frac{95168}{2601} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}$ |
| 51.4-a2 |
51.4-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
51.4 |
\( 3 \cdot 17 \) |
\( 3^{4} \cdot 17 \) |
$0.67542$ |
$(a-1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.064059212$ |
$7.122411322$ |
0.322621752 |
\( -\frac{4268288}{1377} a + \frac{2027584}{1377} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( a + 2\) , \( -a\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+2\right){x}-a$ |
| 54.1-a1 |
54.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
54.1 |
\( 2 \cdot 3^{3} \) |
\( 2^{3} \cdot 3^{3} \) |
$0.68514$ |
$(a), (-a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$8.206562124$ |
0.644768414 |
\( \frac{6935}{4} a - \frac{9251}{2} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -a - 1\) , \( -1\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a-1\right){x}-1$ |
| 54.1-a2 |
54.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
54.1 |
\( 2 \cdot 3^{3} \) |
\( 2 \cdot 3^{5} \) |
$0.68514$ |
$(a), (-a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$8.206562124$ |
0.644768414 |
\( -\frac{269}{2} a + 1619 \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -a - 1\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}$ |
| 54.1-a3 |
54.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
54.1 |
\( 2 \cdot 3^{3} \) |
\( 2^{27} \cdot 3^{11} \) |
$0.68514$ |
$(a), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$0.911840236$ |
0.644768414 |
\( \frac{241123607}{16384} a + \frac{59710933}{8192} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -51 a + 69\) , \( 62 a + 339\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-51a+69\right){x}+62a+339$ |
| 54.1-a4 |
54.1-a |
$4$ |
$27$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
54.1 |
\( 2 \cdot 3^{3} \) |
\( 2^{9} \cdot 3^{9} \) |
$0.68514$ |
$(a), (-a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$1$ |
$2.735520708$ |
0.644768414 |
\( -\frac{2628365}{32} a + \frac{183347}{16} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -11 a + 4\) , \( -26\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-11a+4\right){x}-26$ |
| 54.4-a1 |
54.4-a |
$4$ |
$27$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
54.4 |
\( 2 \cdot 3^{3} \) |
\( 2^{3} \cdot 3^{3} \) |
$0.68514$ |
$(a), (a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 1 \) |
$1$ |
$8.206562124$ |
0.644768414 |
\( -\frac{6935}{4} a - \frac{9251}{2} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( a - 1\) , \( -1\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a-1\right){x}-1$ |
| 54.4-a2 |
54.4-a |
$4$ |
$27$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
54.4 |
\( 2 \cdot 3^{3} \) |
\( 2 \cdot 3^{5} \) |
$0.68514$ |
$(a), (a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$8.206562124$ |
0.644768414 |
\( \frac{269}{2} a + 1619 \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}-{x}$ |
| 54.4-a3 |
54.4-a |
$4$ |
$27$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
54.4 |
\( 2 \cdot 3^{3} \) |
\( 2^{27} \cdot 3^{11} \) |
$0.68514$ |
$(a), (a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$0.911840236$ |
0.644768414 |
\( -\frac{241123607}{16384} a + \frac{59710933}{8192} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 51 a + 69\) , \( -62 a + 339\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(51a+69\right){x}-62a+339$ |
| 54.4-a4 |
54.4-a |
$4$ |
$27$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
54.4 |
\( 2 \cdot 3^{3} \) |
\( 2^{9} \cdot 3^{9} \) |
$0.68514$ |
$(a), (a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$1$ |
$2.735520708$ |
0.644768414 |
\( \frac{2628365}{32} a + \frac{183347}{16} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 11 a + 4\) , \( -26\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(11a+4\right){x}-26$ |
| 72.2-a1 |
72.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
72.2 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{16} \) |
$0.73624$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$1.817673508$ |
0.642644632 |
\( \frac{207646}{6561} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 5\) , \( 23\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+5{x}+23$ |
| 72.2-a2 |
72.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
72.2 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$0.73624$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$7.270694035$ |
0.642644632 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+{x}$ |
| 72.2-a3 |
72.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
72.2 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{4} \) |
$0.73624$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$7.270694035$ |
0.642644632 |
\( \frac{35152}{9} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 0\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}$ |
| 72.2-a4 |
72.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
72.2 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$0.73624$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$3.635347017$ |
0.642644632 |
\( \frac{1556068}{81} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -5\) , \( 5\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-5{x}+5$ |
| 72.2-a5 |
72.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
72.2 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{11} \cdot 3^{20} \) |
$0.73624$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.908836754$ |
0.642644632 |
\( -\frac{2327042746553}{43046721} a + \frac{2081263802600}{43046721} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 70 a + 85\) , \( -98 a + 559\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(70a+85\right){x}-98a+559$ |
| 72.2-a6 |
72.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
72.2 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{11} \cdot 3^{20} \) |
$0.73624$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.908836754$ |
0.642644632 |
\( \frac{2327042746553}{43046721} a + \frac{2081263802600}{43046721} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -70 a + 85\) , \( 98 a + 559\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-70a+85\right){x}+98a+559$ |
| 72.2-a7 |
72.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
72.2 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$0.73624$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.635347017$ |
0.642644632 |
\( \frac{28756228}{3} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -15\) , \( -27\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-15{x}-27$ |
| 72.2-a8 |
72.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
72.2 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{4} \) |
$0.73624$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.817673508$ |
0.642644632 |
\( \frac{3065617154}{9} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -95\) , \( 347\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-95{x}+347$ |
| 98.1-a1 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{36} \cdot 7^{2} \) |
$0.79523$ |
$(a), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$0.875417135$ |
0.309506696 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-171{x}-874$ |
| 98.1-a2 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$0.79523$ |
$(a), (7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$7.878754216$ |
0.309506696 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}$ |
| 98.1-a3 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$0.79523$ |
$(a), (7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$2.626251405$ |
0.309506696 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+4{x}-6$ |
| 98.1-a4 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{12} \) |
$0.79523$ |
$(a), (7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.313125702$ |
0.309506696 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-36{x}-70$ |
| 98.1-a5 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{2} \cdot 7^{4} \) |
$0.79523$ |
$(a), (7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$3.939377108$ |
0.309506696 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-11{x}+12$ |
| 98.1-a6 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{4} \) |
$0.79523$ |
$(a), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$0.437708567$ |
0.309506696 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2731{x}-55146$ |
| 99.3-a1 |
99.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
99.3 |
\( 3^{2} \cdot 11 \) |
\( 3^{11} \cdot 11 \) |
$0.79725$ |
$(-a-1), (a-1), (a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.697318412$ |
0.600092679 |
\( \frac{3103043505622}{72171} a - \frac{541923582149}{72171} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -12 a - 90\) , \( 71 a + 302\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-12a-90\right){x}+71a+302$ |
| 99.3-a2 |
99.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
99.3 |
\( 3^{2} \cdot 11 \) |
\( 3^{25} \cdot 11^{2} \) |
$0.79725$ |
$(-a-1), (a-1), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.848659206$ |
0.600092679 |
\( \frac{139338897204254761}{34173973914201} a - \frac{247929747123659233}{34173973914201} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 3 a + 95\) , \( 251 a - 30\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(3a+95\right){x}+251a-30$ |
| 99.3-a3 |
99.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
99.3 |
\( 3^{2} \cdot 11 \) |
\( 3^{10} \cdot 11^{2} \) |
$0.79725$ |
$(-a-1), (a-1), (a+3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$3.394636825$ |
0.600092679 |
\( -\frac{364612508}{88209} a - \frac{393162727}{88209} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -2 a - 5\) , \( a + 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a-5\right){x}+a+4$ |
| 99.3-a4 |
99.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
99.3 |
\( 3^{2} \cdot 11 \) |
\( 3^{5} \cdot 11 \) |
$0.79725$ |
$(-a-1), (a-1), (a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$6.789273651$ |
0.600092679 |
\( \frac{689288}{297} a - \frac{385271}{297} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -2 a\) , \( -a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}-2a{x}-a$ |
| 99.3-a5 |
99.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
99.3 |
\( 3^{2} \cdot 11 \) |
\( 3^{14} \cdot 11^{4} \) |
$0.79725$ |
$(-a-1), (a-1), (a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$1.697318412$ |
0.600092679 |
\( \frac{1026305863102}{7780827681} a - \frac{7150733769793}{7780827681} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 8 a\) , \( 19 a + 22\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+8a{x}+19a+22$ |
| 99.3-a6 |
99.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
99.3 |
\( 3^{2} \cdot 11 \) |
\( 3^{7} \cdot 11^{8} \) |
$0.79725$ |
$(-a-1), (a-1), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.848659206$ |
0.600092679 |
\( -\frac{68547528581042953}{156267624249} a + \frac{367387425943146769}{156267624249} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 173 a - 15\) , \( 859 a + 1006\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(173a-15\right){x}+859a+1006$ |
| 99.4-a1 |
99.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
99.4 |
\( 3^{2} \cdot 11 \) |
\( 3^{11} \cdot 11 \) |
$0.79725$ |
$(-a-1), (a-1), (a-3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.697318412$ |
0.600092679 |
\( -\frac{3103043505622}{72171} a - \frac{541923582149}{72171} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 10 a - 90\) , \( -72 a + 302\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(10a-90\right){x}-72a+302$ |
| 99.4-a2 |
99.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
99.4 |
\( 3^{2} \cdot 11 \) |
\( 3^{25} \cdot 11^{2} \) |
$0.79725$ |
$(-a-1), (a-1), (a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.848659206$ |
0.600092679 |
\( -\frac{139338897204254761}{34173973914201} a - \frac{247929747123659233}{34173973914201} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -5 a + 95\) , \( -252 a - 30\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-5a+95\right){x}-252a-30$ |
| 99.4-a3 |
99.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
99.4 |
\( 3^{2} \cdot 11 \) |
\( 3^{10} \cdot 11^{2} \) |
$0.79725$ |
$(-a-1), (a-1), (a-3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$3.394636825$ |
0.600092679 |
\( \frac{364612508}{88209} a - \frac{393162727}{88209} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -5\) , \( -2 a + 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}-5{x}-2a+4$ |
| 99.4-a4 |
99.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
99.4 |
\( 3^{2} \cdot 11 \) |
\( 3^{5} \cdot 11 \) |
$0.79725$ |
$(-a-1), (a-1), (a-3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$6.789273651$ |
0.600092679 |
\( -\frac{689288}{297} a - \frac{385271}{297} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}$ |
| 99.4-a5 |
99.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
99.4 |
\( 3^{2} \cdot 11 \) |
\( 3^{14} \cdot 11^{4} \) |
$0.79725$ |
$(-a-1), (a-1), (a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$1.697318412$ |
0.600092679 |
\( -\frac{1026305863102}{7780827681} a - \frac{7150733769793}{7780827681} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -10 a\) , \( -20 a + 22\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}-10a{x}-20a+22$ |
| 99.4-a6 |
99.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
99.4 |
\( 3^{2} \cdot 11 \) |
\( 3^{7} \cdot 11^{8} \) |
$0.79725$ |
$(-a-1), (a-1), (a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.848659206$ |
0.600092679 |
\( \frac{68547528581042953}{156267624249} a + \frac{367387425943146769}{156267624249} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -175 a - 15\) , \( -860 a + 1006\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-175a-15\right){x}-860a+1006$ |
| 100.1-a1 |
100.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{12} \) |
$0.79925$ |
$(a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$0.137812304$ |
$2.141031885$ |
0.625917922 |
\( -\frac{20720464}{15625} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -8\) , \( 18\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-8{x}+18$ |
| 100.1-a2 |
100.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{4} \) |
$0.79925$ |
$(a), (5)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.413436914$ |
$6.423095656$ |
0.625917922 |
\( \frac{21296}{25} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 2\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+2{x}$ |
| 100.1-a3 |
100.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{2} \) |
$0.79925$ |
$(a), (5)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$0.826873828$ |
$6.423095656$ |
0.625917922 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-{x}$ |
| 100.1-a4 |
100.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$0.79925$ |
$(a), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 3 \) |
$0.275624609$ |
$2.141031885$ |
0.625917922 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -41\) , \( -116\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-41{x}-116$ |
| 108.2-a1 |
108.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
108.2 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{8} \cdot 3^{13} \) |
$0.81478$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$1$ |
$1.488316936$ |
1.052398998 |
\( -\frac{18202756}{81} a - \frac{253086988}{81} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -59 a + 4\) , \( 122 a - 261\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-59a+4\right){x}+122a-261$ |
| 108.2-a2 |
108.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
108.2 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{8} \cdot 3^{13} \) |
$0.81478$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$1.488316936$ |
1.052398998 |
\( \frac{18202756}{81} a - \frac{253086988}{81} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -48 a + 49\) , \( 7 a + 265\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-48a+49\right){x}+7a+265$ |
*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.
