| 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 |
| 1568.2-a1 |
1568.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{9} \cdot 7^{8} \) |
$1.59045$ |
$(a), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.095403594$ |
$6.280045969$ |
2.541931328 |
\( -4306 a - 5764 \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -9 a + 8\) , \( 22 a - 25\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-9a+8\right){x}+22a-25$ |
| 1568.2-b1 |
1568.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( - 2^{12} \cdot 7^{7} \) |
$1.59045$ |
$(a), (-2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.213819561$ |
$5.736242026$ |
2.461708388 |
\( -\frac{5218816}{7} a + \frac{7380544}{7} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 8 a - 1\) , \( -99 a - 116\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(8a-1\right){x}-99a-116$ |
| 1568.2-b2 |
1568.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{9} \cdot 7^{14} \) |
$1.59045$ |
$(a), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.427639122$ |
$1.434060506$ |
2.461708388 |
\( \frac{2029945534}{5764801} a + \frac{2870783836}{5764801} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( a + 6\) , \( 1518 a - 2139\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+6\right){x}+1518a-2139$ |
| 1568.2-b3 |
1568.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{10} \) |
$1.59045$ |
$(a), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.213819561$ |
$5.736242026$ |
2.461708388 |
\( -\frac{41713104}{2401} a + \frac{65895512}{2401} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -26 a - 44\) , \( 40 a + 49\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-26a-44\right){x}+40a+49$ |
| 1568.2-b4 |
1568.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{8} \) |
$1.59045$ |
$(a), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.606909780$ |
$5.736242026$ |
2.461708388 |
\( \frac{523776}{49} a + \frac{855488}{49} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 44 a - 66\) , \( -88 a + 120\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(44a-66\right){x}-88a+120$ |
| 1568.2-b5 |
1568.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{9} \cdot 7^{8} \) |
$1.59045$ |
$(a), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.427639122$ |
$2.868121013$ |
2.461708388 |
\( -\frac{45461061598}{49} a + \frac{64493458228}{49} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -381 a - 654\) , \( 5384 a + 7135\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-381a-654\right){x}+5384a+7135$ |
| 1568.2-b6 |
1568.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( - 2^{6} \cdot 7^{7} \) |
$1.59045$ |
$(a), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.213819561$ |
$2.868121013$ |
2.461708388 |
\( \frac{2506735792}{7} a + \frac{3545068552}{7} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -44 a + 45\) , \( -110 a + 127\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-44a+45\right){x}-110a+127$ |
| 1568.2-c1 |
1568.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( - 2^{12} \cdot 7^{9} \) |
$1.59045$ |
$(a), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$4.518620871$ |
1.597573729 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -16 a - 13\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-16a-13\right){x}$ |
| 1568.2-c2 |
1568.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( - 2^{12} \cdot 7^{9} \) |
$1.59045$ |
$(a), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$4.518620871$ |
1.597573729 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 16 a + 13\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(16a+13\right){x}$ |
| 1568.2-d1 |
1568.2-d |
$1$ |
$1$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{9} \cdot 7^{8} \) |
$1.59045$ |
$(a), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$2.880254535$ |
1.018323756 |
\( -4306 a - 5764 \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -9 a + 8\) , \( -22 a + 25\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-9a+8\right){x}-22a+25$ |
| 1568.2-e1 |
1568.2-e |
$1$ |
$1$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{9} \cdot 7^{2} \) |
$1.59045$ |
$(a), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.075406523$ |
$22.89830725$ |
2.441896736 |
\( -4306 a - 5764 \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -a\) , \( 1\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-a{x}+1$ |
| 1568.2-f1 |
1568.2-f |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( - 2^{12} \cdot 7^{7} \) |
$1.59045$ |
$(a), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.084372149$ |
1.444043622 |
\( -\frac{5218816}{7} a + \frac{7380544}{7} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 8 a - 1\) , \( 99 a + 116\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(8a-1\right){x}+99a+116$ |
| 1568.2-f2 |
1568.2-f |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{9} \cdot 7^{14} \) |
$1.59045$ |
$(a), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.042186074$ |
1.444043622 |
\( \frac{2029945534}{5764801} a + \frac{2870783836}{5764801} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( a + 6\) , \( -1518 a + 2139\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(a+6\right){x}-1518a+2139$ |
| 1568.2-f3 |
1568.2-f |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{10} \) |
$1.59045$ |
$(a), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$8.168744299$ |
1.444043622 |
\( -\frac{41713104}{2401} a + \frac{65895512}{2401} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -28 a - 45\) , \( -67 a - 94\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-28a-45\right){x}-67a-94$ |
| 1568.2-f4 |
1568.2-f |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{8} \) |
$1.59045$ |
$(a), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$8.168744299$ |
1.444043622 |
\( \frac{523776}{49} a + \frac{855488}{49} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 44 a - 66\) , \( 88 a - 120\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(44a-66\right){x}+88a-120$ |
| 1568.2-f5 |
1568.2-f |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{9} \cdot 7^{8} \) |
$1.59045$ |
$(a), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.084372149$ |
1.444043622 |
\( -\frac{45461061598}{49} a + \frac{64493458228}{49} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -383 a - 655\) , \( -5766 a - 7790\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-383a-655\right){x}-5766a-7790$ |
| 1568.2-f6 |
1568.2-f |
$6$ |
$8$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( - 2^{6} \cdot 7^{7} \) |
$1.59045$ |
$(a), (-2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$8.168744299$ |
1.444043622 |
\( \frac{2506735792}{7} a + \frac{3545068552}{7} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -44 a + 45\) , \( 110 a - 128\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-44a+45\right){x}+110a-128$ |
| 1568.2-g1 |
1568.2-g |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( - 2^{12} \cdot 7^{3} \) |
$1.59045$ |
$(a), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.294548727$ |
$11.95514709$ |
2.489986982 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a + 5\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(4a+5\right){x}$ |
| 1568.2-g2 |
1568.2-g |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( - 2^{12} \cdot 7^{3} \) |
$1.59045$ |
$(a), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.147274363$ |
$11.95514709$ |
2.489986982 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a - 5\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-4a-5\right){x}$ |
| 1568.2-h1 |
1568.2-h |
$1$ |
$1$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{9} \cdot 7^{2} \) |
$1.59045$ |
$(a), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$5.529531715$ |
1.954984686 |
\( -4306 a - 5764 \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -a\) , \( -1\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}-1$ |
| 1568.2-i1 |
1568.2-i |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( - 2^{9} \cdot 7^{6} \) |
$1.59045$ |
$(a), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-64$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$4$ |
\( 2 \) |
$1$ |
$2.598575984$ |
1.837470700 |
\( -29071392966 a + 41113158120 \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -55 a - 97\) , \( 1397 a + 1934\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-55a-97\right){x}+1397a+1934$ |
| 1568.2-i2 |
1568.2-i |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( - 2^{9} \cdot 7^{6} \) |
$1.59045$ |
$(a), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-64$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$5.197151969$ |
1.837470700 |
\( -29071392966 a + 41113158120 \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -55 a - 96\) , \( -1452 a - 2031\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-55a-96\right){x}-1452a-2031$ |
| 1568.2-i3 |
1568.2-i |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$1.59045$ |
$(a), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$5.197151969$ |
1.837470700 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a + 9\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-4a+9\right){x}$ |
| 1568.2-i4 |
1568.2-i |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$1.59045$ |
$(a), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$10.39430393$ |
1.837470700 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 9\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(4a-9\right){x}$ |
| 1568.2-i5 |
1568.2-i |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{6} \) |
$1.59045$ |
$(a), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$10.39430393$ |
1.837470700 |
\( 287496 \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 11 a - 24\) , \( 44 a - 56\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(11a-24\right){x}+44a-56$ |
| 1568.2-i6 |
1568.2-i |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{6} \) |
$1.59045$ |
$(a), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$10.39430393$ |
1.837470700 |
\( 287496 \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 11 a - 25\) , \( -33 a + 31\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(11a-25\right){x}-33a+31$ |
| 1568.2-i7 |
1568.2-i |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( - 2^{9} \cdot 7^{6} \) |
$1.59045$ |
$(a), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-64$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$5.197151969$ |
1.837470700 |
\( 29071392966 a + 41113158120 \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -44 a - 84\) , \( 286 a + 208\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-44a-84\right){x}+286a+208$ |
| 1568.2-i8 |
1568.2-i |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( - 2^{9} \cdot 7^{6} \) |
$1.59045$ |
$(a), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-64$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$2.598575984$ |
1.837470700 |
\( 29071392966 a + 41113158120 \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -44 a - 85\) , \( -330 a - 293\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-44a-85\right){x}-330a-293$ |
*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.
