| 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 |
| 1.1-a5 |
1.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.43777$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-72$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$5.639994193$ |
0.287814748 |
\( 77092288000 a + 188837384000 \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -68 a - 161\) , \( -459 a - 1122\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-68a-161\right){x}-459a-1122$ |
| 1.1-a6 |
1.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.43777$ |
$\textsf{none}$ |
0 |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-72$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$50.75994773$ |
0.287814748 |
\( 77092288000 a + 188837384000 \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 17 a - 41\) , \( -57 a + 138\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(17a-41\right){x}-57a+138$ |
| 16.1-a5 |
16.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$0.87554$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-72$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$25.37997386$ |
1.295166367 |
\( 77092288000 a + 188837384000 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 64 a - 166\) , \( -418 a + 1056\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(64a-166\right){x}-418a+1056$ |
| 16.1-a6 |
16.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$0.87554$ |
$(-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-72$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$9$ |
\( 1 \) |
$1$ |
$2.819997096$ |
1.295166367 |
\( 77092288000 a + 188837384000 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -264 a - 646\) , \( -3782 a - 9264\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-264a-646\right){x}-3782a-9264$ |
| 225.2-e5 |
225.2-e |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
225.2 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{6} \) |
$1.69547$ |
$(a+3), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-72$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1.792599469$ |
$3.089152043$ |
2.260720761 |
\( 77092288000 a + 188837384000 \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( -4119 a - 10086\) , \( -223834 a - 548279\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-4119a-10086\right){x}-223834a-548279$ |
| 225.2-e6 |
225.2-e |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
225.2 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{6} \) |
$1.69547$ |
$(a+3), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-72$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.896299734$ |
$6.178304087$ |
2.260720761 |
\( 77092288000 a + 188837384000 \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( 16 a - 246\) , \( 714 a - 547\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(16a-246\right){x}+714a-547$ |
| 225.3-e5 |
225.3-e |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
225.3 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{6} \) |
$1.69547$ |
$(a+3), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-72$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1.792599469$ |
$3.089152043$ |
2.260720761 |
\( 77092288000 a + 188837384000 \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( 1028 a - 2526\) , \( -28451 a + 69661\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(1028a-2526\right){x}-28451a+69661$ |
| 225.3-e6 |
225.3-e |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
225.3 |
\( 3^{2} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{6} \) |
$1.69547$ |
$(a+3), (-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-72$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.896299734$ |
$6.178304087$ |
2.260720761 |
\( 77092288000 a + 188837384000 \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( -227 a - 606\) , \( 2841 a + 6833\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-227a-606\right){x}+2841a+6833$ |
| 529.2-e5 |
529.2-e |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
529.2 |
\( 23^{2} \) |
\( 23^{6} \) |
$2.09946$ |
$(-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-72$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$3.756467216$ |
$2.494715329$ |
3.825823879 |
\( 77092288000 a + 188837384000 \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -998 a - 2475\) , \( -27255 a - 66707\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-998a-2475\right){x}-27255a-66707$ |
| 529.2-e6 |
529.2-e |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
529.2 |
\( 23^{2} \) |
\( 23^{6} \) |
$2.09946$ |
$(-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-72$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1.878233608$ |
$4.989430659$ |
3.825823879 |
\( 77092288000 a + 188837384000 \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( 564 a - 1433\) , \( 11356 a - 27731\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(564a-1433\right){x}+11356a-27731$ |
| 529.3-e5 |
529.3-e |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
529.3 |
\( 23^{2} \) |
\( 23^{6} \) |
$2.09946$ |
$(2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-72$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1.878233608$ |
$4.989430659$ |
3.825823879 |
\( 77092288000 a + 188837384000 \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -2295 a - 5633\) , \( 95268 a + 233329\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2295a-5633\right){x}+95268a+233329$ |
| 529.3-e6 |
529.3-e |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
529.3 |
\( 23^{2} \) |
\( 23^{6} \) |
$2.09946$ |
$(2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-72$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$3.756467216$ |
$2.494715329$ |
3.825823879 |
\( 77092288000 a + 188837384000 \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 227 a - 675\) , \( -3441 a + 7933\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(227a-675\right){x}-3441a+7933$ |
| 625.1-b5 |
625.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
625.1 |
\( 5^{4} \) |
\( 5^{12} \) |
$2.18884$ |
$(-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-72$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$10.15198954$ |
2.072266188 |
\( 77092288000 a + 188837384000 \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 395 a - 1053\) , \( -6657 a + 16645\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(395a-1053\right){x}-6657a+16645$ |
| 625.1-b6 |
625.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
625.1 |
\( 5^{4} \) |
\( 5^{12} \) |
$2.18884$ |
$(-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-72$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$9$ |
\( 2^{2} \) |
$1$ |
$1.127998838$ |
2.072266188 |
\( 77092288000 a + 188837384000 \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -1646 a - 4053\) , \( -58719 a - 143855\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-1646a-4053\right){x}-58719a-143855$ |
*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.
