| 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 |
| 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 |
\( \frac{364612508}{88209} a - \frac{393162727}{88209} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -5\) , \( -2 a + 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}-5{x}-2a+4$ |
| 891.6-c3 |
891.6-c |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
891.6 |
\( 3^{4} \cdot 11 \) |
\( 3^{22} \cdot 11^{2} \) |
$1.38087$ |
$(-a-1), (a-1), (a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.131545608$ |
1.600247146 |
\( \frac{364612508}{88209} a - \frac{393162727}{88209} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 7 a - 50\) , \( -2 a - 165\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(7a-50\right){x}-2a-165$ |
| 1584.4-a3 |
1584.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1584.4 |
\( 2^{4} \cdot 3^{2} \cdot 11 \) |
\( 2^{12} \cdot 3^{10} \cdot 11^{2} \) |
$1.59449$ |
$(a), (-a-1), (a-1), (a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \cdot 3 \) |
$0.172611554$ |
$1.697318412$ |
2.485990333 |
\( \frac{364612508}{88209} a - \frac{393162727}{88209} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 2 a - 21\) , \( -15 a + 53\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2a-21\right){x}-15a+53$ |
| 3267.6-c3 |
3267.6-c |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3267.6 |
\( 3^{3} \cdot 11^{2} \) |
\( 3^{16} \cdot 11^{8} \) |
$1.91082$ |
$(-a-1), (a-1), (a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.590930421$ |
2.507105449 |
\( \frac{364612508}{88209} a - \frac{393162727}{88209} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -99 a - 124\) , \( -720 a - 355\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-99a-124\right){x}-720a-355$ |
| 3267.9-b3 |
3267.9-b |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3267.9 |
\( 3^{3} \cdot 11^{2} \) |
\( 3^{16} \cdot 11^{8} \) |
$1.91082$ |
$(-a-1), (a-1), (a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.941754184$ |
$0.590930421$ |
1.574051365 |
\( \frac{364612508}{88209} a - \frac{393162727}{88209} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 20 a + 183\) , \( 724 a - 414\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(20a+183\right){x}+724a-414$ |
| 14256.6-m3 |
14256.6-m |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
14256.6 |
\( 2^{4} \cdot 3^{4} \cdot 11 \) |
\( 2^{12} \cdot 3^{22} \cdot 11^{2} \) |
$2.76174$ |
$(a), (-a-1), (a-1), (a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$0.707881418$ |
$0.565772804$ |
4.531140880 |
\( \frac{364612508}{88209} a - \frac{393162727}{88209} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 27 a - 197\) , \( 157 a - 1068\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(27a-197\right){x}+157a-1068$ |
| 28611.10-c3 |
28611.10-c |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
28611.10 |
\( 3^{2} \cdot 11 \cdot 17^{2} \) |
\( 3^{10} \cdot 11^{2} \cdot 17^{6} \) |
$3.28713$ |
$(-a-1), (a-1), (a-3), (-2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.823320364$ |
1.164350825 |
\( \frac{364612508}{88209} a - \frac{393162727}{88209} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 67 a + 13\) , \( -142 a - 298\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(67a+13\right){x}-142a-298$ |
| 28611.12-c3 |
28611.12-c |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
28611.12 |
\( 3^{2} \cdot 11 \cdot 17^{2} \) |
\( 3^{10} \cdot 11^{2} \cdot 17^{6} \) |
$3.28713$ |
$(-a-1), (a-1), (a-3), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \cdot 3 \) |
$0.563361828$ |
$0.823320364$ |
7.871409715 |
\( \frac{364612508}{88209} a - \frac{393162727}{88209} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -66 a - 24\) , \( 235 a - 185\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-66a-24\right){x}+235a-185$ |
| 35937.10-d3 |
35937.10-d |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
35937.10 |
\( 3^{3} \cdot 11^{3} \) |
\( 3^{16} \cdot 11^{8} \) |
$3.47992$ |
$(-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1.297927874$ |
$0.590930421$ |
4.338722729 |
\( \frac{364612508}{88209} a - \frac{393162727}{88209} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 123 a - 65\) , \( 760 a + 261\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(123a-65\right){x}+760a+261$ |
| 35937.6-c3 |
35937.6-c |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
35937.6 |
\( 3^{3} \cdot 11^{3} \) |
\( 3^{16} \cdot 11^{8} \) |
$3.47992$ |
$(-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \cdot 3 \) |
$0.402901347$ |
$0.590930421$ |
4.040464655 |
\( \frac{364612508}{88209} a - \frac{393162727}{88209} \) |
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -68 a + 160\) , \( -520 a - 687\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-68a+160\right){x}-520a-687$ |
*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.
