| 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 |
| 99.3-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 |
\( \frac{3103043505622}{72171} a - \frac{541923582149}{72171} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -12 a - 90\) , \( 71 a + 302\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-12a-90\right){x}+71a+302$ |
| 891.5-c1 |
891.5-c |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
891.5 |
\( 3^{4} \cdot 11 \) |
\( 3^{23} \cdot 11 \) |
$1.38087$ |
$(-a-1), (a-1), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.565772804$ |
1.600247146 |
\( \frac{3103043505622}{72171} a - \frac{541923582149}{72171} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -96 a - 816\) , \( -2028 a - 8963\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-96a-816\right){x}-2028a-8963$ |
| 1584.3-b1 |
1584.3-b |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1584.3 |
\( 2^{4} \cdot 3^{2} \cdot 11 \) |
\( 2^{12} \cdot 3^{11} \cdot 11 \) |
$1.59449$ |
$(a), (-a-1), (a-1), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.345223109$ |
$0.848659206$ |
2.485990333 |
\( \frac{3103043505622}{72171} a - \frac{541923582149}{72171} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -42 a - 361\) , \( 615 a + 2777\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-42a-361\right){x}+615a+2777$ |
| 3267.4-b1 |
3267.4-b |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3267.4 |
\( 3^{3} \cdot 11^{2} \) |
\( 3^{17} \cdot 11^{7} \) |
$1.91082$ |
$(-a-1), (a-1), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.883508368$ |
$0.295465210$ |
1.574051365 |
\( \frac{3103043505622}{72171} a - \frac{541923582149}{72171} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -391 a + 2978\) , \( -43997 a - 18814\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-391a+2978\right){x}-43997a-18814$ |
| 3267.7-c1 |
3267.7-c |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3267.7 |
\( 3^{3} \cdot 11^{2} \) |
\( 3^{17} \cdot 11^{7} \) |
$1.91082$ |
$(-a-1), (a-1), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.295465210$ |
2.507105449 |
\( \frac{3103043505622}{72171} a - \frac{541923582149}{72171} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 1628 a - 1969\) , \( 43677 a - 19390\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(1628a-1969\right){x}+43677a-19390$ |
| 14256.5-h1 |
14256.5-h |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
14256.5 |
\( 2^{4} \cdot 3^{4} \cdot 11 \) |
\( 2^{12} \cdot 3^{23} \cdot 11 \) |
$2.76174$ |
$(a), (-a-1), (a-1), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.415762837$ |
$0.282886402$ |
4.531140880 |
\( \frac{3103043505622}{72171} a - \frac{541923582149}{72171} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -387 a - 3257\) , \( -12577 a - 69216\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-387a-3257\right){x}-12577a-69216$ |
| 28611.7-c1 |
28611.7-c |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
28611.7 |
\( 3^{2} \cdot 11 \cdot 17^{2} \) |
\( 3^{11} \cdot 11 \cdot 17^{6} \) |
$3.28713$ |
$(-a-1), (a-1), (a+3), (-2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1.126723656$ |
$0.411660182$ |
7.871409715 |
\( \frac{3103043505622}{72171} a - \frac{541923582149}{72171} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( 1075 a - 349\) , \( -15035 a - 10295\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(1075a-349\right){x}-15035a-10295$ |
| 28611.9-c1 |
28611.9-c |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
28611.9 |
\( 3^{2} \cdot 11 \cdot 17^{2} \) |
\( 3^{11} \cdot 11 \cdot 17^{6} \) |
$3.28713$ |
$(-a-1), (a-1), (a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.411660182$ |
1.164350825 |
\( \frac{3103043505622}{72171} a - \frac{541923582149}{72171} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -1097 a + 168\) , \( 9346 a - 19183\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-1097a+168\right){x}+9346a-19183$ |
| 35937.11-c1 |
35937.11-c |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
35937.11 |
\( 3^{3} \cdot 11^{3} \) |
\( 3^{17} \cdot 11^{7} \) |
$3.47992$ |
$(-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.805802695$ |
$0.295465210$ |
4.040464655 |
\( \frac{3103043505622}{72171} a - \frac{541923582149}{72171} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( 1057 a + 2635\) , \( 31903 a - 44742\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(1057a+2635\right){x}+31903a-44742$ |
| 35937.7-d1 |
35937.7-d |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
35937.7 |
\( 3^{3} \cdot 11^{3} \) |
\( 3^{17} \cdot 11^{7} \) |
$3.47992$ |
$(-a-1), (a-1), (a+3), (a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$2.595855749$ |
$0.295465210$ |
4.338722729 |
\( \frac{3103043505622}{72171} a - \frac{541923582149}{72171} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( -1993 a - 1110\) , \( -44782 a + 15441\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-1993a-1110\right){x}-44782a+15441$ |
*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.
