| 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 |
| 43659.3-a1 |
43659.3-a |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
43659.3 |
\( 3^{4} \cdot 7^{2} \cdot 11 \) |
\( 3^{12} \cdot 7^{4} \cdot 11^{2} \) |
$4.28404$ |
$(-a), (a-1), (-2a+1), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cn, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$0.745116266$ |
$0.601329074$ |
2.161523128 |
\( -\frac{78843215872}{539} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -804\) , \( -8775\bigr] \) |
${y}^2+{y}={x}^{3}-804{x}-8775$ |
| 43659.3-a2 |
43659.3-a |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
43659.3 |
\( 3^{4} \cdot 7^{2} \cdot 11 \) |
\( 3^{12} \cdot 7^{12} \cdot 11^{6} \) |
$4.28404$ |
$(-a), (a-1), (-2a+1), (7)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cn, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$2.235348799$ |
$0.200443024$ |
2.161523128 |
\( -\frac{13278380032}{156590819} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -444\) , \( -16650\bigr] \) |
${y}^2+{y}={x}^{3}-444{x}-16650$ |
| 43659.3-a3 |
43659.3-a |
$3$ |
$9$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
43659.3 |
\( 3^{4} \cdot 7^{2} \cdot 11 \) |
\( 3^{12} \cdot 7^{4} \cdot 11^{18} \) |
$4.28404$ |
$(-a), (a-1), (-2a+1), (7)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cn, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$6.706046397$ |
$0.066814341$ |
2.161523128 |
\( \frac{9463555063808}{115539436859} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 3966\) , \( 430965\bigr] \) |
${y}^2+{y}={x}^{3}+3966{x}+430965$ |
| 43659.3-b1 |
43659.3-b |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
43659.3 |
\( 3^{4} \cdot 7^{2} \cdot 11 \) |
\( 3^{12} \cdot 7^{4} \cdot 11^{2} \) |
$4.28404$ |
$(-a), (a-1), (-2a+1), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cn |
$1$ |
\( 2^{2} \) |
$0.563972113$ |
$1.607524622$ |
4.373598420 |
\( \frac{884736}{539} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 18\) , \( -7\bigr] \) |
${y}^2+{y}={x}^{3}+18{x}-7$ |
| 43659.3-c1 |
43659.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
43659.3 |
\( 3^{4} \cdot 7^{2} \cdot 11 \) |
\( 3^{12} \cdot 7^{6} \cdot 11^{4} \) |
$4.28404$ |
$(-a), (a-1), (-2a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.791816199$ |
2.864898802 |
\( \frac{4657463}{41503} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 31\) , \( -264\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+31{x}-264$ |
| 43659.3-c2 |
43659.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
43659.3 |
\( 3^{4} \cdot 7^{2} \cdot 11 \) |
\( 3^{12} \cdot 7^{12} \cdot 11^{2} \) |
$4.28404$ |
$(-a), (a-1), (-2a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.395908099$ |
2.864898802 |
\( \frac{15124197817}{1294139} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -464\) , \( -3432\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-464{x}-3432$ |
| 43659.3-d1 |
43659.3-d |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
43659.3 |
\( 3^{4} \cdot 7^{2} \cdot 11 \) |
\( 3^{16} \cdot 7^{2} \cdot 11^{16} \) |
$4.28404$ |
$(-a), (a-1), (-2a+1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$3.391811818$ |
$0.095924652$ |
6.278351309 |
\( \frac{3288008303}{13504609503} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 279\) , \( 150880\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+279{x}+150880$ |
| 43659.3-d2 |
43659.3-d |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
43659.3 |
\( 3^{4} \cdot 7^{2} \cdot 11 \) |
\( 3^{14} \cdot 7^{16} \cdot 11^{2} \) |
$4.28404$ |
$(-a), (a-1), (-2a+1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1.695905909$ |
$0.191849304$ |
6.278351309 |
\( \frac{221115865823}{190238433} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 1134\) , \( -10535\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+1134{x}-10535$ |
| 43659.3-d3 |
43659.3-d |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
43659.3 |
\( 3^{4} \cdot 7^{2} \cdot 11 \) |
\( 3^{16} \cdot 7^{8} \cdot 11^{4} \) |
$4.28404$ |
$(-a), (a-1), (-2a+1), (7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$0.847952954$ |
$0.383698608$ |
6.278351309 |
\( \frac{6570725617}{2614689} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -351\) , \( -1328\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-351{x}-1328$ |
| 43659.3-d4 |
43659.3-d |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
43659.3 |
\( 3^{4} \cdot 7^{2} \cdot 11 \) |
\( 3^{20} \cdot 7^{4} \cdot 11^{8} \) |
$4.28404$ |
$(-a), (a-1), (-2a+1), (7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$1.695905909$ |
$0.191849304$ |
6.278351309 |
\( \frac{2533811507137}{58110129} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -2556\) , \( 49387\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-2556{x}+49387$ |
| 43659.3-d5 |
43659.3-d |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
43659.3 |
\( 3^{4} \cdot 7^{2} \cdot 11 \) |
\( 3^{14} \cdot 7^{4} \cdot 11^{2} \) |
$4.28404$ |
$(-a), (a-1), (-2a+1), (7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1.695905909$ |
$0.767397216$ |
6.278351309 |
\( \frac{4354703137}{1617} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -306\) , \( -1985\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-306{x}-1985$ |
| 43659.3-d6 |
43659.3-d |
$6$ |
$8$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
43659.3 |
\( 3^{4} \cdot 7^{2} \cdot 11 \) |
\( 3^{28} \cdot 7^{2} \cdot 11^{4} \) |
$4.28404$ |
$(-a), (a-1), (-2a+1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$3.391811818$ |
$0.095924652$ |
6.278351309 |
\( \frac{10206027697760497}{5557167} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -40671\) , \( 3167194\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-40671{x}+3167194$ |
| 43659.3-e1 |
43659.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
43659.3 |
\( 3^{4} \cdot 7^{2} \cdot 11 \) |
\( 3^{16} \cdot 7^{4} \cdot 11^{2} \) |
$4.28404$ |
$(-a), (a-1), (-2a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.074911737$ |
2.592784665 |
\( \frac{2003231191}{1178793} a - \frac{61370998}{392931} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -17 a + 45\) , \( -57 a - 74\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-17a+45\right){x}-57a-74$ |
| 43659.3-e2 |
43659.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
43659.3 |
\( 3^{4} \cdot 7^{2} \cdot 11 \) |
\( 3^{23} \cdot 7^{2} \cdot 11^{4} \) |
$4.28404$ |
$(-a), (a-1), (-2a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.537455868$ |
2.592784665 |
\( -\frac{3279075278687}{4051174743} a + \frac{100237645523}{192913083} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 88 a - 60\) , \( -267 a - 557\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(88a-60\right){x}-267a-557$ |
| 43659.3-f1 |
43659.3-f |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
43659.3 |
\( 3^{4} \cdot 7^{2} \cdot 11 \) |
\( 3^{23} \cdot 7^{2} \cdot 11^{4} \) |
$4.28404$ |
$(-a), (a-1), (-2a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.537455868$ |
2.592784665 |
\( \frac{3279075278687}{4051174743} a - \frac{1174084722704}{4051174743} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -90 a + 28\) , \( 266 a - 824\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-90a+28\right){x}+266a-824$ |
| 43659.3-f2 |
43659.3-f |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
43659.3 |
\( 3^{4} \cdot 7^{2} \cdot 11 \) |
\( 3^{16} \cdot 7^{4} \cdot 11^{2} \) |
$4.28404$ |
$(-a), (a-1), (-2a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.074911737$ |
2.592784665 |
\( -\frac{2003231191}{1178793} a + \frac{1819118197}{1178793} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 15 a + 28\) , \( 56 a - 131\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(15a+28\right){x}+56a-131$ |
*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.
