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 |
1452.1-a1 |
1452.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1452.1 |
\( 2^{2} \cdot 3 \cdot 11^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 11^{8} \) |
$2.52778$ |
$(-a+2), (2), (11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$1.214828373$ |
2.120778277 |
\( -\frac{192100033}{2371842} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -12\) , \( -81\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-12{x}-81$ |
1452.1-a2 |
1452.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1452.1 |
\( 2^{2} \cdot 3 \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 11^{2} \) |
$2.52778$ |
$(-a+2), (2), (11)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$19.43725397$ |
2.120778277 |
\( \frac{912673}{528} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -2\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-2{x}-1$ |
1452.1-a3 |
1452.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1452.1 |
\( 2^{2} \cdot 3 \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 11^{4} \) |
$2.52778$ |
$(-a+2), (2), (11)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$4.859313493$ |
2.120778277 |
\( \frac{1180932193}{4356} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -22\) , \( -49\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-22{x}-49$ |
1452.1-a4 |
1452.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1452.1 |
\( 2^{2} \cdot 3 \cdot 11^{2} \) |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
$2.52778$ |
$(-a+2), (2), (11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$1.214828373$ |
2.120778277 |
\( \frac{4824238966273}{66} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -352\) , \( -2689\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-352{x}-2689$ |
1452.1-b1 |
1452.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1452.1 |
\( 2^{2} \cdot 3 \cdot 11^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 11^{20} \) |
$2.52778$ |
$(-a+2), (2), (11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$4$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$0.884125736$ |
3.858641056 |
\( -\frac{112427521449300721}{466873642818} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 50275 a - 140771\) , \( -9317141 a + 26009932\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(50275a-140771\right){x}-9317141a+26009932$ |
1452.1-b2 |
1452.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1452.1 |
\( 2^{2} \cdot 3 \cdot 11^{2} \) |
\( 2^{10} \cdot 3^{20} \cdot 11^{4} \) |
$2.52778$ |
$(-a+2), (2), (11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$4$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$0.884125736$ |
3.858641056 |
\( \frac{168105213359}{228637728} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -575 a + 1609\) , \( 12889 a - 35978\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-575a+1609\right){x}+12889a-35978$ |
1452.1-b3 |
1452.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1452.1 |
\( 2^{2} \cdot 3 \cdot 11^{2} \) |
\( 2^{20} \cdot 3^{10} \cdot 11^{2} \) |
$2.52778$ |
$(-a+2), (2), (11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$3.536502944$ |
3.858641056 |
\( \frac{10091699281}{2737152} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 225 a - 631\) , \( 2169 a - 6058\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(225a-631\right){x}+2169a-6058$ |
1452.1-b4 |
1452.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1452.1 |
\( 2^{2} \cdot 3 \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 11^{10} \) |
$2.52778$ |
$(-a+2), (2), (11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$3.536502944$ |
3.858641056 |
\( \frac{112763292123580561}{1932612} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -50327 a - 90586\) , \( 9297650 a + 16657871\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-50327a-90586\right){x}+9297650a+16657871$ |
1452.1-c1 |
1452.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1452.1 |
\( 2^{2} \cdot 3 \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 11^{4} \) |
$2.52778$ |
$(-a+2), (2), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.102553931$ |
$5.787714375$ |
4.144763299 |
\( -\frac{65315105246375}{3175524} a + \frac{91344237347125}{1587762} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -423 a - 860\) , \( 7025 a + 13001\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-423a-860\right){x}+7025a+13001$ |
1452.1-c2 |
1452.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1452.1 |
\( 2^{2} \cdot 3 \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 11^{2} \) |
$2.52778$ |
$(-a+2), (2), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.205107862$ |
$11.57542875$ |
4.144763299 |
\( \frac{42886322528375}{14256} a + \frac{25607299252625}{4752} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -443 a - 800\) , \( 7149 a + 12813\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-443a-800\right){x}+7149a+12813$ |
1452.1-d1 |
1452.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1452.1 |
\( 2^{2} \cdot 3 \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 11^{2} \) |
$2.52778$ |
$(-a+2), (2), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.205107862$ |
$11.57542875$ |
4.144763299 |
\( -\frac{42886322528375}{14256} a + \frac{59854110143125}{7128} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 445 a - 1245\) , \( -7593 a + 21206\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(445a-1245\right){x}-7593a+21206$ |
1452.1-d2 |
1452.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1452.1 |
\( 2^{2} \cdot 3 \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 11^{4} \) |
$2.52778$ |
$(-a+2), (2), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.102553931$ |
$5.787714375$ |
4.144763299 |
\( \frac{65315105246375}{3175524} a + \frac{39124456482625}{1058508} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 425 a - 1285\) , \( -7449 a + 21310\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(425a-1285\right){x}-7449a+21310$ |
1452.1-e1 |
1452.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1452.1 |
\( 2^{2} \cdot 3 \cdot 11^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 11^{8} \) |
$2.52778$ |
$(-a+2), (2), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.195042991$ |
$4.813898015$ |
3.278216031 |
\( -\frac{192100033}{2371842} \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 62 a - 164\) , \( -1818 a + 5081\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(62a-164\right){x}-1818a+5081$ |
1452.1-e2 |
1452.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1452.1 |
\( 2^{2} \cdot 3 \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 11^{2} \) |
$2.52778$ |
$(-a+2), (2), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.195042991$ |
$19.25559206$ |
3.278216031 |
\( \frac{912673}{528} \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 12 a - 24\) , \( 2 a + 1\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(12a-24\right){x}+2a+1$ |
1452.1-e3 |
1452.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1452.1 |
\( 2^{2} \cdot 3 \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 11^{4} \) |
$2.52778$ |
$(-a+2), (2), (11)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.390085982$ |
$19.25559206$ |
3.278216031 |
\( \frac{1180932193}{4356} \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 112 a - 304\) , \( -950 a + 2657\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(112a-304\right){x}-950a+2657$ |
1452.1-e4 |
1452.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1452.1 |
\( 2^{2} \cdot 3 \cdot 11^{2} \) |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
$2.52778$ |
$(-a+2), (2), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.780171965$ |
$19.25559206$ |
3.278216031 |
\( \frac{4824238966273}{66} \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 1762 a - 4924\) , \( -61010 a + 170297\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(1762a-4924\right){x}-61010a+170297$ |
1452.1-f1 |
1452.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1452.1 |
\( 2^{2} \cdot 3 \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 11^{2} \) |
$2.52778$ |
$(-a+2), (2), (11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.131863578$ |
0.465210772 |
\( -\frac{42886322528375}{14256} a + \frac{59854110143125}{7128} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -13 a - 112\) , \( -105 a - 486\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-13a-112\right){x}-105a-486$ |
1452.1-f2 |
1452.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1452.1 |
\( 2^{2} \cdot 3 \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 11^{4} \) |
$2.52778$ |
$(-a+2), (2), (11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.065931789$ |
0.465210772 |
\( \frac{65315105246375}{3175524} a + \frac{39124456482625}{1058508} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -493 a - 972\) , \( -9949 a - 18118\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-493a-972\right){x}-9949a-18118$ |
1452.1-g1 |
1452.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1452.1 |
\( 2^{2} \cdot 3 \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{16} \cdot 11^{4} \) |
$2.52778$ |
$(-a+2), (2), (11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.065931789$ |
0.465210772 |
\( -\frac{65315105246375}{3175524} a + \frac{91344237347125}{1587762} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( 493 a - 1465\) , \( 9949 a - 28067\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(493a-1465\right){x}+9949a-28067$ |
1452.1-g2 |
1452.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1452.1 |
\( 2^{2} \cdot 3 \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 11^{2} \) |
$2.52778$ |
$(-a+2), (2), (11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.131863578$ |
0.465210772 |
\( \frac{42886322528375}{14256} a + \frac{25607299252625}{4752} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( 13 a - 125\) , \( 105 a - 591\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(13a-125\right){x}+105a-591$ |
1452.1-h1 |
1452.1-h |
$4$ |
$6$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1452.1 |
\( 2^{2} \cdot 3 \cdot 11^{2} \) |
\( 2^{6} \cdot 3^{4} \cdot 11^{12} \) |
$2.52778$ |
$(-a+2), (2), (11)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$2.444595345$ |
2.133817754 |
\( -\frac{7357983625}{127552392} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 202 a - 568\) , \( -13136 a + 36667\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(202a-568\right){x}-13136a+36667$ |
1452.1-h2 |
1452.1-h |
$4$ |
$6$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1452.1 |
\( 2^{2} \cdot 3 \cdot 11^{2} \) |
\( 2^{2} \cdot 3^{12} \cdot 11^{4} \) |
$2.52778$ |
$(-a+2), (2), (11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2^{2} \) |
$1$ |
$2.444595345$ |
2.133817754 |
\( \frac{9938375}{176418} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( -23 a + 62\) , \( 463 a - 1295\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-23a+62\right){x}+463a-1295$ |
1452.1-h3 |
1452.1-h |
$4$ |
$6$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1452.1 |
\( 2^{2} \cdot 3 \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 11^{2} \) |
$2.52778$ |
$(-a+2), (2), (11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$9.778381380$ |
2.133817754 |
\( \frac{18609625}{1188} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 27 a - 78\) , \( 129 a - 363\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(27a-78\right){x}+129a-363$ |
1452.1-h4 |
1452.1-h |
$4$ |
$6$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1452.1 |
\( 2^{2} \cdot 3 \cdot 11^{2} \) |
\( 2^{12} \cdot 3^{2} \cdot 11^{6} \) |
$2.52778$ |
$(-a+2), (2), (11)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$9.778381380$ |
2.133817754 |
\( \frac{57736239625}{255552} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 402 a - 1128\) , \( -6408 a + 17883\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(402a-1128\right){x}-6408a+17883$ |
1452.1-i1 |
1452.1-i |
$4$ |
$10$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1452.1 |
\( 2^{2} \cdot 3 \cdot 11^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 11^{20} \) |
$2.52778$ |
$(-a+2), (2), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$1$ |
\( 2^{3} \cdot 5 \) |
$9.780331572$ |
$0.056797834$ |
2.424407990 |
\( -\frac{112427521449300721}{466873642818} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -10055\) , \( -390309\bigr] \) |
${y}^2+{x}{y}={x}^{3}-10055{x}-390309$ |
1452.1-i2 |
1452.1-i |
$4$ |
$10$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1452.1 |
\( 2^{2} \cdot 3 \cdot 11^{2} \) |
\( 2^{10} \cdot 3^{20} \cdot 11^{4} \) |
$2.52778$ |
$(-a+2), (2), (11)$ |
$1$ |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2^{3} \cdot 5^{2} \) |
$1.956066314$ |
$1.419945868$ |
2.424407990 |
\( \frac{168105213359}{228637728} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 115\) , \( 561\bigr] \) |
${y}^2+{x}{y}={x}^{3}+115{x}+561$ |
1452.1-i3 |
1452.1-i |
$4$ |
$10$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1452.1 |
\( 2^{2} \cdot 3 \cdot 11^{2} \) |
\( 2^{20} \cdot 3^{10} \cdot 11^{2} \) |
$2.52778$ |
$(-a+2), (2), (11)$ |
$1$ |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2^{2} \cdot 5^{2} \) |
$0.978033157$ |
$5.679783475$ |
2.424407990 |
\( \frac{10091699281}{2737152} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -45\) , \( 81\bigr] \) |
${y}^2+{x}{y}={x}^{3}-45{x}+81$ |
1452.1-i4 |
1452.1-i |
$4$ |
$10$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1452.1 |
\( 2^{2} \cdot 3 \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 11^{10} \) |
$2.52778$ |
$(-a+2), (2), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$1$ |
\( 2^{2} \cdot 5 \) |
$4.890165786$ |
$0.227191339$ |
2.424407990 |
\( \frac{112763292123580561}{1932612} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -10065\) , \( -389499\bigr] \) |
${y}^2+{x}{y}={x}^{3}-10065{x}-389499$ |
1452.1-j1 |
1452.1-j |
$4$ |
$6$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1452.1 |
\( 2^{2} \cdot 3 \cdot 11^{2} \) |
\( 2^{6} \cdot 3^{4} \cdot 11^{12} \) |
$2.52778$ |
$(-a+2), (2), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1.088014913$ |
$0.635354791$ |
5.430552431 |
\( -\frac{7357983625}{127552392} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -41\) , \( -556\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-41{x}-556$ |
1452.1-j2 |
1452.1-j |
$4$ |
$6$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1452.1 |
\( 2^{2} \cdot 3 \cdot 11^{2} \) |
\( 2^{2} \cdot 3^{12} \cdot 11^{4} \) |
$2.52778$ |
$(-a+2), (2), (11)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$3.264044740$ |
$5.718193122$ |
5.430552431 |
\( \frac{9938375}{176418} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( 20\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+4{x}+20$ |
1452.1-j3 |
1452.1-j |
$4$ |
$6$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1452.1 |
\( 2^{2} \cdot 3 \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 11^{2} \) |
$2.52778$ |
$(-a+2), (2), (11)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1.632022370$ |
$22.87277248$ |
5.430552431 |
\( \frac{18609625}{1188} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -6\) , \( 4\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-6{x}+4$ |
1452.1-j4 |
1452.1-j |
$4$ |
$6$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1452.1 |
\( 2^{2} \cdot 3 \cdot 11^{2} \) |
\( 2^{12} \cdot 3^{2} \cdot 11^{6} \) |
$2.52778$ |
$(-a+2), (2), (11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.544007456$ |
$2.541419165$ |
5.430552431 |
\( \frac{57736239625}{255552} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -81\) , \( -284\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-81{x}-284$ |
*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.