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 |
450.1-a1 |
450.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{16} \cdot 3^{7} \cdot 5^{7} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \cdot 5 \) |
$0.049563843$ |
$5.755368069$ |
4.658246279 |
\( -\frac{17221922359}{600000} a + \frac{55514971133}{800000} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -20 a - 83\) , \( 163 a + 523\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-20a-83\right){x}+163a+523$ |
450.1-a2 |
450.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{7} \cdot 5^{22} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \cdot 5 \) |
$0.198255373$ |
$0.719421008$ |
4.658246279 |
\( -\frac{144104343228910390069}{1144409179687500} a + \frac{118584102988852401257}{381469726562500} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -440 a - 1823\) , \( 7675 a + 11731\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-440a-1823\right){x}+7675a+11731$ |
450.1-a3 |
450.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 5^{14} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \cdot 5 \) |
$0.099127686$ |
$2.877684034$ |
4.658246279 |
\( \frac{113326116501547}{234375000} a + \frac{556034224929629}{468750000} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -500 a - 1283\) , \( 9571 a + 23467\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-500a-1283\right){x}+9571a+23467$ |
450.1-a4 |
450.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{4} \cdot 3^{10} \cdot 5^{13} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \cdot 5 \) |
$0.198255373$ |
$1.438842017$ |
4.658246279 |
\( \frac{16121263453136683247}{14062500} a + \frac{39488869492259539423}{14062500} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -8240 a - 19943\) , \( 627019 a + 1535299\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-8240a-19943\right){x}+627019a+1535299$ |
450.1-b1 |
450.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{2} \cdot 3^{3} \cdot 5^{5} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$6.999986990$ |
2.857732722 |
\( -\frac{724788}{125} a + \frac{3535839}{250} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -8 a - 20\) , \( -104 a - 255\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-8a-20\right){x}-104a-255$ |
450.1-b2 |
450.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{6} \cdot 3^{9} \cdot 5^{7} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$6.999986990$ |
2.857732722 |
\( -\frac{344106051}{15625} a + \frac{6750335403}{125000} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 72 a + 175\) , \( 2760 a + 6761\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(72a+175\right){x}+2760a+6761$ |
450.1-b3 |
450.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{3} \cdot 3^{9} \cdot 5^{14} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$3.499993495$ |
2.857732722 |
\( \frac{3087201332697}{976562500} a + \frac{1888761268962}{244140625} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1398 a - 3425\) , \( 42324 a + 103673\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-1398a-3425\right){x}+42324a+103673$ |
450.1-b4 |
450.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2 \cdot 3^{3} \cdot 5^{10} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$1$ |
$3.499993495$ |
2.857732722 |
\( \frac{1464328611}{31250} a + \frac{1793540988}{15625} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -66 a + 160\) , \( 7008 a - 17169\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-66a+160\right){x}+7008a-17169$ |
450.1-c1 |
450.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{16} \cdot 3^{7} \cdot 5^{7} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.307175741$ |
1.067304524 |
\( -\frac{17221922359}{600000} a + \frac{55514971133}{800000} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 738 a - 1809\) , \( 17478 a - 42813\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(738a-1809\right){x}+17478a-42813$ |
450.1-c2 |
450.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{7} \cdot 5^{22} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.307175741$ |
1.067304524 |
\( -\frac{144104343228910390069}{1144409179687500} a + \frac{118584102988852401257}{381469726562500} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 14958 a - 36669\) , \( -1547478 a + 3790503\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(14958a-36669\right){x}-1547478a+3790503$ |
450.1-c3 |
450.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 5^{14} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$1.307175741$ |
1.067304524 |
\( \frac{113326116501547}{234375000} a + \frac{556034224929629}{468750000} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 1218 a - 3009\) , \( -7290 a + 17811\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1218a-3009\right){x}-7290a+17811$ |
450.1-c4 |
450.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{4} \cdot 3^{10} \cdot 5^{13} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.326793935$ |
1.067304524 |
\( \frac{16121263453136683247}{14062500} a + \frac{39488869492259539423}{14062500} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -4842 a + 11451\) , \( -67614 a + 162495\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4842a+11451\right){x}-67614a+162495$ |
450.1-d1 |
450.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{6} \cdot 5^{2} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$3.291609677$ |
$2.017094010$ |
2.710558876 |
\( -\frac{1860867}{320} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 154 a - 375\) , \( 1701 a - 4165\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(154a-375\right){x}+1701a-4165$ |
450.1-d2 |
450.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 5^{6} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1.097203225$ |
$6.051282030$ |
2.710558876 |
\( \frac{804357}{500} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 6\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+6{x}$ |
450.1-d3 |
450.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{12} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$0.548601612$ |
$6.051282030$ |
2.710558876 |
\( \frac{57960603}{31250} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -24\) , \( 18\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-24{x}+18$ |
450.1-d4 |
450.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{3} \cdot 3^{6} \cdot 5^{5} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$3.291609677$ |
$1.008547005$ |
2.710558876 |
\( -\frac{927618580461475773}{2500} a + \frac{568048049518434408}{625} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -2643 a - 6492\) , \( -105330 a - 258022\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2643a-6492\right){x}-105330a-258022$ |
450.1-d5 |
450.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2 \cdot 3^{6} \cdot 5^{15} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1.097203225$ |
$3.025641015$ |
2.710558876 |
\( -\frac{59305689907281}{488281250} a + \frac{102611946982248}{244140625} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 15 a - 264\) , \( -681 a + 414\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(15a-264\right){x}-681a+414$ |
450.1-d6 |
450.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2 \cdot 3^{6} \cdot 5^{15} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1.097203225$ |
$3.025641015$ |
2.710558876 |
\( \frac{59305689907281}{488281250} a + \frac{102611946982248}{244140625} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -15 a - 264\) , \( 681 a + 414\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-15a-264\right){x}+681a+414$ |
450.1-d7 |
450.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{6} \cdot 5^{4} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{5} \) |
$1.645804838$ |
$2.017094010$ |
2.710558876 |
\( \frac{8527173507}{200} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -2553 a - 6252\) , \( -113724 a - 278566\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2553a-6252\right){x}-113724a-278566$ |
450.1-d8 |
450.1-d |
$8$ |
$12$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{3} \cdot 3^{6} \cdot 5^{5} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$3.291609677$ |
$1.008547005$ |
2.710558876 |
\( \frac{927618580461475773}{2500} a + \frac{568048049518434408}{625} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 2644 a - 6495\) , \( 98835 a - 242161\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2644a-6495\right){x}+98835a-242161$ |
450.1-e1 |
450.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{4} \cdot 3^{10} \cdot 5^{13} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \cdot 5 \) |
$0.198255373$ |
$1.438842017$ |
4.658246279 |
\( -\frac{16121263453136683247}{14062500} a + \frac{39488869492259539423}{14062500} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 8240 a - 19943\) , \( -627019 a + 1535299\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(8240a-19943\right){x}-627019a+1535299$ |
450.1-e2 |
450.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 5^{14} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \cdot 5 \) |
$0.099127686$ |
$2.877684034$ |
4.658246279 |
\( -\frac{113326116501547}{234375000} a + \frac{556034224929629}{468750000} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 500 a - 1283\) , \( -9571 a + 23467\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(500a-1283\right){x}-9571a+23467$ |
450.1-e3 |
450.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{16} \cdot 3^{7} \cdot 5^{7} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \cdot 5 \) |
$0.049563843$ |
$5.755368069$ |
4.658246279 |
\( \frac{17221922359}{600000} a + \frac{55514971133}{800000} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 20 a - 83\) , \( -163 a + 523\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(20a-83\right){x}-163a+523$ |
450.1-e4 |
450.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{7} \cdot 5^{22} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \cdot 5 \) |
$0.198255373$ |
$0.719421008$ |
4.658246279 |
\( \frac{144104343228910390069}{1144409179687500} a + \frac{118584102988852401257}{381469726562500} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 440 a - 1823\) , \( -7675 a + 11731\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(440a-1823\right){x}-7675a+11731$ |
450.1-f1 |
450.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{3} \cdot 3^{9} \cdot 5^{14} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$2.351895791$ |
$1.243038705$ |
2.387025714 |
\( -\frac{3087201332697}{976562500} a + \frac{1888761268962}{244140625} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 9 a - 45\) , \( -174 a - 571\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(9a-45\right){x}-174a-571$ |
450.1-f2 |
450.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2 \cdot 3^{3} \cdot 5^{10} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.783965263$ |
$11.18734835$ |
2.387025714 |
\( -\frac{1464328611}{31250} a + \frac{1793540988}{15625} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 4 a\) , \( 3 a + 36\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+4a{x}+3a+36$ |
450.1-f3 |
450.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{2} \cdot 3^{3} \cdot 5^{5} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.391982631$ |
$22.37469670$ |
2.387025714 |
\( \frac{724788}{125} a + \frac{3535839}{250} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -a\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}-a{x}$ |
450.1-f4 |
450.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{6} \cdot 3^{9} \cdot 5^{7} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1.175947895$ |
$2.486077411$ |
2.387025714 |
\( \frac{344106051}{15625} a + \frac{6750335403}{125000} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -21 a - 45\) , \( -108 a - 283\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-21a-45\right){x}-108a-283$ |
450.1-g1 |
450.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{4} \cdot 3^{10} \cdot 5^{13} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.326793935$ |
1.067304524 |
\( -\frac{16121263453136683247}{14062500} a + \frac{39488869492259539423}{14062500} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 4842 a + 11451\) , \( 67614 a + 162495\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(4842a+11451\right){x}+67614a+162495$ |
450.1-g2 |
450.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 5^{14} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$1.307175741$ |
1.067304524 |
\( -\frac{113326116501547}{234375000} a + \frac{556034224929629}{468750000} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -1218 a - 3009\) , \( 7290 a + 17811\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-1218a-3009\right){x}+7290a+17811$ |
450.1-g3 |
450.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{16} \cdot 3^{7} \cdot 5^{7} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.307175741$ |
1.067304524 |
\( \frac{17221922359}{600000} a + \frac{55514971133}{800000} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -738 a - 1809\) , \( -17478 a - 42813\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-738a-1809\right){x}-17478a-42813$ |
450.1-g4 |
450.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{7} \cdot 5^{22} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.307175741$ |
1.067304524 |
\( \frac{144104343228910390069}{1144409179687500} a + \frac{118584102988852401257}{381469726562500} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -14958 a - 36669\) , \( 1547478 a + 3790503\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-14958a-36669\right){x}+1547478a+3790503$ |
450.1-h1 |
450.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{6} \cdot 5^{2} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$15.76958961$ |
2.145969333 |
\( -\frac{1860867}{320} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -8\) , \( 11\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-8{x}+11$ |
450.1-h2 |
450.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 5^{6} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$5.256529870$ |
2.145969333 |
\( \frac{804357}{500} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -116 a + 289\) , \( 405 a - 989\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-116a+289\right){x}+405a-989$ |
450.1-h3 |
450.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{12} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{5} \) |
$1$ |
$5.256529870$ |
2.145969333 |
\( \frac{57960603}{31250} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -484 a - 1184\) , \( -3083 a - 7553\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-484a-1184\right){x}-3083a-7553$ |
450.1-h4 |
450.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{3} \cdot 3^{6} \cdot 5^{5} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$7.884794805$ |
2.145969333 |
\( -\frac{927618580461475773}{2500} a + \frac{568048049518434408}{625} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 390 a - 1088\) , \( -7248 a + 18299\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(390a-1088\right){x}-7248a+18299$ |
450.1-h5 |
450.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2 \cdot 3^{6} \cdot 5^{15} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2^{2} \) |
$1$ |
$2.628264935$ |
2.145969333 |
\( -\frac{59305689907281}{488281250} a + \frac{102611946982248}{244140625} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -4549 a - 11144\) , \( 252859 a + 619375\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-4549a-11144\right){x}+252859a+619375$ |
450.1-h6 |
450.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2 \cdot 3^{6} \cdot 5^{15} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2^{2} \) |
$1$ |
$2.628264935$ |
2.145969333 |
\( \frac{59305689907281}{488281250} a + \frac{102611946982248}{244140625} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 4549 a - 11141\) , \( -264003 a + 646669\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(4549a-11141\right){x}-264003a+646669$ |
450.1-h7 |
450.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{6} \cdot 5^{4} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$15.76958961$ |
2.145969333 |
\( \frac{8527173507}{200} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -128\) , \( 587\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-128{x}+587$ |
450.1-h8 |
450.1-h |
$8$ |
$12$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{3} \cdot 3^{6} \cdot 5^{5} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$7.884794805$ |
2.145969333 |
\( \frac{927618580461475773}{2500} a + \frac{568048049518434408}{625} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -390 a - 1088\) , \( 7248 a + 18299\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-390a-1088\right){x}+7248a+18299$ |
450.1-i1 |
450.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2 \cdot 3^{7} \cdot 5^{12} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$1.076282690$ |
3.515124546 |
\( -\frac{5302578721327}{2343750} a + \frac{2164212835878}{390625} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 73 a - 212\) , \( 570 a - 1505\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(73a-212\right){x}+570a-1505$ |
450.1-i2 |
450.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{4} \cdot 3^{7} \cdot 5^{3} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$8.610261521$ |
3.515124546 |
\( \frac{35018}{75} a + \frac{177729}{100} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -2 a - 2\) , \( -5\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-2a-2\right){x}-5$ |
450.1-i3 |
450.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 5^{6} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$4.305130760$ |
3.515124546 |
\( \frac{549984362}{625} a + \frac{8098588777}{3750} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -2 a - 32\) , \( -12 a - 65\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-2a-32\right){x}-12a-65$ |
450.1-i4 |
450.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2 \cdot 3^{10} \cdot 5^{3} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$2.152565380$ |
3.515124546 |
\( \frac{569928368126839}{150} a + \frac{2094050541745066}{225} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -77 a - 332\) , \( -1122 a - 2105\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-77a-332\right){x}-1122a-2105$ |
450.1-j1 |
450.1-j |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{2} \cdot 3^{3} \cdot 5^{5} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.391982631$ |
$22.37469670$ |
2.387025714 |
\( -\frac{724788}{125} a + \frac{3535839}{250} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 2 a - 3\) , \( -3 a + 9\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2a-3\right){x}-3a+9$ |
450.1-j2 |
450.1-j |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{6} \cdot 3^{9} \cdot 5^{7} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1.175947895$ |
$2.486077411$ |
2.387025714 |
\( -\frac{344106051}{15625} a + \frac{6750335403}{125000} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 22 a - 48\) , \( 60 a - 154\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(22a-48\right){x}+60a-154$ |
450.1-j3 |
450.1-j |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{3} \cdot 3^{9} \cdot 5^{14} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$2.351895791$ |
$1.243038705$ |
2.387025714 |
\( \frac{3087201332697}{976562500} a + \frac{1888761268962}{244140625} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -8 a - 48\) , \( 126 a - 622\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-8a-48\right){x}+126a-622$ |
450.1-j4 |
450.1-j |
$4$ |
$6$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2 \cdot 3^{3} \cdot 5^{10} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.783965263$ |
$11.18734835$ |
2.387025714 |
\( \frac{1464328611}{31250} a + \frac{1793540988}{15625} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -3 a - 3\) , \( -6 a + 15\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a-3\right){x}-6a+15$ |
450.1-k1 |
450.1-k |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2 \cdot 3^{7} \cdot 5^{12} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.382855989$ |
$6.755999934$ |
2.111929673 |
\( -\frac{5302578721327}{2343750} a + \frac{2164212835878}{390625} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -570 a - 1398\) , \( 17897 a + 43838\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-570a-1398\right){x}+17897a+43838$ |
450.1-k2 |
450.1-k |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{4} \cdot 3^{7} \cdot 5^{3} \) |
$2.01626$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.095713997$ |
$13.51199986$ |
2.111929673 |
\( \frac{35018}{75} a + \frac{177729}{100} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -45 a - 108\) , \( 212 a + 518\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-45a-108\right){x}+212a+518$ |
*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.