| 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 |
| 144.2-a1 |
144.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{30} \cdot 3^{15} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.988479270$ |
2.107044108 |
\( -\frac{222921251407}{1019215872} a + \frac{1213752124997}{1019215872} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 996 a + 3261\) , \( 82977 a + 271743\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(996a+3261\right){x}+82977a+271743$ |
| 144.2-a2 |
144.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{15} \cdot 3^{24} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$1.988479270$ |
2.107044108 |
\( \frac{32092177139}{40310784} a + \frac{168120570415}{40310784} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -97 a + 437\) , \( 376 a - 1603\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-97a+437\right){x}+376a-1603$ |
| 144.2-b1 |
144.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{30} \cdot 3^{15} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 11 \) |
$1$ |
$1.538634617$ |
4.483536939 |
\( -\frac{222921251407}{1019215872} a + \frac{1213752124997}{1019215872} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 13750 a - 58793\) , \( -506377 a + 2164713\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(13750a-58793\right){x}-506377a+2164713$ |
| 144.2-b2 |
144.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{15} \cdot 3^{24} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 11 \) |
$1$ |
$1.538634617$ |
4.483536939 |
\( \frac{32092177139}{40310784} a + \frac{168120570415}{40310784} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -332608 a - 1089262\) , \( -178415422 a - 584295737\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-332608a-1089262\right){x}-178415422a-584295737$ |
| 144.2-c1 |
144.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{18} \cdot 3^{9} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.775929193$ |
1.265174550 |
\( -\frac{167058741}{256} a + \frac{678122727}{256} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -626112 a - 2050467\) , \( 525710832 a + 1721659454\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-626112a-2050467\right){x}+525710832a+1721659454$ |
| 144.2-c2 |
144.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{9} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.775929193$ |
1.265174550 |
\( \frac{42445476687}{16} a + \frac{139005397947}{16} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -3582 a - 11733\) , \( 218478 a + 715496\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-3582a-11733\right){x}+218478a+715496$ |
| 144.2-d1 |
144.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{18} \cdot 3^{9} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$3.096860716$ |
3.281513779 |
\( -\frac{167058741}{256} a + \frac{678122727}{256} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 12 a - 87\) , \( -99 a + 171\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(12a-87\right){x}-99a+171$ |
| 144.2-d2 |
144.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{9} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$3.096860716$ |
3.281513779 |
\( \frac{42445476687}{16} a + \frac{139005397947}{16} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 2622 a - 11193\) , \( -205863 a + 880059\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(2622a-11193\right){x}-205863a+880059$ |
| 144.2-e1 |
144.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{6} \cdot 3^{9} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$6.913668697$ |
1.831475579 |
\( -\frac{23997}{4} a - \frac{41025}{4} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -6\) , \( -3 a - 10\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-6{x}-3a-10$ |
| 144.2-e2 |
144.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{9} \cdot 3^{9} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$3.456834348$ |
1.831475579 |
\( \frac{355655661}{2} a + \frac{1164756561}{2} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -15 a - 66\) , \( -114 a - 400\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-15a-66\right){x}-114a-400$ |
| 144.2-f1 |
144.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{16} \cdot 3^{11} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$4.812239831$ |
3.824380419 |
\( -\frac{49866463}{110592} a + \frac{402592373}{110592} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 74 a - 280\) , \( 478 a - 1981\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(74a-280\right){x}+478a-1981$ |
| 144.2-f2 |
144.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{16} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$2.406119915$ |
3.824380419 |
\( -\frac{38553913631}{15552} a + \frac{164841901877}{15552} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 1049 a - 4450\) , \( 35347 a - 151051\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(1049a-4450\right){x}+35347a-151051$ |
| 144.2-f3 |
144.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{13} \cdot 3^{11} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.601529978$ |
3.824380419 |
\( -\frac{10023098548616947}{216} a + \frac{42847916605213553}{216} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 16709 a - 71410\) , \( 2278183 a - 9739075\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(16709a-71410\right){x}+2278183a-9739075$ |
| 144.2-f4 |
144.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{13} \cdot 3^{26} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.203059957$ |
3.824380419 |
\( \frac{24879955441}{472392} a + \frac{26588853943}{157464} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 989 a - 4210\) , \( 39487 a - 168787\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(989a-4210\right){x}+39487a-168787$ |
| 144.2-g1 |
144.2-g |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{6} \cdot 3^{9} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$16.03467447$ |
4.247689036 |
\( -\frac{23997}{4} a - \frac{41025}{4} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 47964 a - 205026\) , \( 10055385 a - 42985926\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(47964a-205026\right){x}+10055385a-42985926$ |
| 144.2-g2 |
144.2-g |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{9} \cdot 3^{9} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$16.03467447$ |
4.247689036 |
\( \frac{355655661}{2} a + \frac{1164756561}{2} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 179349 a - 766686\) , \( -69393564 a + 296651754\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(179349a-766686\right){x}-69393564a+296651754$ |
| 144.2-h1 |
144.2-h |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{16} \cdot 3^{11} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$6.255183969$ |
1.657038713 |
\( -\frac{49866463}{110592} a + \frac{402592373}{110592} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 4706 a + 15416\) , \( -29575 a - 96854\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(4706a+15416\right){x}-29575a-96854$ |
| 144.2-h2 |
144.2-h |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{16} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$6.255183969$ |
1.657038713 |
\( -\frac{38553913631}{15552} a + \frac{164841901877}{15552} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -18919 a - 61954\) , \( -268894 a - 880604\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-18919a-61954\right){x}-268894a-880604$ |
| 144.2-h3 |
144.2-h |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{13} \cdot 3^{11} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$6.255183969$ |
1.657038713 |
\( -\frac{10023098548616947}{216} a + \frac{42847916605213553}{216} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -197659 a - 647314\) , \( 92446190 a + 302753620\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-197659a-647314\right){x}+92446190a+302753620$ |
| 144.2-h4 |
144.2-h |
$4$ |
$4$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{13} \cdot 3^{26} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$1.563795992$ |
1.657038713 |
\( \frac{24879955441}{472392} a + \frac{26588853943}{157464} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -218179 a - 714514\) , \( -107664874 a - 352593548\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-218179a-714514\right){x}-107664874a-352593548$ |
| 144.2-i1 |
144.2-i |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{14} \cdot 3^{7} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.394760576$ |
$5.988047340$ |
2.504791370 |
\( -\frac{116143}{192} a + \frac{56165}{192} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -223 a - 730\) , \( -5798 a - 18988\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-223a-730\right){x}-5798a-18988$ |
| 144.2-i2 |
144.2-i |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{7} \cdot 3^{8} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.789521152$ |
$5.988047340$ |
2.504791370 |
\( \frac{28106971}{24} a + \frac{30693053}{8} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 4 a + 22\) , \( a + 6\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4a+22\right){x}+a+6$ |
| 144.2-j1 |
144.2-j |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{15} \cdot 3^{6} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.658803172$ |
1.014433261 |
\( -\frac{925430099}{32} a + \frac{3956137073}{32} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 10 a + 31\) , \( -443 a - 1449\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(10a+31\right){x}-443a-1449$ |
| 144.2-j2 |
144.2-j |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{21} \cdot 3^{6} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.658803172$ |
1.014433261 |
\( \frac{7754659}{1024} a + \frac{11013279}{1024} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -77068 a - 252391\) , \( -22486187 a - 73640401\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-77068a-252391\right){x}-22486187a-73640401$ |
| 144.2-k1 |
144.2-k |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{14} \cdot 3^{7} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.123637310$ |
$13.25492517$ |
5.209555179 |
\( -\frac{116143}{192} a + \frac{56165}{192} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 171 a - 744\) , \( 1383 a - 5919\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(171a-744\right){x}+1383a-5919$ |
| 144.2-k2 |
144.2-k |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{7} \cdot 3^{8} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.247274620$ |
$13.25492517$ |
5.209555179 |
\( \frac{28106971}{24} a + \frac{30693053}{8} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -103642 a + 443048\) , \( 20181596 a - 86274659\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-103642a+443048\right){x}+20181596a-86274659$ |
| 144.2-l1 |
144.2-l |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{15} \cdot 3^{6} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$4.249666479$ |
2.814410379 |
\( -\frac{925430099}{32} a + \frac{3956137073}{32} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 25004 a - 106903\) , \( 4211705 a - 18004697\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(25004a-106903\right){x}+4211705a-18004697$ |
| 144.2-l2 |
144.2-l |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{21} \cdot 3^{6} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$4.249666479$ |
2.814410379 |
\( \frac{7754659}{1024} a + \frac{11013279}{1024} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 6 a - 45\) , \( 39 a - 171\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(6a-45\right){x}+39a-171$ |
| 144.2-m1 |
144.2-m |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{6} \cdot 3^{3} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.098084743$ |
$40.05693794$ |
2.081621533 |
\( -\frac{23997}{4} a - \frac{41025}{4} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -103 a - 337\) , \( 804 a + 2633\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-103a-337\right){x}+804a+2633$ |
| 144.2-m2 |
144.2-m |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{9} \cdot 3^{3} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.196169486$ |
$20.02846897$ |
2.081621533 |
\( \frac{355655661}{2} a + \frac{1164756561}{2} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -1758 a - 5757\) , \( 71207 a + 233197\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1758a-5757\right){x}+71207a+233197$ |
| 144.2-n1 |
144.2-n |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$13.35389039$ |
1.768765991 |
\( \frac{4171}{2} a - \frac{14469}{2} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 5 a - 34\) , \( -13 a + 49\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(5a-34\right){x}-13a+49$ |
| 144.2-o1 |
144.2-o |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{6} \cdot 3^{3} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.043504245$ |
$8.302563754$ |
4.590172459 |
\( -\frac{23997}{4} a - \frac{41025}{4} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 51 a - 231\) , \( 430 a - 1845\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(51a-231\right){x}+430a-1845$ |
| 144.2-o2 |
144.2-o |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{9} \cdot 3^{3} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.087008490$ |
$8.302563754$ |
4.590172459 |
\( \frac{355655661}{2} a + \frac{1164756561}{2} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 196 a - 851\) , \( -2313 a + 9881\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(196a-851\right){x}-2313a+9881$ |
| 144.2-p1 |
144.2-p |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{18} \cdot 3^{3} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.322668450$ |
$2.191169358$ |
2.696408766 |
\( -\frac{167058741}{256} a + \frac{678122727}{256} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 1698 a - 7209\) , \( 73013 a - 312057\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(1698a-7209\right){x}+73013a-312057$ |
| 144.2-p2 |
144.2-p |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{3} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.161334225$ |
$2.191169358$ |
2.696408766 |
\( \frac{42445476687}{16} a + \frac{139005397947}{16} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 263748 a - 1127451\) , \( 208978169 a - 893364305\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(263748a-1127451\right){x}+208978169a-893364305$ |
| 144.2-q1 |
144.2-q |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{18} \cdot 3^{3} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.127902231$ |
$20.24999224$ |
5.488902757 |
\( -\frac{167058741}{256} a + \frac{678122727}{256} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -693 a - 2268\) , \( 18943 a + 62037\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-693a-2268\right){x}+18943a+62037$ |
| 144.2-q2 |
144.2-q |
$2$ |
$2$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{3} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.255804462$ |
$20.24999224$ |
5.488902757 |
\( \frac{42445476687}{16} a + \frac{139005397947}{16} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -3 a - 30\) , \( a + 35\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3a-30\right){x}+a+35$ |
| 144.2-r1 |
144.2-r |
$1$ |
$1$ |
\(\Q(\sqrt{57}) \) |
$2$ |
$[2, 0]$ |
144.2 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$2.33704$ |
$(a-4), (a+3), (4a+13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$4.181681841$ |
0.553877290 |
\( \frac{4171}{2} a - \frac{14469}{2} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 4171 a + 13660\) , \( -30620 a - 100278\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4171a+13660\right){x}-30620a-100278$ |
*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.
