| 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 |
| 576.1-a1 |
576.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{8} \cdot 3^{7} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$13.54628100$ |
1.113497439 |
\( -\frac{1792}{81} a + \frac{143872}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4 a - 7\) , \( -2 a + 11\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(4a-7\right){x}-2a+11$ |
| 576.1-a2 |
576.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{8} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$6.773140501$ |
1.113497439 |
\( -\frac{15635312}{729} a + \frac{6294736}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 29 a - 97\) , \( 127 a - 448\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(29a-97\right){x}+127a-448$ |
| 576.1-a3 |
576.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{20} \cdot 3^{13} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.693285125$ |
1.113497439 |
\( \frac{16331082796}{531441} a + \frac{4610608696}{59049} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 9 a - 37\) , \( 311 a - 1132\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(9a-37\right){x}+311a-1132$ |
| 576.1-a4 |
576.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{4} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$3.386570250$ |
1.113497439 |
\( -\frac{76723863524}{27} a + \frac{30191175944}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 449 a - 1597\) , \( 8839 a - 31300\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(449a-1597\right){x}+8839a-31300$ |
| 576.1-b1 |
576.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{8} \cdot 3^{23} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.658473796$ |
1.090605650 |
\( -\frac{535768999168}{387420489} a - \frac{666511660544}{387420489} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -53 a - 143\) , \( -410 a - 1041\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-53a-143\right){x}-410a-1041$ |
| 576.1-b2 |
576.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{19} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.829236898$ |
1.090605650 |
\( \frac{516954899344}{59049} a + \frac{448864064848}{19683} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -883 a - 2348\) , \( -25275 a - 64608\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-883a-2348\right){x}-25275a-64608$ |
| 576.1-c1 |
576.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{16} \cdot 3^{8} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$9.673027696$ |
1.590235957 |
\( -\frac{453099070112}{81} a + \frac{1604596505008}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -272 a - 696\) , \( 7788 a + 19800\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-272a-696\right){x}+7788a+19800$ |
| 576.1-c2 |
576.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{16} \cdot 3^{17} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.836513848$ |
1.590235957 |
\( \frac{15633062848}{43046721} a + \frac{4233991888}{4782969} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -402 a - 1021\) , \( 2861 a + 7271\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-402a-1021\right){x}+2861a+7271$ |
| 576.1-c3 |
576.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{10} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$19.34605539$ |
1.590235957 |
\( \frac{1504202752}{6561} a + \frac{559765504}{729} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -337 a - 856\) , \( 5386 a + 13688\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-337a-856\right){x}+5386a+13688$ |
| 576.1-c4 |
576.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{5} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$9.673027696$ |
1.590235957 |
\( \frac{33201711483616}{81} a + \frac{9375356408656}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 1905 a - 6741\) , \( 9651 a - 34176\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(1905a-6741\right){x}+9651a-34176$ |
| 576.1-d1 |
576.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{16} \cdot 3^{2} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.511589732$ |
$4.659790430$ |
3.848081111 |
\( -\frac{42688544}{3} a + \frac{151181488}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 33 a - 109\) , \( 155 a - 544\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(33a-109\right){x}+155a-544$ |
| 576.1-d2 |
576.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{4} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.255794866$ |
$18.63916172$ |
3.848081111 |
\( -\frac{4096}{3} a + \frac{59392}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 3 a - 4\) , \( 2 a - 4\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(3a-4\right){x}+2a-4$ |
| 576.1-d3 |
576.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{5} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.627897433$ |
$18.63916172$ |
3.848081111 |
\( \frac{2317472}{81} a + \frac{6410800}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 8 a - 24\) , \( -20 a + 72\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(8a-24\right){x}-20a+72$ |
| 576.1-d4 |
576.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{16} \cdot 3^{5} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.511589732$ |
$4.659790430$ |
3.848081111 |
\( \frac{6211264}{81} a + \frac{1755280}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2 a + 11\) , \( 13 a - 49\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a+11\right){x}+13a-49$ |
| 576.1-e1 |
576.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{20} \cdot 3^{2} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$64$ |
\( 2 \) |
$1$ |
$0.819644183$ |
4.311957557 |
\( -\frac{14483185829000}{3} a + \frac{51290482949500}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1040 a - 2648\) , \( -45856 a - 116544\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-1040a-2648\right){x}-45856a-116544$ |
| 576.1-e2 |
576.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{16} \cdot 3^{10} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$6.557153465$ |
4.311957557 |
\( -\frac{28420000}{6561} a + \frac{106486000}{6561} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 225 a + 572\) , \( -3033 a - 7708\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(225a+572\right){x}-3033a-7708$ |
| 576.1-e3 |
576.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$1$ |
$13.11430693$ |
4.311957557 |
\( \frac{256000}{81} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -80 a - 203\) , \( -484 a - 1230\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-80a-203\right){x}-484a-1230$ |
| 576.1-e4 |
576.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{16} \cdot 3^{10} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$6.557153465$ |
4.311957557 |
\( \frac{28420000}{6561} a + \frac{8674000}{729} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -225 a + 797\) , \( 3033 a - 10741\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-225a+797\right){x}+3033a-10741$ |
| 576.1-e5 |
576.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{4} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$16$ |
\( 2^{3} \) |
$1$ |
$3.278576732$ |
4.311957557 |
\( \frac{48778000}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1160 a - 2948\) , \( -37888 a - 96288\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-1160a-2948\right){x}-37888a-96288$ |
| 576.1-e6 |
576.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{20} \cdot 3^{2} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$64$ |
\( 2 \) |
$1$ |
$0.819644183$ |
4.311957557 |
\( \frac{14483185829000}{3} a + \frac{36807297120500}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 1040 a - 3688\) , \( 45856 a - 162400\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(1040a-3688\right){x}+45856a-162400$ |
| 576.1-f1 |
576.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{8} \cdot 3^{3} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.548391086$ |
$14.96298121$ |
2.697973326 |
\( \frac{3328}{9} a + \frac{2816}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -8 a - 20\) , \( 13 a + 33\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-8a-20\right){x}+13a+33$ |
| 576.1-f2 |
576.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{3} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.096782173$ |
$7.481490608$ |
2.697973326 |
\( -\frac{28624}{9} a + \frac{625408}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -63 a - 160\) , \( -447 a - 1136\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-63a-160\right){x}-447a-1136$ |
| 576.1-g1 |
576.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{8} \cdot 3^{9} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.605074972$ |
$11.03942381$ |
3.271371379 |
\( -\frac{419363166976}{243} a + \frac{495041681152}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 19 a + 34\) , \( 64 a + 189\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(19a+34\right){x}+64a+189$ |
| 576.1-g2 |
576.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{18} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.802537486$ |
$5.519711907$ |
3.271371379 |
\( -\frac{966369872}{59049} a + \frac{404236256}{6561} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -101 a - 271\) , \( 755 a + 1945\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-101a-271\right){x}+755a+1945$ |
| 576.1-g3 |
576.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{20} \cdot 3^{24} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.605074972$ |
$1.379927976$ |
3.271371379 |
\( \frac{12208548932788}{3486784401} a + \frac{3445104661132}{387420489} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -601 a - 1531\) , \( -13237 a - 33587\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-601a-1531\right){x}-13237a-33587$ |
| 576.1-g4 |
576.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{21} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.605074972$ |
$2.759855953$ |
3.271371379 |
\( \frac{57040808081036}{43046721} a + \frac{145044976597924}{43046721} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -1521 a - 3891\) , \( 57051 a + 144981\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-1521a-3891\right){x}+57051a+144981$ |
| 576.1-h1 |
576.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{16} \cdot 3^{3} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$6.661833980$ |
2.190397519 |
\( -\frac{19468624}{9} a + \frac{68945824}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2 a + 3\) , \( 25 a + 63\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+3\right){x}+25a+63$ |
| 576.1-h2 |
576.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{8} \cdot 3^{3} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$13.32366796$ |
2.190397519 |
\( \frac{66304}{9} a + \frac{47360}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -3 a - 7\) , \( 2 a + 5\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-3a-7\right){x}+2a+5$ |
| 576.1-i1 |
576.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{20} \cdot 3^{6} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.240368878$ |
0.736628749 |
\( -\frac{3969434500}{81} a + \frac{14057400868}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 959 a + 2437\) , \( -11853 a - 30123\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(959a+2437\right){x}-11853a-30123$ |
| 576.1-i2 |
576.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{6} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$8.961475512$ |
0.736628749 |
\( -\frac{213200}{81} a + \frac{101984}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 115 a - 407\) , \( 1075 a - 3807\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(115a-407\right){x}+1075a-3807$ |
| 576.1-i3 |
576.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{8} \cdot 3^{3} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$17.92295102$ |
0.736628749 |
\( \frac{124672}{9} a + \frac{105728}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -5 a + 18\) , \( 72 a - 255\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-5a+18\right){x}+72a-255$ |
| 576.1-i4 |
576.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{9} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.480737756$ |
0.736628749 |
\( \frac{1210319812}{6561} a + \frac{344737036}{729} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 335 a - 1187\) , \( -4533 a + 16053\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(335a-1187\right){x}-4533a+16053$ |
| 576.1-j1 |
576.1-j |
$1$ |
$1$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{16} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 7 \) |
$1$ |
$0.542528782$ |
0.624338276 |
\( \frac{13229378551886}{19683} a - \frac{46850372668562}{19683} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 504 a - 1984\) , \( 12352 a - 42116\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(504a-1984\right){x}+12352a-42116$ |
| 576.1-k1 |
576.1-k |
$2$ |
$2$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{8} \cdot 3^{11} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.275820388$ |
$9.584356535$ |
4.345987420 |
\( -\frac{588544}{729} a + \frac{2103808}{729} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 2 a + 4\) , \( 3 a + 6\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a+4\right){x}+3a+6$ |
| 576.1-k2 |
576.1-k |
$2$ |
$2$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{16} \cdot 3^{13} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.551640777$ |
$4.792178267$ |
4.345987420 |
\( \frac{191722768}{59049} a + \frac{57396112}{6561} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -18 a - 41\) , \( 99 a + 249\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-18a-41\right){x}+99a+249$ |
| 576.1-l1 |
576.1-l |
$1$ |
$1$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{16} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 7 \) |
$1$ |
$0.542528782$ |
0.624338276 |
\( -\frac{13229378551886}{19683} a - \frac{3735666012964}{2187} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -502 a - 1481\) , \( -12855 a - 31245\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-502a-1481\right){x}-12855a-31245$ |
| 576.1-m1 |
576.1-m |
$2$ |
$2$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{16} \cdot 3^{5} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.264407945$ |
$5.765310773$ |
4.292462661 |
\( -\frac{108323480272}{27} a + \frac{127871576848}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -482 a - 1225\) , \( -22283 a - 56629\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-482a-1225\right){x}-22283a-56629$ |
| 576.1-m2 |
576.1-m |
$2$ |
$2$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{8} \cdot 3^{7} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.132203972$ |
$11.53062154$ |
4.292462661 |
\( \frac{153572608}{729} a + \frac{30771712}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 186 a - 652\) , \( -2497 a + 8846\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(186a-652\right){x}-2497a+8846$ |
| 576.1-n1 |
576.1-n |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{20} \cdot 3^{24} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.605074972$ |
$1.379927976$ |
3.271371379 |
\( -\frac{12208548932788}{3486784401} a + \frac{43214490882976}{3486784401} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 601 a - 2132\) , \( 13237 a - 46824\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(601a-2132\right){x}+13237a-46824$ |
| 576.1-n2 |
576.1-n |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{21} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.605074972$ |
$2.759855953$ |
3.271371379 |
\( -\frac{57040808081036}{43046721} a + \frac{22453976075440}{4782969} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1521 a - 5412\) , \( -57051 a + 202032\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(1521a-5412\right){x}-57051a+202032$ |
| 576.1-n3 |
576.1-n |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{18} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.802537486$ |
$5.519711907$ |
3.271371379 |
\( \frac{966369872}{59049} a + \frac{2671756432}{59049} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 101 a - 372\) , \( -755 a + 2700\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(101a-372\right){x}-755a+2700$ |
| 576.1-n4 |
576.1-n |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{8} \cdot 3^{9} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.605074972$ |
$11.03942381$ |
3.271371379 |
\( \frac{419363166976}{243} a + \frac{1065761876480}{243} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -19 a + 53\) , \( -64 a + 253\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-19a+53\right){x}-64a+253$ |
| 576.1-o1 |
576.1-o |
$2$ |
$2$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{11} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.096618862$ |
$9.074505318$ |
2.882796677 |
\( -\frac{38808859984}{729} a + \frac{137439547264}{729} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 69 a - 261\) , \( -531 a + 1944\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(69a-261\right){x}-531a+1944$ |
| 576.1-o2 |
576.1-o |
$2$ |
$2$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{8} \cdot 3^{13} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.193237724$ |
$9.074505318$ |
2.882796677 |
\( \frac{385656064}{59049} a - \frac{4355840}{6561} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 4 a - 16\) , \( -7 a + 25\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(4a-16\right){x}-7a+25$ |
| 576.1-p1 |
576.1-p |
$1$ |
$1$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{20} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 19 \) |
$1$ |
$1.083183859$ |
3.383412260 |
\( \frac{127856998304}{1162261467} a - \frac{452766038858}{1162261467} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 50 a + 127\) , \( 93201 a + 236859\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(50a+127\right){x}+93201a+236859$ |
| 576.1-q1 |
576.1-q |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{8} \cdot 3^{3} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$17.92295102$ |
0.736628749 |
\( -\frac{124672}{9} a + \frac{441856}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 5 a + 13\) , \( -72 a - 183\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(5a+13\right){x}-72a-183$ |
| 576.1-q2 |
576.1-q |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{9} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.480737756$ |
0.736628749 |
\( -\frac{1210319812}{6561} a + \frac{4312953136}{6561} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -335 a - 852\) , \( 4533 a + 11520\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-335a-852\right){x}+4533a+11520$ |
| 576.1-q3 |
576.1-q |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{6} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$8.961475512$ |
0.736628749 |
\( \frac{213200}{81} a + \frac{704656}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -115 a - 292\) , \( -1075 a - 2732\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-115a-292\right){x}-1075a-2732$ |
| 576.1-q4 |
576.1-q |
$4$ |
$4$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{20} \cdot 3^{6} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.240368878$ |
0.736628749 |
\( \frac{3969434500}{81} a + \frac{373628384}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -959 a + 3396\) , \( 11853 a - 41976\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-959a+3396\right){x}+11853a-41976$ |
| 576.1-r1 |
576.1-r |
$6$ |
$8$ |
\(\Q(\sqrt{37}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{25} \) |
$2.66284$ |
$(a-3), (a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$64$ |
\( 2 \) |
$1$ |
$0.496458618$ |
2.611753412 |
\( -\frac{400624520355598}{282429536481} a - \frac{800263026085370}{282429536481} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -4543 a + 16091\) , \( -326047 a + 1154656\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4543a+16091\right){x}-326047a+1154656$ |
*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.
