| 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 |
| 64.4-a1 |
64.4-a |
$2$ |
$3$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{21} \) |
$4.83861$ |
$(a^2-6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$32.89239640$ |
2.429816763 |
\( -\frac{10660370837109409609}{8} a^{2} - \frac{16184561139235635311}{8} a + \frac{33866655049773828215}{8} \) |
\( \bigl[0\) , \( -a - 1\) , \( a^{2} - 4\) , \( -899 a^{2} + 3309 a - 2633\) , \( 46108 a^{2} - 170423 a + 136781\bigr] \) |
${y}^2+\left(a^{2}-4\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-899a^{2}+3309a-2633\right){x}+46108a^{2}-170423a+136781$ |
| 64.4-a2 |
64.4-a |
$2$ |
$3$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{27} \) |
$4.83861$ |
$(a^2-6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$32.89239640$ |
2.429816763 |
\( -\frac{153560745}{512} a^{2} - \frac{233924111}{512} a + \frac{486084887}{512} \) |
\( \bigl[0\) , \( -a - 1\) , \( a^{2} - 4\) , \( 31 a^{2} - 111 a + 87\) , \( 358 a^{2} - 1324 a + 1061\bigr] \) |
${y}^2+\left(a^{2}-4\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(31a^{2}-111a+87\right){x}+358a^{2}-1324a+1061$ |
| 64.4-b1 |
64.4-b |
$2$ |
$2$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{14} \) |
$4.83861$ |
$(a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$83.33984394$ |
3.078227371 |
\( 26933208 a^{2} - 99554907 a + 79908472 \) |
\( \bigl[a^{2} - 4\) , \( a\) , \( a^{2} - 4\) , \( 7 a^{2} + 15 a - 28\) , \( 15 a^{2} + 19 a - 44\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+a{x}^{2}+\left(7a^{2}+15a-28\right){x}+15a^{2}+19a-44$ |
| 64.4-b2 |
64.4-b |
$2$ |
$2$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{16} \) |
$4.83861$ |
$(a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$166.6796878$ |
3.078227371 |
\( -1723 a^{2} + 4372 a + 1724 \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( a^{2} + a - 9\) , \( a^{2} - 7\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a^{2}+a-9\right){x}+a^{2}-7$ |
| 64.4-c1 |
64.4-c |
$4$ |
$6$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{54} \) |
$4.83861$ |
$(a^2-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$2.247842879$ |
$13.42404928$ |
3.343634184 |
\( \frac{2936145822907481}{68719476736} a^{2} - \frac{2650603679005985}{68719476736} a - \frac{11963566012280679}{68719476736} \) |
\( \bigl[a^{2} + a - 4\) , \( a^{2} - 4\) , \( 0\) , \( -860 a^{2} + 3199 a - 2580\) , \( -44766 a^{2} + 165480 a - 132816\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-860a^{2}+3199a-2580\right){x}-44766a^{2}+165480a-132816$ |
| 64.4-c2 |
64.4-c |
$4$ |
$6$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{30} \) |
$4.83861$ |
$(a^2-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.749280959$ |
$40.27214784$ |
3.343634184 |
\( \frac{2615577}{4096} a^{2} - \frac{11083745}{4096} a + \frac{12352857}{4096} \) |
\( \bigl[a^{2} + a - 4\) , \( a^{2} - 4\) , \( 0\) , \( -55 a^{2} + 219 a - 180\) , \( 659 a^{2} - 2420 a + 1936\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-55a^{2}+219a-180\right){x}+659a^{2}-2420a+1936$ |
| 64.4-c3 |
64.4-c |
$4$ |
$6$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{36} \) |
$4.83861$ |
$(a^2-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1.123921439$ |
$26.84809856$ |
3.343634184 |
\( -\frac{1308241604941929}{262144} a^{2} - \frac{233087636858447}{262144} a + \frac{8883119257726807}{262144} \) |
\( \bigl[a^{2} + a - 4\) , \( a + 1\) , \( 0\) , \( 26312511 a^{2} + 4706405 a - 178707809\) , \( -118384210425 a^{2} - 21084547314 a + 803807796043\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(26312511a^{2}+4706405a-178707809\right){x}-118384210425a^{2}-21084547314a+803807796043$ |
| 64.4-c4 |
64.4-c |
$4$ |
$6$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{24} \) |
$4.83861$ |
$(a^2-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.374640479$ |
$80.54429568$ |
3.343634184 |
\( \frac{23863}{64} a^{2} + \frac{97489}{64} a + \frac{93431}{64} \) |
\( \bigl[a^{2} + a - 4\) , \( a + 1\) , \( 0\) , \( 351841 a^{2} + 60750 a - 2384089\) , \( -134032993 a^{2} - 24271011 a + 911065987\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(351841a^{2}+60750a-2384089\right){x}-134032993a^{2}-24271011a+911065987$ |
| 64.4-d1 |
64.4-d |
$4$ |
$4$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{6} \) |
$4.83861$ |
$(a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$302.7039195$ |
2.795156093 |
\( 14761386864 a^{2} + 22412197395 a - 46891080360 \) |
\( \bigl[a^{2} - 4\) , \( a + 1\) , \( a\) , \( -5667684 a^{2} - 8604670 a + 18005524\) , \( 13719160589 a^{2} + 20828411763 a - 43584044714\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-5667684a^{2}-8604670a+18005524\right){x}+13719160589a^{2}+20828411763a-43584044714$ |
| 64.4-d2 |
64.4-d |
$4$ |
$4$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{15} \) |
$4.83861$ |
$(a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$151.3519597$ |
2.795156093 |
\( -729 a + 1728 \) |
\( \bigl[a^{2} + a - 4\) , \( a - 1\) , \( a\) , \( -a^{2} - 2 a + 7\) , \( 11 a^{2} + 18 a - 35\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a^{2}-2a+7\right){x}+11a^{2}+18a-35$ |
| 64.4-d3 |
64.4-d |
$4$ |
$4$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{12} \) |
$4.83861$ |
$(a^2-6)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$302.7039195$ |
2.795156093 |
\( 455625 a^{2} - 1446336 a + 1074816 \) |
\( \bigl[a\) , \( -a^{2} + 6\) , \( 0\) , \( -4813 a^{2} - 7305 a + 15296\) , \( 336664 a^{2} + 511124 a - 1069536\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(-4813a^{2}-7305a+15296\right){x}+336664a^{2}+511124a-1069536$ |
| 64.4-d4 |
64.4-d |
$4$ |
$4$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{15} \) |
$4.83861$ |
$(a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$75.67597989$ |
2.795156093 |
\( 3398653993032 a^{2} - 12562760097675 a + 10083557663280 \) |
\( \bigl[a\) , \( -a^{2} + 6\) , \( 0\) , \( -6878 a^{2} - 10440 a + 21856\) , \( 16893 a^{2} + 25648 a - 53664\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(-6878a^{2}-10440a+21856\right){x}+16893a^{2}+25648a-53664$ |
| 64.4-e1 |
64.4-e |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{26} \) |
$4.83861$ |
$(a^2-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.373398606$ |
$55.50090546$ |
2.296370864 |
\( \frac{333491649913}{256} a^{2} - \frac{1232712023873}{256} a + \frac{989435030713}{256} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - 4\) , \( a\) , \( 86394542 a^{2} + 131164087 a - 274464580\) , \( -2319719820802 a^{2} - 3521795614748 a + 7369457609280\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(86394542a^{2}+131164087a-274464580\right){x}-2319719820802a^{2}-3521795614748a+7369457609280$ |
| 64.4-e2 |
64.4-e |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{19} \) |
$4.83861$ |
$(a^2-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.746797212$ |
$27.75045273$ |
2.296370864 |
\( \frac{49479}{2} a^{2} - \frac{194047}{2} a + \frac{159977}{2} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} + a - 4\) , \( a\) , \( -8 a^{2} - 13 a + 28\) , \( -51 a^{2} - 76 a + 160\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+a{y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(-8a^{2}-13a+28\right){x}-51a^{2}-76a+160$ |
| 64.4-e3 |
64.4-e |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{20} \) |
$4.83861$ |
$(a^2-6)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1.493594424$ |
$55.50090546$ |
2.296370864 |
\( \frac{38239925}{4} a^{2} + \frac{58077475}{4} a - \frac{121417863}{4} \) |
\( \bigl[a^{2} + a - 4\) , \( a^{2} + a - 4\) , \( 0\) , \( -11371 a^{2} - 17263 a + 36124\) , \( -1275372 a^{2} - 1936268 a + 4051696\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(-11371a^{2}-17263a+36124\right){x}-1275372a^{2}-1936268a+4051696$ |
| 64.4-e4 |
64.4-e |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{19} \) |
$4.83861$ |
$(a^2-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.987188848$ |
$6.937613183$ |
2.296370864 |
\( \frac{1278354816368585}{2} a^{2} + \frac{1940796619489295}{2} a - \frac{4061172191721673}{2} \) |
\( \bigl[a^{2} + a - 4\) , \( a^{2} + a - 4\) , \( 0\) , \( -182016 a^{2} - 276338 a + 578244\) , \( -79665661 a^{2} - 120948303 a + 253087768\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(-182016a^{2}-276338a+578244\right){x}-79665661a^{2}-120948303a+253087768$ |
| 64.4-e5 |
64.4-e |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{22} \) |
$4.83861$ |
$(a^2-6)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.746797212$ |
$111.0018109$ |
2.296370864 |
\( -\frac{1494139287}{16} a^{2} - \frac{266719409}{16} a + \frac{10146617913}{16} \) |
\( \bigl[a\) , \( a^{2} - a - 6\) , \( a^{2} - 4\) , \( -862807 a^{2} - 1309912 a + 2741040\) , \( -732248066 a^{2} - 1111698063 a + 2326259844\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-862807a^{2}-1309912a+2741040\right){x}-732248066a^{2}-1111698063a+2326259844$ |
| 64.4-e6 |
64.4-e |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{20} \) |
$4.83861$ |
$(a^2-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.373398606$ |
$55.50090546$ |
2.296370864 |
\( -\frac{181142138460569645}{4} a^{2} - \frac{32278456715968139}{4} a + \frac{1229964682609035911}{4} \) |
\( \bigl[a\) , \( a^{2} - a - 6\) , \( a^{2} - 4\) , \( -3292327 a^{2} - 4998407 a + 10459320\) , \( 5296745678 a^{2} + 8041512394 a - 16827093684\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-3292327a^{2}-4998407a+10459320\right){x}+5296745678a^{2}+8041512394a-16827093684$ |
| 64.4-f1 |
64.4-f |
$2$ |
$2$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{14} \) |
$4.83861$ |
$(a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$100.0808919$ |
3.696572087 |
\( -12237 a^{2} - 1963 a + 84888 \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} - a + 6\) , \( a^{2} + a - 4\) , \( 8 a^{2} - 38 a + 40\) , \( 46 a^{2} - 177 a + 148\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}-a+6\right){x}^{2}+\left(8a^{2}-38a+40\right){x}+46a^{2}-177a+148$ |
| 64.4-f2 |
64.4-f |
$2$ |
$2$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{10} \) |
$4.83861$ |
$(a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$50.04044596$ |
3.696572087 |
\( -809793037 a^{2} - 144300549 a + 5498539288 \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{2} + 4\) , \( a^{2} + a - 4\) , \( -19 a^{2} + 65 a - 48\) , \( 90 a^{2} - 333 a + 268\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-19a^{2}+65a-48\right){x}+90a^{2}-333a+268$ |
| 64.4-g1 |
64.4-g |
$1$ |
$1$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{17} \) |
$4.83861$ |
$(a^2-6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$33.13267774$ |
2.447566750 |
\( -919922 a^{2} + 3416322 a - 2769394 \) |
\( \bigl[0\) , \( -1\) , \( a^{2} - 4\) , \( 7 a^{2} + 2 a - 49\) , \( -20 a^{2} - 3 a + 133\bigr] \) |
${y}^2+\left(a^{2}-4\right){y}={x}^{3}-{x}^{2}+\left(7a^{2}+2a-49\right){x}-20a^{2}-3a+133$ |
| 64.4-h1 |
64.4-h |
$1$ |
$1$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{17} \) |
$4.83861$ |
$(a^2-6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.049468682$ |
$176.5734515$ |
3.871551209 |
\( -919922 a^{2} + 3416322 a - 2769394 \) |
\( \bigl[0\) , \( -a + 1\) , \( a^{2} - 4\) , \( -2 a^{2} + 9 a - 9\) , \( 4 a^{2} - 15 a + 11\bigr] \) |
${y}^2+\left(a^{2}-4\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a^{2}+9a-9\right){x}+4a^{2}-15a+11$ |
| 64.4-i1 |
64.4-i |
$2$ |
$2$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{10} \) |
$4.83861$ |
$(a^2-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.626129519$ |
$42.83770479$ |
3.859407168 |
\( -809793037 a^{2} - 144300549 a + 5498539288 \) |
\( \bigl[a^{2} - 4\) , \( -1\) , \( 0\) , \( -a^{2} + 5 a - 5\) , \( -2 a^{2} + 8 a - 7\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}={x}^{3}-{x}^{2}+\left(-a^{2}+5a-5\right){x}-2a^{2}+8a-7$ |
| 64.4-i2 |
64.4-i |
$2$ |
$2$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{14} \) |
$4.83861$ |
$(a^2-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.813064759$ |
$85.67540958$ |
3.859407168 |
\( -12237 a^{2} - 1963 a + 84888 \) |
\( \bigl[a\) , \( -a - 1\) , \( a^{2} - 4\) , \( 4 a^{2} - 4 a - 17\) , \( 4 a^{2} - 27\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(4a^{2}-4a-17\right){x}+4a^{2}-27$ |
| 64.4-j1 |
64.4-j |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{20} \) |
$4.83861$ |
$(a^2-6)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$58.13590838$ |
0.536824692 |
\( \frac{38239925}{4} a^{2} + \frac{58077475}{4} a - \frac{121417863}{4} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} - a + 6\) , \( a^{2} - 4\) , \( -4937 a^{2} - 7494 a + 15688\) , \( -350350 a^{2} - 531900 a + 1113020\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}-a+6\right){x}^{2}+\left(-4937a^{2}-7494a+15688\right){x}-350350a^{2}-531900a+1113020$ |
| 64.4-j2 |
64.4-j |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{19} \) |
$4.83861$ |
$(a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$7.266988548$ |
0.536824692 |
\( \frac{1278354816368585}{2} a^{2} + \frac{1940796619489295}{2} a - \frac{4061172191721673}{2} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} - a + 6\) , \( a^{2} - 4\) , \( -78972 a^{2} - 119894 a + 250888\) , \( -22540110 a^{2} - 34220365 a + 71607092\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}-a+6\right){x}^{2}+\left(-78972a^{2}-119894a+250888\right){x}-22540110a^{2}-34220365a+71607092$ |
| 64.4-j3 |
64.4-j |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{22} \) |
$4.83861$ |
$(a^2-6)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$58.13590838$ |
0.536824692 |
\( -\frac{1494139287}{16} a^{2} - \frac{266719409}{16} a + \frac{10146617913}{16} \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{2} + 4\) , \( a^{2} - 4\) , \( -374331 a^{2} - 568309 a + 1189204\) , \( -209746460 a^{2} - 318436802 a + 666338076\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-374331a^{2}-568309a+1189204\right){x}-209746460a^{2}-318436802a+666338076$ |
| 64.4-j4 |
64.4-j |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{20} \) |
$4.83861$ |
$(a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$29.06795419$ |
0.536824692 |
\( -\frac{181142138460569645}{4} a^{2} - \frac{32278456715968139}{4} a + \frac{1229964682609035911}{4} \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{2} + 4\) , \( a^{2} - 4\) , \( -1428386 a^{2} - 2168574 a + 4537804\) , \( 1511760684 a^{2} + 2295153105 a - 4802673228\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-1428386a^{2}-2168574a+4537804\right){x}+1511760684a^{2}+2295153105a-4802673228$ |
| 64.4-j5 |
64.4-j |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{26} \) |
$4.83861$ |
$(a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$14.53397709$ |
0.536824692 |
\( \frac{333491649913}{256} a^{2} - \frac{1232712023873}{256} a + \frac{989435030713}{256} \) |
\( \bigl[a\) , \( a^{2} + a - 5\) , \( 0\) , \( 37482547 a^{2} + 56905955 a - 119077329\) , \( -662865065372 a^{2} - 1006360880076 a + 2105838798341\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(37482547a^{2}+56905955a-119077329\right){x}-662865065372a^{2}-1006360880076a+2105838798341$ |
| 64.4-j6 |
64.4-j |
$6$ |
$8$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{19} \) |
$4.83861$ |
$(a^2-6)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$58.13590838$ |
0.536824692 |
\( \frac{49479}{2} a^{2} - \frac{194047}{2} a + \frac{159977}{2} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -4 a^{2} - 5 a + 12\) , \( -15 a^{2} - 22 a + 48\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-4a^{2}-5a+12\right){x}-15a^{2}-22a+48$ |
| 64.4-k1 |
64.4-k |
$4$ |
$4$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{12} \) |
$4.83861$ |
$(a^2-6)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$119.3927739$ |
1.102468180 |
\( 455625 a^{2} - 1446336 a + 1074816 \) |
\( \bigl[a^{2} - 4\) , \( a + 1\) , \( a^{2} - 4\) , \( -11090 a^{2} - 16835 a + 35231\) , \( 1167014 a^{2} + 1771760 a - 3707457\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-11090a^{2}-16835a+35231\right){x}+1167014a^{2}+1771760a-3707457$ |
| 64.4-k2 |
64.4-k |
$4$ |
$4$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{15} \) |
$4.83861$ |
$(a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$14.92409673$ |
1.102468180 |
\( 3398653993032 a^{2} - 12562760097675 a + 10083557663280 \) |
\( \bigl[a^{2} - 4\) , \( a + 1\) , \( a^{2} - 4\) , \( -15850 a^{2} - 24060 a + 50351\) , \( 43267 a^{2} + 65691 a - 137457\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-15850a^{2}-24060a+50351\right){x}+43267a^{2}+65691a-137457$ |
| 64.4-k3 |
64.4-k |
$4$ |
$4$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{6} \) |
$4.83861$ |
$(a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$119.3927739$ |
1.102468180 |
\( 14761386864 a^{2} + 22412197395 a - 46891080360 \) |
\( \bigl[a^{2} + a - 4\) , \( a - 1\) , \( a\) , \( -13063597 a^{2} - 19833137 a + 41501404\) , \( 48007974693 a^{2} + 72885644737 a - 152515287078\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-13063597a^{2}-19833137a+41501404\right){x}+48007974693a^{2}+72885644737a-152515287078$ |
| 64.4-k4 |
64.4-k |
$4$ |
$4$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{15} \) |
$4.83861$ |
$(a^2-6)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$119.3927739$ |
1.102468180 |
\( -729 a + 1728 \) |
\( \bigl[a\) , \( -a^{2} + 6\) , \( a^{2} + a - 4\) , \( -8 a^{2} - 10 a + 32\) , \( 50 a^{2} + 77 a - 156\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(-8a^{2}-10a+32\right){x}+50a^{2}+77a-156$ |
| 64.4-l1 |
64.4-l |
$4$ |
$6$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{36} \) |
$4.83861$ |
$(a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$52.93233119$ |
0.977550130 |
\( -\frac{1308241604941929}{262144} a^{2} - \frac{233087636858447}{262144} a + \frac{8883119257726807}{262144} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} + a - 6\) , \( a^{2} + a - 4\) , \( 828801944 a^{2} + 147688893 a - 5627612208\) , \( -20926676404274 a^{2} - 3729010063602 a + 142093238039116\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}+a-6\right){x}^{2}+\left(828801944a^{2}+147688893a-5627612208\right){x}-20926676404274a^{2}-3729010063602a+142093238039116$ |
| 64.4-l2 |
64.4-l |
$4$ |
$6$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{24} \) |
$4.83861$ |
$(a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$52.93233119$ |
0.977550130 |
\( \frac{23863}{64} a^{2} + \frac{97489}{64} a + \frac{93431}{64} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} + a - 6\) , \( a^{2} + a - 4\) , \( 11064569 a^{2} + 1971498 a - 75128648\) , \( -23767945004 a^{2} - 4235299468 a + 161385582076\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}+a-6\right){x}^{2}+\left(11064569a^{2}+1971498a-75128648\right){x}-23767945004a^{2}-4235299468a+161385582076$ |
| 64.4-l3 |
64.4-l |
$4$ |
$6$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{54} \) |
$4.83861$ |
$(a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$26.46616559$ |
0.977550130 |
\( \frac{2936145822907481}{68719476736} a^{2} - \frac{2650603679005985}{68719476736} a - \frac{11963566012280679}{68719476736} \) |
\( \bigl[a^{2} - 4\) , \( -a + 1\) , \( 0\) , \( -25 a^{2} + 238 a - 441\) , \( 548 a^{2} - 2744 a + 3435\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-25a^{2}+238a-441\right){x}+548a^{2}-2744a+3435$ |
| 64.4-l4 |
64.4-l |
$4$ |
$6$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{30} \) |
$4.83861$ |
$(a^2-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$26.46616559$ |
0.977550130 |
\( \frac{2615577}{4096} a^{2} - \frac{11083745}{4096} a + \frac{12352857}{4096} \) |
\( \bigl[a^{2} - 4\) , \( -a + 1\) , \( 0\) , \( -5 a^{2} + 13 a - 1\) , \( -25 a^{2} + 84 a - 53\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-5a^{2}+13a-1\right){x}-25a^{2}+84a-53$ |
| 64.4-m1 |
64.4-m |
$2$ |
$2$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{16} \) |
$4.83861$ |
$(a^2-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.221163368$ |
$52.06520696$ |
1.275939441 |
\( -1723 a^{2} + 4372 a + 1724 \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - 6\) , \( a^{2} + a - 4\) , \( -2 a^{2} + 3 a\) , \( -5 a^{2} + 15 a - 12\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(-2a^{2}+3a\right){x}-5a^{2}+15a-12$ |
| 64.4-m2 |
64.4-m |
$2$ |
$2$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{14} \) |
$4.83861$ |
$(a^2-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.442326736$ |
$26.03260348$ |
1.275939441 |
\( 26933208 a^{2} - 99554907 a + 79908472 \) |
\( \bigl[a^{2} + a - 4\) , \( 0\) , \( a^{2} - 4\) , \( 10 a^{2} + 58 a - 84\) , \( 9 a^{2} + 229 a - 284\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(10a^{2}+58a-84\right){x}+9a^{2}+229a-284$ |
| 64.4-n1 |
64.4-n |
$2$ |
$3$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{27} \) |
$4.83861$ |
$(a^2-6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.355900500$ |
$25.87488915$ |
4.081655584 |
\( -\frac{153560745}{512} a^{2} - \frac{233924111}{512} a + \frac{486084887}{512} \) |
\( \bigl[0\) , \( -a^{2} + 6\) , \( a^{2} - 4\) , \( 15 a^{2} - 6 a - 80\) , \( 67 a^{2} + 42 a - 532\bigr] \) |
${y}^2+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(15a^{2}-6a-80\right){x}+67a^{2}+42a-532$ |
| 64.4-n2 |
64.4-n |
$2$ |
$3$ |
3.3.733.1 |
$3$ |
$[3, 0]$ |
64.4 |
\( 2^{6} \) |
\( - 2^{21} \) |
$4.83861$ |
$(a^2-6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1.067701501$ |
$8.624963052$ |
4.081655584 |
\( -\frac{10660370837109409609}{8} a^{2} - \frac{16184561139235635311}{8} a + \frac{33866655049773828215}{8} \) |
\( \bigl[0\) , \( -a^{2} + 6\) , \( a^{2} - 4\) , \( -165 a^{2} + 224 a + 480\) , \( -1313 a^{2} + 3235 a + 180\bigr] \) |
${y}^2+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(-165a^{2}+224a+480\right){x}-1313a^{2}+3235a+180$ |
*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.
