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 |
2.1-a1 |
2.1-a |
$2$ |
$3$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{3} \) |
$4.42240$ |
$(-3a^2+2a+26)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$50.14493536$ |
3.411930689 |
\( -\frac{231286995}{8} a^{2} + \frac{298848933}{4} a + \frac{536997087}{8} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} + 5\) , \( 1\) , \( -2 a^{2} + 2 a + 18\) , \( -23 a^{2} + 20 a + 205\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-2a^{2}+2a+18\right){x}-23a^{2}+20a+205$ |
2.1-a2 |
2.1-a |
$2$ |
$3$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{9} \) |
$4.42240$ |
$(-3a^2+2a+26)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$150.4348060$ |
3.411930689 |
\( \frac{4853058525}{512} a^{2} - \frac{1821154347}{256} a - \frac{41822439057}{512} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} + a + 5\) , \( a^{2} - a - 5\) , \( -35526937144931610 a^{2} - 116881672171796627 a - 64791848342728224\) , \( 12491164466752140835903919 a^{2} + 41095245117554565088270590 a + 22780619405839823143502983\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(-35526937144931610a^{2}-116881672171796627a-64791848342728224\right){x}+12491164466752140835903919a^{2}+41095245117554565088270590a+22780619405839823143502983$ |
2.1-b1 |
2.1-b |
$4$ |
$6$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{9} \) |
$4.42240$ |
$(-3a^2+2a+26)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$240.5857859$ |
1.364149108 |
\( -\frac{97696351413}{512} a^{2} + \frac{34120136979}{256} a + \frac{832934639817}{512} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -11497 a^{2} - 37825 a - 20968\) , \( -1549252 a^{2} - 5096954 a - 2825431\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-11497a^{2}-37825a-20968\right){x}-1549252a^{2}-5096954a-2825431$ |
2.1-b2 |
2.1-b |
$4$ |
$6$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{6} \) |
$4.42240$ |
$(-3a^2+2a+26)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$40.09763099$ |
1.364149108 |
\( -\frac{949077}{64} a^{2} - \frac{279693}{32} a + \frac{4964841}{64} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -66337314681777537595477217779403789653 a^{2} - 218246122252590257320457875154291669740 a - 120981924639083439881827828769145985683\) , \( -1015281862962035975236245282836134255483392518710550546772 a^{2} - 3340221572847553834918246833508825592275020200226944595032 a - 1851608772853178935262319327183949823515216446616617287239\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-66337314681777537595477217779403789653a^{2}-218246122252590257320457875154291669740a-120981924639083439881827828769145985683\right){x}-1015281862962035975236245282836134255483392518710550546772a^{2}-3340221572847553834918246833508825592275020200226944595032a-1851608772853178935262319327183949823515216446616617287239$ |
2.1-b3 |
2.1-b |
$4$ |
$6$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{3} \) |
$4.42240$ |
$(-3a^2+2a+26)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$80.19526199$ |
1.364149108 |
\( \frac{4308491979}{8} a^{2} + \frac{7087349907}{4} a + \frac{7857578313}{8} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -78020102714868490390930924 a^{2} - 256681853297058661470977629 a - 142288276700121112532677123\) , \( -1285066656349458963598570537870098842278 a^{2} - 4227798727303809847566235258320339527586 a - 2343625727397371010862200890916534181825\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-78020102714868490390930924a^{2}-256681853297058661470977629a-142288276700121112532677123\right){x}-1285066656349458963598570537870098842278a^{2}-4227798727303809847566235258320339527586a-2343625727397371010862200890916534181825$ |
2.1-b4 |
2.1-b |
$4$ |
$6$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{18} \) |
$4.42240$ |
$(-3a^2+2a+26)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$120.2928929$ |
1.364149108 |
\( -\frac{1392029397}{262144} a^{2} + \frac{559436787}{131072} a + \frac{11619128169}{262144} \) |
\( \bigl[a + 1\) , \( -a^{2} + 2 a + 5\) , \( 1\) , \( 27539842811569005 a^{2} + 90604570442792525 a + 50225475715806702\) , \( -8273623459640160238723853 a^{2} - 27219766819119320543200075 a - 15088926868504915180247083\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+\left(27539842811569005a^{2}+90604570442792525a+50225475715806702\right){x}-8273623459640160238723853a^{2}-27219766819119320543200075a-15088926868504915180247083$ |
2.1-c1 |
2.1-c |
$2$ |
$5$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( -2 \) |
$4.42240$ |
$(-3a^2+2a+26)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 1 \) |
$1$ |
$0.584204697$ |
0.331250790 |
\( \frac{52868302937118749}{2} a^{2} - 18655098633206251 a - \frac{449484193753986001}{2} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - a - 5\) , \( 1\) , \( -517 a^{2} + 1321 a + 1192\) , \( -15820 a^{2} + 40711 a + 36609\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-517a^{2}+1321a+1192\right){x}-15820a^{2}+40711a+36609$ |
2.1-c2 |
2.1-c |
$2$ |
$5$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{5} \) |
$4.42240$ |
$(-3a^2+2a+26)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5 \) |
$1$ |
$73.02558719$ |
0.331250790 |
\( \frac{9885}{32} a^{2} - \frac{3947}{16} a - \frac{80977}{32} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - a - 5\) , \( 1\) , \( 93416729759735 a^{2} + 307335910737137 a + 170367700502150\) , \( 59107009756310749194745 a^{2} + 194458816114912159812506 a + 107795738104301959039455\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(93416729759735a^{2}+307335910737137a+170367700502150\right){x}+59107009756310749194745a^{2}+194458816114912159812506a+107795738104301959039455$ |
2.2-a1 |
2.2-a |
$2$ |
$3$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
2.2 |
\( 2 \) |
\( 2^{3} \) |
$4.42240$ |
$(-a-1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$0.545888302$ |
$330.3722744$ |
1.363446171 |
\( \frac{78268347}{4} a^{2} - \frac{32595021}{4} a - \frac{303462225}{2} \) |
\( \bigl[a^{2} - 6\) , \( -a^{2} + a + 6\) , \( 1\) , \( -3978891624255813 a^{2} - 13090334934761505 a - 7256458434321020\) , \( 468002078994781181377154 a^{2} + 1539701138593398064485796 a + 853513479155557514351794\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(-3978891624255813a^{2}-13090334934761505a-7256458434321020\right){x}+468002078994781181377154a^{2}+1539701138593398064485796a+853513479155557514351794$ |
2.2-a2 |
2.2-a |
$2$ |
$3$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
2.2 |
\( 2 \) |
\( 2^{9} \) |
$4.42240$ |
$(-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$0.181962767$ |
$110.1240914$ |
1.363446171 |
\( \frac{1377}{32} a^{2} + \frac{12393}{32} a + \frac{2781}{16} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( 66 a^{2} - 47 a - 560\) , \( -2708 a^{2} + 1911 a + 23023\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(66a^{2}-47a-560\right){x}-2708a^{2}+1911a+23023$ |
3.1-a1 |
3.1-a |
$2$ |
$2$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{2} \) |
$4.73159$ |
$(-2a^2+2a+15)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.189357624$ |
$165.2750122$ |
1.064714388 |
\( -\frac{64055}{3} a^{2} + \frac{48578}{3} a + 177713 \) |
\( \bigl[a + 1\) , \( a^{2} - a - 5\) , \( a^{2} - a - 5\) , \( -30 a^{2} + 79 a + 76\) , \( -294 a^{2} + 764 a + 680\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-30a^{2}+79a+76\right){x}-294a^{2}+764a+680$ |
3.1-a2 |
3.1-a |
$2$ |
$2$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3 \) |
$4.73159$ |
$(-2a^2+2a+15)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.378715248$ |
$165.2750122$ |
1.064714388 |
\( \frac{15098731}{3} a^{2} - 12920798 a - 11623261 \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 7\) , \( a^{2} - a - 5\) , \( -82 a^{2} + 209 a + 200\) , \( -886 a^{2} + 2289 a + 2060\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(-a^{2}+a+7\right){x}^{2}+\left(-82a^{2}+209a+200\right){x}-886a^{2}+2289a+2060$ |
4.1-a1 |
4.1-a |
$4$ |
$6$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{21} \) |
$4.96398$ |
$(-3a^2+2a+26), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$57.21285653$ |
1.946420906 |
\( \frac{409472091}{262144} a^{2} - \frac{399464541}{131072} a - \frac{766402695}{262144} \) |
\( \bigl[a^{2} - a - 5\) , \( a^{2} - a - 7\) , \( a\) , \( -6937040106561 a^{2} - 22822480988028 a - 12651348149737\) , \( 25569933416356074919 a^{2} + 84123676714179418547 a + 46632875817231992253\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-7\right){x}^{2}+\left(-6937040106561a^{2}-22822480988028a-12651348149737\right){x}+25569933416356074919a^{2}+84123676714179418547a+46632875817231992253$ |
4.1-a2 |
4.1-a |
$4$ |
$6$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{21} \) |
$4.96398$ |
$(-3a^2+2a+26), (-a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$171.6385696$ |
1.946420906 |
\( -\frac{10673253}{512} a^{2} - \frac{1947753}{128} a + \frac{12778407}{128} \) |
\( \bigl[a^{2} - a - 5\) , \( -1\) , \( a\) , \( -217770998369941 a^{2} - 716454625293577 a - 397157386302938\) , \( 6021978241354682111186 a^{2} + 19811977704701324754621 a + 10982514460656949601618\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-217770998369941a^{2}-716454625293577a-397157386302938\right){x}+6021978241354682111186a^{2}+19811977704701324754621a+10982514460656949601618$ |
4.1-a3 |
4.1-a |
$4$ |
$6$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{15} \) |
$4.96398$ |
$(-3a^2+2a+26), (-a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$171.6385696$ |
1.946420906 |
\( \frac{85049425377}{64} a^{2} + 4371875802 a + \frac{155102357421}{64} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 7\) , \( 0\) , \( -1006924413442368757474847151020 a^{2} - 3312726022894426474503962764731 a - 1836366969159230699112828905530\) , \( 1884131464290869016112233216388330927760689969 a^{2} + 6198689046551537188998768230619105410291660780 a + 3436163370742819718462286668834470197043262244\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a^{2}-2a-7\right){x}^{2}+\left(-1006924413442368757474847151020a^{2}-3312726022894426474503962764731a-1836366969159230699112828905530\right){x}+1884131464290869016112233216388330927760689969a^{2}+6198689046551537188998768230619105410291660780a+3436163370742819718462286668834470197043262244$ |
4.1-a4 |
4.1-a |
$4$ |
$6$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{15} \) |
$4.96398$ |
$(-3a^2+2a+26), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$57.21285653$ |
1.946420906 |
\( -\frac{2046141}{512} a^{2} + \frac{748683}{256} a + \frac{17564337}{512} \) |
\( \bigl[1\) , \( a^{2} - 7\) , \( 0\) , \( 2 a^{2} - 7 a + 7\) , \( -43 a^{2} + 114 a + 93\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a^{2}-7\right){x}^{2}+\left(2a^{2}-7a+7\right){x}-43a^{2}+114a+93$ |
6.1-a1 |
6.1-a |
$2$ |
$2$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{5} \cdot 3^{12} \) |
$5.31103$ |
$(-3a^2+2a+26), (-2a^2+2a+15)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.721419213$ |
$54.85740217$ |
3.212661820 |
\( \frac{1009712101}{2592} a^{2} + \frac{1659422365}{1296} a + \frac{1838042951}{2592} \) |
\( \bigl[a + 1\) , \( a^{2} - 2 a - 5\) , \( a\) , \( 6202 a^{2} - 4380 a - 52721\) , \( 1094753 a^{2} - 772591 a - 9307539\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(6202a^{2}-4380a-52721\right){x}+1094753a^{2}-772591a-9307539$ |
6.1-a2 |
6.1-a |
$2$ |
$2$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{10} \cdot 3^{6} \) |
$5.31103$ |
$(-3a^2+2a+26), (-2a^2+2a+15)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.860709606$ |
$54.85740217$ |
3.212661820 |
\( -\frac{1381115581}{9216} a^{2} + \frac{484148299}{4608} a + \frac{11741611249}{9216} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a^{2} - 6\) , \( 60 a^{2} - 45 a - 510\) , \( 525 a^{2} - 372 a - 4464\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(60a^{2}-45a-510\right){x}+525a^{2}-372a-4464$ |
6.1-b1 |
6.1-b |
$2$ |
$2$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{5} \cdot 3^{9} \) |
$5.31103$ |
$(-3a^2+2a+26), (-2a^2+2a+15)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 5 \) |
$1$ |
$46.49855821$ |
1.318260895 |
\( \frac{76429079873}{288} a^{2} + \frac{377082124043}{432} a + \frac{418039251025}{864} \) |
\( \bigl[a^{2} - a - 5\) , \( a^{2} - 2 a - 5\) , \( 1\) , \( 31 a^{2} - 29 a - 244\) , \( -122 a^{2} + 78 a + 1061\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+{y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(31a^{2}-29a-244\right){x}-122a^{2}+78a+1061$ |
6.1-b2 |
6.1-b |
$2$ |
$2$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{10} \cdot 3^{18} \) |
$5.31103$ |
$(-3a^2+2a+26), (-2a^2+2a+15)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$11.62463955$ |
1.318260895 |
\( -\frac{3628866533}{746496} a^{2} - \frac{3677616797}{373248} a + \frac{5118289081}{746496} \) |
\( \bigl[a^{2} - a - 5\) , \( 1\) , \( a + 1\) , \( -867 a^{2} - 2853 a - 1574\) , \( -48850 a^{2} - 160718 a - 89089\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-867a^{2}-2853a-1574\right){x}-48850a^{2}-160718a-89089$ |
6.1-c1 |
6.1-c |
$2$ |
$2$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{2} \cdot 3^{7} \) |
$5.31103$ |
$(-3a^2+2a+26), (-2a^2+2a+15)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$50.15209300$ |
2.274945136 |
\( -\frac{22809932069}{108} a^{2} - \frac{963145781}{6} a + \frac{101308492627}{36} \) |
\( \bigl[a + 1\) , \( a^{2} - a - 5\) , \( a^{2} - a - 5\) , \( -416 a^{2} + 1163 a + 688\) , \( 12248 a^{2} - 31138 a - 30115\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-416a^{2}+1163a+688\right){x}+12248a^{2}-31138a-30115$ |
6.1-c2 |
6.1-c |
$2$ |
$2$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{4} \cdot 3^{14} \) |
$5.31103$ |
$(-3a^2+2a+26), (-2a^2+2a+15)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$50.15209300$ |
2.274945136 |
\( -\frac{42394279}{3888} a^{2} + \frac{29378545}{1944} a + \frac{90678529}{1296} \) |
\( \bigl[a + 1\) , \( -a^{2} + 7\) , \( 1\) , \( -183 a^{2} + 469 a + 436\) , \( 3123 a^{2} - 8073 a - 7243\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+7\right){x}^{2}+\left(-183a^{2}+469a+436\right){x}+3123a^{2}-8073a-7243$ |
6.1-d1 |
6.1-d |
$2$ |
$2$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2 \cdot 3^{3} \) |
$5.31103$ |
$(-3a^2+2a+26), (-2a^2+2a+15)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.474132231$ |
$144.9087415$ |
1.168711177 |
\( \frac{39017}{6} a^{2} + \frac{10993}{3} a + \frac{9097}{6} \) |
\( \bigl[a^{2} - a - 5\) , \( -a^{2} + a + 7\) , \( a\) , \( -95 a^{2} - 301 a - 137\) , \( -1657 a^{2} - 5434 a - 2979\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+7\right){x}^{2}+\left(-95a^{2}-301a-137\right){x}-1657a^{2}-5434a-2979$ |
6.1-d2 |
6.1-d |
$2$ |
$2$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{2} \cdot 3^{6} \) |
$5.31103$ |
$(-3a^2+2a+26), (-2a^2+2a+15)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.237066115$ |
$72.45437079$ |
1.168711177 |
\( -\frac{7541881}{36} a^{2} + \frac{2661215}{18} a + \frac{64120777}{36} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -5109504516258932 a^{2} - 16809989259512917 a - 9318400862235969\) , \( -20393612336764953601823914 a^{2} - 67093864630672974206954208 a - 37192619006070817754693943\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-5109504516258932a^{2}-16809989259512917a-9318400862235969\right){x}-20393612336764953601823914a^{2}-67093864630672974206954208a-37192619006070817754693943$ |
6.2-a1 |
6.2-a |
$1$ |
$1$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{15} \cdot 3^{2} \) |
$5.31103$ |
$(-a-1), (-2a^2+2a+15)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
|
\( 2 \) |
$1$ |
$6.891566669$ |
3.856324815 |
\( -\frac{353799541}{768} a^{2} + \frac{1155564799}{768} a + \frac{164187617}{128} \) |
\( \bigl[a^{2} - 6\) , \( -a^{2} + 5\) , \( 1\) , \( -27 a^{2} + 50 a + 100\) , \( -107 a^{2} + 248 a + 293\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-27a^{2}+50a+100\right){x}-107a^{2}+248a+293$ |
6.2-b1 |
6.2-b |
$2$ |
$2$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{6} \cdot 3^{5} \) |
$5.31103$ |
$(-a-1), (-2a^2+2a+15)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$34.88184839$ |
1.186704581 |
\( -\frac{2703157}{72} a^{2} + \frac{470533}{18} a + \frac{1919035}{6} \) |
\( \bigl[a^{2} - a - 5\) , \( a + 1\) , \( a^{2} - 5\) , \( -2 a - 5\) , \( -3 a^{2} - 12 a - 10\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a-5\right){x}-3a^{2}-12a-10$ |
6.2-b2 |
6.2-b |
$2$ |
$2$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{3} \cdot 3^{10} \) |
$5.31103$ |
$(-a-1), (-2a^2+2a+15)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$34.88184839$ |
1.186704581 |
\( \frac{16991533}{324} a^{2} + \frac{18518821}{108} a + \frac{5119435}{54} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 5\) , \( a + 1\) , \( -3956835257113268 a^{2} - 13017770698133457 a - 7216233385112336\) , \( -463801046970715793981528 a^{2} - 1525879973942561257449161 a - 845851894688656146081076\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(-3956835257113268a^{2}-13017770698133457a-7216233385112336\right){x}-463801046970715793981528a^{2}-1525879973942561257449161a-845851894688656146081076$ |
6.2-c1 |
6.2-c |
$1$ |
$1$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2 \cdot 3^{2} \) |
$5.31103$ |
$(-a-1), (-2a^2+2a+15)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.019331256$ |
$338.4302165$ |
0.890291709 |
\( -\frac{3847}{6} a^{2} + \frac{12581}{6} a + 1819 \) |
\( \bigl[a\) , \( -a^{2} + a + 5\) , \( a + 1\) , \( -6 a^{2} + 3 a + 48\) , \( -117 a^{2} + 82 a + 992\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(-6a^{2}+3a+48\right){x}-117a^{2}+82a+992$ |
8.2-a1 |
8.2-a |
$2$ |
$3$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{11} \) |
$5.57188$ |
$(-3a^2+2a+26), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$3.779888221$ |
0.771566452 |
\( -\frac{58778299661}{4} a^{2} + \frac{195582353651}{4} a + \frac{83650133503}{2} \) |
\( \bigl[a\) , \( -a^{2} + 2 a + 7\) , \( a^{2} - 6\) , \( -20511 a^{2} - 67475 a - 37396\) , \( -5514583 a^{2} - 18142676 a - 10057161\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(-a^{2}+2a+7\right){x}^{2}+\left(-20511a^{2}-67475a-37396\right){x}-5514583a^{2}-18142676a-10057161$ |
8.2-a2 |
8.2-a |
$2$ |
$3$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{9} \) |
$5.57188$ |
$(-3a^2+2a+26), (-a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$102.0569819$ |
0.771566452 |
\( \frac{63369}{2} a^{2} - \frac{41559}{2} a - 270259 \) |
\( \bigl[a\) , \( -a^{2} + 2 a + 7\) , \( a^{2} - 6\) , \( -271 a^{2} - 890 a - 486\) , \( -6920 a^{2} - 22767 a - 12623\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(-a^{2}+2a+7\right){x}^{2}+\left(-271a^{2}-890a-486\right){x}-6920a^{2}-22767a-12623$ |
9.1-a1 |
9.1-a |
$2$ |
$2$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$5.68234$ |
$(-2a^2+2a+15)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$70.19494166$ |
1.592053607 |
\( -\frac{64055}{3} a^{2} + \frac{48578}{3} a + 177713 \) |
\( \bigl[a + 1\) , \( a^{2} - 7\) , \( a^{2} - 6\) , \( 163 a^{2} - 113 a - 1380\) , \( 1858 a^{2} - 1309 a - 15791\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(a^{2}-7\right){x}^{2}+\left(163a^{2}-113a-1380\right){x}+1858a^{2}-1309a-15791$ |
9.1-a2 |
9.1-a |
$2$ |
$2$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{7} \) |
$5.68234$ |
$(-2a^2+2a+15)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$140.3898833$ |
1.592053607 |
\( \frac{15098731}{3} a^{2} - 12920798 a - 11623261 \) |
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( 35538 a^{2} - 25080 a - 302145\) , \( -1342951 a^{2} + 947747 a + 11417714\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(35538a^{2}-25080a-302145\right){x}-1342951a^{2}+947747a+11417714$ |
9.1-b1 |
9.1-b |
$2$ |
$3$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{3} \) |
$5.68234$ |
$(-2a^2+2a+15)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$0.416735560$ |
$49.62331419$ |
2.814164287 |
\( 0 \) |
\( \bigl[0\) , \( a^{2} - 6\) , \( a^{2} - a - 5\) , \( -a^{2} + 2 a + 12\) , \( -28672910668821 a^{2} - 94332301468396 a - 52291895358739\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(-a^{2}+2a+12\right){x}-28672910668821a^{2}-94332301468396a-52291895358739$ |
9.1-b2 |
9.1-b |
$2$ |
$3$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{9} \) |
$5.68234$ |
$(-2a^2+2a+15)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1.250206682$ |
$148.8699425$ |
2.814164287 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a^{2} - a - 5\) , \( 0\) , \( 624 a^{2} - 1612 a - 1452\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){y}={x}^{3}+624a^{2}-1612a-1452$ |
12.1-a1 |
12.1-a |
$2$ |
$2$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{23} \cdot 3 \) |
$5.96143$ |
$(-3a^2+2a+26), (-a-1), (-2a^2+2a+15)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$138.8161158$ |
1.574206721 |
\( \frac{146111893}{6144} a^{2} + \frac{20396641}{256} a + \frac{25220869}{512} \) |
\( \bigl[a^{2} - a - 5\) , \( 0\) , \( a^{2} - a - 5\) , \( -3 a^{2} + 5 a + 2\) , \( -a^{2} + 5 a + 2\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(-3a^{2}+5a+2\right){x}-a^{2}+5a+2$ |
12.1-a2 |
12.1-a |
$2$ |
$2$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{13} \cdot 3^{2} \) |
$5.96143$ |
$(-3a^2+2a+26), (-a-1), (-2a^2+2a+15)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$69.40805792$ |
1.574206721 |
\( \frac{2639524566797}{192} a^{2} + \frac{8683884393071}{192} a + \frac{802299748845}{32} \) |
\( \bigl[1\) , \( -a^{2} + 2 a + 6\) , \( a^{2} - 5\) , \( -2294897506704391 a^{2} - 7550086768027373 a - 4185293277884018\) , \( 205003296624088788835138 a^{2} + 674449587714394439434902 a + 373872435173382964924814\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a^{2}+2a+6\right){x}^{2}+\left(-2294897506704391a^{2}-7550086768027373a-4185293277884018\right){x}+205003296624088788835138a^{2}+674449587714394439434902a+373872435173382964924814$ |
12.1-b1 |
12.1-b |
$4$ |
$10$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{3} \cdot 3^{2} \) |
$5.96143$ |
$(-3a^2+2a+26), (-a-1), (-2a^2+2a+15)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$625$ |
\( 2^{2} \) |
$1$ |
$0.412859420$ |
5.852401135 |
\( \frac{16184521736620385304712519}{12} a^{2} + \frac{13311546926772227307496871}{3} a + \frac{9838779267506647842677949}{4} \) |
\( \bigl[1\) , \( a^{2} - 6\) , \( a^{2} - 6\) , \( -6710 a^{2} - 17794 a - 9204\) , \( -897954 a^{2} - 2805435 a - 1532646\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(-6710a^{2}-17794a-9204\right){x}-897954a^{2}-2805435a-1532646$ |
12.1-b2 |
12.1-b |
$4$ |
$10$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{15} \cdot 3^{10} \) |
$5.96143$ |
$(-3a^2+2a+26), (-a-1), (-2a^2+2a+15)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2^{2} \cdot 5^{3} \) |
$1$ |
$51.60742758$ |
5.852401135 |
\( \frac{494523427}{82944} a^{2} + \frac{226580089}{13824} a + \frac{226948955}{27648} \) |
\( \bigl[1\) , \( a^{2} - 6\) , \( a\) , \( -85473127070922247 a^{2} - 281201894130270986 a - 155880645268290402\) , \( -46278311918684132994141889 a^{2} - 152253104743521801945372522 a - 84399546044757345078054456\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(-85473127070922247a^{2}-281201894130270986a-155880645268290402\right){x}-46278311918684132994141889a^{2}-152253104743521801945372522a-84399546044757345078054456$ |
12.1-b3 |
12.1-b |
$4$ |
$10$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{3} \cdot 3 \) |
$5.96143$ |
$(-3a^2+2a+26), (-a-1), (-2a^2+2a+15)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$625$ |
\( 2 \) |
$1$ |
$0.825718841$ |
5.852401135 |
\( \frac{41730662325679724996}{3} a^{2} - 35947145039985187499 a - \frac{64592911042188335977}{2} \) |
\( \bigl[1\) , \( -a^{2} + 2 a + 6\) , \( a^{2} - 6\) , \( 9847 a^{2} - 6400 a - 85528\) , \( 1085139 a^{2} - 754756 a - 9262162\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(-a^{2}+2a+6\right){x}^{2}+\left(9847a^{2}-6400a-85528\right){x}+1085139a^{2}-754756a-9262162$ |
12.1-b4 |
12.1-b |
$4$ |
$10$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{15} \cdot 3^{5} \) |
$5.96143$ |
$(-3a^2+2a+26), (-a-1), (-2a^2+2a+15)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2 \cdot 5^{3} \) |
$1$ |
$103.2148551$ |
5.852401135 |
\( -\frac{1069192}{9} a^{2} + \frac{11832265}{144} a + \frac{32555703}{32} \) |
\( \bigl[1\) , \( -a^{2} + 2 a + 6\) , \( a\) , \( -1259538616049 a^{2} - 4143812876643 a - 2297069253670\) , \( 663954254276661137 a^{2} + 2184373034152922082 a + 1210879034522678072\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+2a+6\right){x}^{2}+\left(-1259538616049a^{2}-4143812876643a-2297069253670\right){x}+663954254276661137a^{2}+2184373034152922082a+1210879034522678072$ |
12.1-c1 |
12.1-c |
$4$ |
$4$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{7} \cdot 3^{2} \) |
$5.96143$ |
$(-3a^2+2a+26), (-a-1), (-2a^2+2a+15)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$29.80100010$ |
1.351800816 |
\( \frac{6998798261}{48} a^{2} + \frac{11370994855}{24} a + \frac{4187897905}{16} \) |
\( \bigl[a^{2} - a - 5\) , \( a^{2} - a - 5\) , \( a + 1\) , \( -347404375329118258220673200 a^{2} - 1142941316404999119800930528 a - 633574786030652157786143931\) , \( -12074487978785798479663421898723743100387 a^{2} - 39724402354794039332537054051236896704841 a - 22020710390712483323594717684921333526321\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-347404375329118258220673200a^{2}-1142941316404999119800930528a-633574786030652157786143931\right){x}-12074487978785798479663421898723743100387a^{2}-39724402354794039332537054051236896704841a-22020710390712483323594717684921333526321$ |
12.1-c2 |
12.1-c |
$4$ |
$4$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{8} \) |
$5.96143$ |
$(-3a^2+2a+26), (-a-1), (-2a^2+2a+15)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$119.2040004$ |
1.351800816 |
\( -\frac{647674159168159}{108} a^{2} + \frac{457076373981485}{108} a + \frac{458874971626321}{9} \) |
\( \bigl[a^{2} - a - 5\) , \( -a^{2} + 7\) , \( 1\) , \( 58 a^{2} - 57 a - 529\) , \( -339 a^{2} + 276 a + 2981\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+7\right){x}^{2}+\left(58a^{2}-57a-529\right){x}-339a^{2}+276a+2981$ |
12.1-c3 |
12.1-c |
$4$ |
$4$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{4} \) |
$5.96143$ |
$(-3a^2+2a+26), (-a-1), (-2a^2+2a+15)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$119.2040004$ |
1.351800816 |
\( -\frac{64156363}{72} a^{2} + \frac{1276373}{2} a + \frac{91248649}{12} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 5\) , \( a^{2} - a - 5\) , \( -75546347735 a^{2} - 248543335270 a - 137776794135\) , \( -38149267306879982 a^{2} - 125508994393937333 a - 69574293208841919\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(-75546347735a^{2}-248543335270a-137776794135\right){x}-38149267306879982a^{2}-125508994393937333a-69574293208841919$ |
12.1-c4 |
12.1-c |
$4$ |
$4$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{13} \cdot 3^{2} \) |
$5.96143$ |
$(-3a^2+2a+26), (-a-1), (-2a^2+2a+15)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$59.60200020$ |
1.351800816 |
\( -\frac{76301}{192} a^{2} + \frac{16577}{96} a + \frac{14933}{4} \) |
\( \bigl[1\) , \( -a^{2} + 2 a + 7\) , \( a^{2} - a - 5\) , \( -27931 a^{2} - 91888 a - 50925\) , \( -2783901290 a^{2} - 9158882355 a - 5077108371\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(-a^{2}+2a+7\right){x}^{2}+\left(-27931a^{2}-91888a-50925\right){x}-2783901290a^{2}-9158882355a-5077108371$ |
12.1-d1 |
12.1-d |
$2$ |
$2$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{15} \cdot 3 \) |
$5.96143$ |
$(-3a^2+2a+26), (-a-1), (-2a^2+2a+15)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$65.40453581$ |
1.483404996 |
\( -\frac{768619325}{6144} a^{2} + \frac{90051225}{1024} a + \frac{2185834619}{2048} \) |
\( \bigl[1\) , \( -a + 1\) , \( a^{2} - a - 6\) , \( 35 a^{2} - 25 a - 296\) , \( 244 a^{2} - 172 a - 2076\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(35a^{2}-25a-296\right){x}+244a^{2}-172a-2076$ |
12.1-d2 |
12.1-d |
$2$ |
$2$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{24} \cdot 3^{2} \) |
$5.96143$ |
$(-3a^2+2a+26), (-a-1), (-2a^2+2a+15)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$32.70226790$ |
1.483404996 |
\( -\frac{2018446775}{12582912} a^{2} + \frac{1340944225}{6291456} a + \frac{9108295537}{4194304} \) |
\( \bigl[1\) , \( -a^{2} + a + 7\) , \( a\) , \( 36 a^{2} + 121 a + 80\) , \( -309 a^{2} - 1006 a - 548\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+7\right){x}^{2}+\left(36a^{2}+121a+80\right){x}-309a^{2}-1006a-548$ |
12.1-e1 |
12.1-e |
$6$ |
$8$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{10} \cdot 3 \) |
$5.96143$ |
$(-3a^2+2a+26), (-a-1), (-2a^2+2a+15)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.416675358$ |
$166.1274189$ |
4.709906214 |
\( -\frac{57245}{48} a^{2} + \frac{8421}{8} a + \frac{37821}{4} \) |
\( \bigl[a^{2} - a - 5\) , \( 0\) , \( a\) , \( 31 a^{2} + 97 a + 56\) , \( 4139 a^{2} + 13617 a + 7550\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+a{y}={x}^{3}+\left(31a^{2}+97a+56\right){x}+4139a^{2}+13617a+7550$ |
12.1-e2 |
12.1-e |
$6$ |
$8$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{5} \cdot 3^{2} \) |
$5.96143$ |
$(-3a^2+2a+26), (-a-1), (-2a^2+2a+15)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$0.208337679$ |
$41.53185472$ |
4.709906214 |
\( -\frac{5452410859290587}{16} a^{2} + \frac{5771810163916667}{24} a + \frac{46356177925189551}{16} \) |
\( \bigl[a^{2} - a - 5\) , \( -a^{2} + 2 a + 6\) , \( a^{2} - a - 6\) , \( -3664840166293531837563809269636963 a^{2} - 12057122884849178653144118993066663 a - 6683710652740722962184684630890178\) , \( -413649434581843010324207353650138931409862234660605 a^{2} - 1360883923362402878028234381723354872699439498525453 a - 754388460878215526855971731397996299899972144451090\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(-a^{2}+2a+6\right){x}^{2}+\left(-3664840166293531837563809269636963a^{2}-12057122884849178653144118993066663a-6683710652740722962184684630890178\right){x}-413649434581843010324207353650138931409862234660605a^{2}-1360883923362402878028234381723354872699439498525453a-754388460878215526855971731397996299899972144451090$ |
12.1-e3 |
12.1-e |
$6$ |
$8$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{10} \cdot 3^{4} \) |
$5.96143$ |
$(-3a^2+2a+26), (-a-1), (-2a^2+2a+15)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.104168839$ |
$166.1274189$ |
4.709906214 |
\( -\frac{15523784237}{2304} a^{2} + \frac{608646083}{128} a + \frac{14665485529}{256} \) |
\( \bigl[a^{2} - a - 5\) , \( -a^{2} + 2 a + 6\) , \( a^{2} - a - 6\) , \( -252189437489532536778178060104948 a^{2} - 829689399837456347168231159293778 a - 459927623954794829960401271739048\) , \( -5078266729818194753975568824085809010815544505500 a^{2} - 16707218657610362000303523401272285242191238359148 a - 9261431303802769478366298996640935599948849175576\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(-a^{2}+2a+6\right){x}^{2}+\left(-252189437489532536778178060104948a^{2}-829689399837456347168231159293778a-459927623954794829960401271739048\right){x}-5078266729818194753975568824085809010815544505500a^{2}-16707218657610362000303523401272285242191238359148a-9261431303802769478366298996640935599948849175576$ |
12.1-e4 |
12.1-e |
$6$ |
$8$ |
3.3.1944.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{17} \cdot 3^{8} \) |
$5.96143$ |
$(-3a^2+2a+26), (-a-1), (-2a^2+2a+15)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$0.052084419$ |
$41.53185472$ |
4.709906214 |
\( \frac{193662881}{196608} a^{2} - \frac{643032383}{884736} a - \frac{1454578277}{196608} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 202544683240975370990697160340396413815720182825 a^{2} + 666360884703776169648281762246055024666627948740 a + 369388566924278564262178168101928600000554151712\) , \( -168397529837671466434733724449937883381471079415463301527293507612836752 a^{2} - 554018625268264680355188822323649608591076583177245802948875686064213689 a - 307113083518066053761780487309983653315699133354868219939217389954841870\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(202544683240975370990697160340396413815720182825a^{2}+666360884703776169648281762246055024666627948740a+369388566924278564262178168101928600000554151712\right){x}-168397529837671466434733724449937883381471079415463301527293507612836752a^{2}-554018625268264680355188822323649608591076583177245802948875686064213689a-307113083518066053761780487309983653315699133354868219939217389954841870$ |
*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.