| 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 |
$4$ |
$6$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{6} \) |
$2.17218$ |
$(a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \cdot 3 \) |
$1$ |
$1.773507123$ |
1.105554824 |
\( -\frac{2566132861253}{64} a^{2} + \frac{2520228955985}{64} a + \frac{17449596177405}{64} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} - 4\) , \( a^{2} - 4\) , \( -103096 a^{2} - 274089 a - 110298\) , \( -63392506 a^{2} - 119266092 a + 38807148\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-103096a^{2}-274089a-110298\right){x}-63392506a^{2}-119266092a+38807148$ |
| 2.1-a2 |
2.1-a |
$4$ |
$6$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{18} \) |
$2.17218$ |
$(a-2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$47.88469232$ |
1.105554824 |
\( -\frac{195962533}{262144} a^{2} + \frac{398930673}{262144} a + \frac{1725009309}{262144} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} - 4\) , \( a^{2} - 4\) , \( -1341 a^{2} - 3539 a - 1378\) , \( -81027 a^{2} - 151064 a + 52588\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-1341a^{2}-3539a-1378\right){x}-81027a^{2}-151064a+52588$ |
| 2.1-a3 |
2.1-a |
$4$ |
$6$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{3} \) |
$2.17218$ |
$(a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 3 \) |
$1$ |
$3.547014246$ |
1.105554824 |
\( \frac{87555872470048749}{8} a^{2} - \frac{277048488967881345}{8} a + \frac{161822258750058731}{8} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a^{2} + a - 3\) , \( 422 a^{2} - 52 a - 2297\) , \( 7747 a^{2} - 1447 a - 40849\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(422a^{2}-52a-2297\right){x}+7747a^{2}-1447a-40849$ |
| 2.1-a4 |
2.1-a |
$4$ |
$6$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{9} \) |
$2.17218$ |
$(a-2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$95.76938464$ |
1.105554824 |
\( \frac{19279053}{512} a^{2} - \frac{63659385}{512} a + \frac{42176123}{512} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a^{2} + a - 3\) , \( 22 a^{2} - 7 a - 117\) , \( -78 a^{2} + 17 a + 399\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(22a^{2}-7a-117\right){x}-78a^{2}+17a+399$ |
| 2.1-b1 |
2.1-b |
$8$ |
$12$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{9} \) |
$2.17218$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$1.571679326$ |
$11.21959465$ |
0.610683167 |
\( -\frac{2638200006150459}{512} a^{2} + \frac{599226037309295}{512} a + \frac{13654121353016131}{512} \) |
\( \bigl[a^{2} - 3\) , \( 0\) , \( a + 1\) , \( 26 a^{2} + 35 a - 46\) , \( -179 a^{2} - 252 a + 292\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(26a^{2}+35a-46\right){x}-179a^{2}-252a+292$ |
| 2.1-b2 |
2.1-b |
$8$ |
$12$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{3} \) |
$2.17218$ |
$(a-2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$0.523893108$ |
$302.9290556$ |
0.610683167 |
\( -\frac{45043}{8} a^{2} - \frac{8369}{8} a + \frac{271715}{8} \) |
\( \bigl[a^{2} - 3\) , \( 0\) , \( a + 1\) , \( -4 a^{2} - 5 a + 9\) , \( 8 a^{2} + 11 a - 14\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-4a^{2}-5a+9\right){x}+8a^{2}+11a-14$ |
| 2.1-b3 |
2.1-b |
$8$ |
$12$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{6} \) |
$2.17218$ |
$(a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2 \) |
$1.047786217$ |
$302.9290556$ |
0.610683167 |
\( \frac{15697899}{64} a^{2} + \frac{21764449}{64} a - \frac{26004979}{64} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -39839206 a^{2} - 55431570 a + 66637951\) , \( 262729290191 a^{2} + 365556905248 a - 439460108627\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-39839206a^{2}-55431570a+66637951\right){x}+262729290191a^{2}+365556905248a-439460108627$ |
| 2.1-b4 |
2.1-b |
$8$ |
$12$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{18} \) |
$2.17218$ |
$(a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2 \) |
$3.143358652$ |
$11.21959465$ |
0.610683167 |
\( \frac{3785170722522539}{262144} a^{2} - \frac{11978019650270751}{262144} a + \frac{6997733838897613}{262144} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -124243571 a^{2} - 172870340 a + 207818776\) , \( -1136903010696 a^{2} - 1581866817636 a + 1901666617296\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-124243571a^{2}-172870340a+207818776\right){x}-1136903010696a^{2}-1581866817636a+1901666617296$ |
| 2.1-b5 |
2.1-b |
$8$ |
$12$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{3} \) |
$2.17218$ |
$(a-2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$2.095572434$ |
$75.73226392$ |
0.610683167 |
\( \frac{3550019059843}{8} a^{2} + \frac{4939342938081}{8} a - \frac{5937949567651}{8} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -637342746 a^{2} - 886787465 a + 1066065811\) , \( 16817357805569 a^{2} + 23399375339435 a - 28129935123351\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-637342746a^{2}-886787465a+1066065811\right){x}+16817357805569a^{2}+23399375339435a-28129935123351$ |
| 2.1-b6 |
2.1-b |
$8$ |
$12$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{9} \) |
$2.17218$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$6.286717304$ |
$2.804898663$ |
0.610683167 |
\( \frac{1428541495842676867841339}{512} a^{2} - \frac{4520259483225056660735855}{512} a + \frac{2640254788661664235572413}{512} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -647652436 a^{2} - 901132210 a + 1083310496\) , \( 16245186149495 a^{2} + 22603265778390 a - 27172879220296\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-647652436a^{2}-901132210a+1083310496\right){x}+16245186149495a^{2}+22603265778390a-27172879220296$ |
| 2.1-b7 |
2.1-b |
$8$ |
$12$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{12} \) |
$2.17218$ |
$(a-2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$0.523893108$ |
$151.4645278$ |
0.610683167 |
\( -\frac{4062829301}{4096} a^{2} + \frac{924537857}{4096} a + \frac{21032423789}{4096} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a^{2} + a - 4\) , \( -31739420781552 a^{2} - 44161670847006 a + 53089662345040\) , \( 89855360614175766264 a^{2} + 125023165563799963220 a - 150298607770907612816\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-31739420781552a^{2}-44161670847006a+53089662345040\right){x}+89855360614175766264a^{2}+125023165563799963220a-150298607770907612816$ |
| 2.1-b8 |
2.1-b |
$8$ |
$12$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{36} \) |
$2.17218$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1.571679326$ |
$5.609797327$ |
0.610683167 |
\( \frac{126298630830047115}{68719476736} a^{2} + \frac{186068400402473857}{68719476736} a - \frac{219036311909610771}{68719476736} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a^{2} + a - 4\) , \( -1261075170815467 a^{2} - 1754637773324056 a + 2109365998560825\) , \( -46802088315244943983637 a^{2} - 65119601058563177515985 a + 78284574971063377749745\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1261075170815467a^{2}-1754637773324056a+2109365998560825\right){x}-46802088315244943983637a^{2}-65119601058563177515985a+78284574971063377749745$ |
| 4.1-a1 |
4.1-a |
$2$ |
$3$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{18} \) |
$2.43819$ |
$(-a^2-a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3^{2} \) |
$1$ |
$2.118197412$ |
0.880283418 |
\( -\frac{57920003315}{512} a^{2} - \frac{81656123603}{512} a + \frac{23642311639}{128} \) |
\( \bigl[a^{2} + a - 4\) , \( a + 1\) , \( a + 1\) , \( -41 a^{2} + 136 a - 79\) , \( -446 a^{2} + 1424 a - 843\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-41a^{2}+136a-79\right){x}-446a^{2}+1424a-843$ |
| 4.1-a2 |
4.1-a |
$2$ |
$3$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{6} \) |
$2.43819$ |
$(-a^2-a+3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$57.19133013$ |
0.880283418 |
\( \frac{463}{8} a^{2} - \frac{1693}{4} a + 295 \) |
\( \bigl[a^{2} + a - 4\) , \( a + 1\) , \( a + 1\) , \( 4 a^{2} - 9 a + 11\) , \( 5 a^{2} - 8 a + 4\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4a^{2}-9a+11\right){x}+5a^{2}-8a+4$ |
| 7.1-a1 |
7.1-a |
$6$ |
$8$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$2.67655$ |
$(-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.738720075$ |
$230.9931969$ |
0.738692936 |
\( \frac{87016}{7} a^{2} + 13640 a - \frac{112985}{7} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + a + 3\) , \( 1\) , \( -22048798 a^{2} - 30678314 a + 36880414\) , \( -107145951093 a^{2} - 149080988513 a + 179220106248\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-22048798a^{2}-30678314a+36880414\right){x}-107145951093a^{2}-149080988513a+179220106248$ |
| 7.1-a2 |
7.1-a |
$6$ |
$8$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{8} \) |
$2.67655$ |
$(-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.954880303$ |
$3.609268702$ |
0.738692936 |
\( -\frac{9113207144642}{2401} a^{2} + \frac{2059007400572}{2401} a + \frac{47191705315541}{2401} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + a + 3\) , \( 1\) , \( -350835118 a^{2} - 488146864 a + 586830024\) , \( -6936875514689 a^{2} - 9651846392309 a + 11603122175894\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-350835118a^{2}-488146864a+586830024\right){x}-6936875514689a^{2}-9651846392309a+11603122175894$ |
| 7.1-a3 |
7.1-a |
$6$ |
$8$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
7.1 |
\( 7 \) |
\( 7^{4} \) |
$2.67655$ |
$(-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1.477440151$ |
$28.87414961$ |
0.738692936 |
\( \frac{50090737860}{49} a^{2} + \frac{69697535020}{49} a - \frac{11968637521}{7} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + a + 3\) , \( 1\) , \( -351808163 a^{2} - 489499744 a + 588459769\) , \( -6896854751303 a^{2} - 9596162183191 a + 11536180590058\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-351808163a^{2}-489499744a+588459769\right){x}-6896854751303a^{2}-9596162183191a+11536180590058$ |
| 7.1-a4 |
7.1-a |
$6$ |
$8$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$2.67655$ |
$(-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.954880303$ |
$3.609268702$ |
0.738692936 |
\( \frac{53939902008122540558}{7} a^{2} + 10721575609579864068 a - \frac{90223801003153618691}{7} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + a + 3\) , \( 1\) , \( -5628931048 a^{2} - 7831995504 a + 9415359194\) , \( -441390174720877 a^{2} - 614142512091065 a + 738301290993602\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-5628931048a^{2}-7831995504a+9415359194\right){x}-441390174720877a^{2}-614142512091065a+738301290993602$ |
| 7.1-a5 |
7.1-a |
$6$ |
$8$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
7.1 |
\( 7 \) |
\( -7 \) |
$2.67655$ |
$(-a-1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.369360037$ |
$230.9931969$ |
0.738692936 |
\( \frac{71944646}{7} a^{2} - \frac{230432910}{7} a + \frac{139622639}{7} \) |
\( \bigl[1\) , \( a^{2} - a - 4\) , \( 0\) , \( -3120362905077 a^{2} - 4341617968279 a + 5219345812838\) , \( -150967313133907537481 a^{2} - 210053259545706912107 a + 252518901797844589295\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-3120362905077a^{2}-4341617968279a+5219345812838\right){x}-150967313133907537481a^{2}-210053259545706912107a+252518901797844589295$ |
| 7.1-a6 |
7.1-a |
$6$ |
$8$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
7.1 |
\( 7 \) |
\( 7 \) |
$2.67655$ |
$(-a-1)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.477440151$ |
$230.9931969$ |
0.738692936 |
\( -\frac{466}{7} a^{2} + \frac{3018}{7} a + \frac{9385}{7} \) |
\( \bigl[a + 1\) , \( a^{2} - 3\) , \( a^{2} + a - 3\) , \( -4 a^{2} - 5 a + 9\) , \( -4 a^{2} - 6 a + 6\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-4a^{2}-5a+9\right){x}-4a^{2}-6a+6$ |
| 7.2-a1 |
7.2-a |
$6$ |
$8$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
7.2 |
\( 7 \) |
\( 7^{8} \) |
$2.67655$ |
$(a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$13.22259432$ |
1.221125352 |
\( \frac{379627388720297}{5764801} a^{2} - \frac{1201241202298038}{5764801} a + \frac{701648219248183}{5764801} \) |
\( \bigl[a^{2} - 3\) , \( -1\) , \( 0\) , \( -36901254179 a^{2} - 51343754763 a + 61723720371\) , \( -1644108121682679015 a^{2} - 2287583072361444580 a + 2750054754938733386\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}={x}^{3}-{x}^{2}+\left(-36901254179a^{2}-51343754763a+61723720371\right){x}-1644108121682679015a^{2}-2287583072361444580a+2750054754938733386$ |
| 7.2-a2 |
7.2-a |
$6$ |
$8$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
7.2 |
\( 7 \) |
\( 7^{4} \) |
$2.67655$ |
$(a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$105.7807546$ |
1.221125352 |
\( \frac{24278860}{2401} a^{2} + \frac{10345889}{2401} a - \frac{18256787}{2401} \) |
\( \bigl[a^{2} - 3\) , \( -1\) , \( 0\) , \( -685003668919 a^{2} - 953102035633 a + 1145786929646\) , \( -584024357944136171 a^{2} - 812601201502745541 a + 976881593967514859\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}={x}^{3}-{x}^{2}+\left(-685003668919a^{2}-953102035633a+1145786929646\right){x}-584024357944136171a^{2}-812601201502745541a+976881593967514859$ |
| 7.2-a3 |
7.2-a |
$6$ |
$8$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{2} \) |
$2.67655$ |
$(a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$52.89037730$ |
1.221125352 |
\( \frac{23744567927}{49} a^{2} + \frac{33045694086}{49} a - \frac{39699747847}{49} \) |
\( \bigl[1\) , \( a^{2} - a - 5\) , \( a\) , \( -7373394084755779081 a^{2} - 10259210614977302471 a + 12333274919940666507\) , \( -20925797775912875958319841484 a^{2} - 29115786326050467524762038826 a + 35002010461233182563243519828\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-7373394084755779081a^{2}-10259210614977302471a+12333274919940666507\right){x}-20925797775912875958319841484a^{2}-29115786326050467524762038826a+35002010461233182563243519828$ |
| 7.2-a4 |
7.2-a |
$6$ |
$8$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
7.2 |
\( 7 \) |
\( -7 \) |
$2.67655$ |
$(a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$105.7807546$ |
1.221125352 |
\( \frac{1816}{7} a^{2} + \frac{167}{7} a - \frac{1453}{7} \) |
\( \bigl[1\) , \( -a^{2} + a + 4\) , \( a + 1\) , \( -a^{2} - a + 7\) , \( -a^{2} + 3\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-a^{2}-a+7\right){x}-a^{2}+3$ |
| 7.2-a5 |
7.2-a |
$6$ |
$8$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
7.2 |
\( 7 \) |
\( 7^{2} \) |
$2.67655$ |
$(a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$211.5615092$ |
1.221125352 |
\( -\frac{1804911}{49} a^{2} + \frac{401794}{49} a + \frac{9469625}{49} \) |
\( \bigl[a + 1\) , \( a^{2} + a - 5\) , \( a\) , \( -127407 a^{2} - 177273 a + 213108\) , \( 22095235 a^{2} + 30742921 a - 36958097\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(-127407a^{2}-177273a+213108\right){x}+22095235a^{2}+30742921a-36958097$ |
| 7.2-a6 |
7.2-a |
$6$ |
$8$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
7.2 |
\( 7 \) |
\( 7 \) |
$2.67655$ |
$(a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$105.7807546$ |
1.221125352 |
\( -\frac{46049067004}{7} a^{2} + \frac{10454958081}{7} a + \frac{238351488253}{7} \) |
\( \bigl[a + 1\) , \( a^{2} + a - 5\) , \( a\) , \( -1721587 a^{2} - 2395413 a + 2879593\) , \( 2356298867 a^{2} + 3278512657 a - 3941316918\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(-1721587a^{2}-2395413a+2879593\right){x}+2356298867a^{2}+3278512657a-3941316918$ |
| 8.1-a1 |
8.1-a |
$4$ |
$6$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{45} \) |
$2.73678$ |
$(a-2), (-a^2-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$4.944282889$ |
1.027375970 |
\( -\frac{129988827807}{262144} a^{2} - \frac{181633809653}{262144} a + \frac{54745868153}{65536} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} + a - 4\) , \( a^{2} - 3\) , \( -15262 a^{2} + 48298 a - 28214\) , \( -2457210 a^{2} + 7775223 a - 4541460\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(-15262a^{2}+48298a-28214\right){x}-2457210a^{2}+7775223a-4541460$ |
| 8.1-a2 |
8.1-a |
$4$ |
$6$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{15} \) |
$2.73678$ |
$(a-2), (-a^2-a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$133.4956380$ |
1.027375970 |
\( -\frac{18975961}{32} a^{2} + \frac{4168565}{64} a + \frac{51767065}{16} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} + a - 4\) , \( a^{2} - 3\) , \( -3047 a^{2} + 9648 a - 5639\) , \( 237121 a^{2} - 750305 a + 438246\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(-3047a^{2}+9648a-5639\right){x}+237121a^{2}-750305a+438246$ |
| 8.1-a3 |
8.1-a |
$4$ |
$6$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{12} \) |
$2.73678$ |
$(a-2), (-a^2-a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$133.4956380$ |
1.027375970 |
\( \frac{478055871971}{64} a^{2} - \frac{1512686296287}{64} a + \frac{883550176349}{64} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + 4\) , \( a^{2} + a - 3\) , \( -4 a^{2} + 3 a + 4\) , \( a^{2} - 11 a + 10\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-4a^{2}+3a+4\right){x}+a^{2}-11a+10$ |
| 8.1-a4 |
8.1-a |
$4$ |
$6$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{36} \) |
$2.73678$ |
$(a-2), (-a^2-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$4.944282889$ |
1.027375970 |
\( \frac{475744153054367611}{262144} a^{2} + \frac{661942031829738833}{262144} a - \frac{795764251837207939}{262144} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + 4\) , \( a^{2} + a - 3\) , \( -59 a^{2} - 67 a + 109\) , \( -390 a^{2} - 554 a + 662\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-59a^{2}-67a+109\right){x}-390a^{2}-554a+662$ |
| 8.1-b1 |
8.1-b |
$4$ |
$10$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{22} \) |
$2.73678$ |
$(a-2), (-a^2-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$25$ |
\( 2^{2} \) |
$1$ |
$1.190612589$ |
1.374434530 |
\( -\frac{102860016434528804373261}{1024} a^{2} + \frac{11681526227262337408373}{512} a + \frac{66544572592563210222749}{128} \) |
\( \bigl[1\) , \( a^{2} - a - 4\) , \( a^{2} - 4\) , \( 574 a^{2} - 54 a - 3158\) , \( 11300 a^{2} - 1626 a - 60736\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(574a^{2}-54a-3158\right){x}+11300a^{2}-1626a-60736$ |
| 8.1-b2 |
8.1-b |
$4$ |
$10$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{14} \) |
$2.73678$ |
$(a-2), (-a^2-a+3)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$148.8265736$ |
1.374434530 |
\( \frac{30939135739}{1024} a^{2} + \frac{43053259985}{1024} a - \frac{51740206851}{1024} \) |
\( \bigl[1\) , \( a^{2} - a - 4\) , \( a^{2} - 4\) , \( -a^{2} + a + 2\) , \( 2 a^{2} - 5 a\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-a^{2}+a+2\right){x}+2a^{2}-5a$ |
| 8.1-b3 |
8.1-b |
$4$ |
$10$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{41} \) |
$2.73678$ |
$(a-2), (-a^2-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$25$ |
\( 2 \) |
$1$ |
$2.381225178$ |
1.374434530 |
\( -\frac{2409888790714557}{524288} a^{2} + \frac{1093848453484533}{1048576} a + \frac{6236774711946667}{262144} \) |
\( \bigl[1\) , \( -a^{2} + a + 4\) , \( a\) , \( -911559 a^{2} + 2884395 a - 1684751\) , \( -1224283759 a^{2} + 3873937359 a - 2262742149\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-911559a^{2}+2884395a-1684751\right){x}-1224283759a^{2}+3873937359a-2262742149$ |
| 8.1-b4 |
8.1-b |
$4$ |
$10$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{13} \) |
$2.73678$ |
$(a-2), (-a^2-a+3)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$297.6531473$ |
1.374434530 |
\( \frac{981903}{32} a^{2} - \frac{3482217}{32} a + \frac{2257835}{32} \) |
\( \bigl[1\) , \( -a^{2} + a + 4\) , \( a\) , \( -26864 a^{2} + 85000 a - 49641\) , \( 6210186 a^{2} - 19650571 a + 11477777\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-26864a^{2}+85000a-49641\right){x}+6210186a^{2}-19650571a+11477777$ |
| 8.2-a1 |
8.2-a |
$2$ |
$2$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{10} \) |
$2.73678$ |
$(a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$57.53567929$ |
1.328375410 |
\( -30942535 a^{2} + 7030797 a + 160150272 \) |
\( \bigl[a^{2} + a - 4\) , \( a^{2} - 4\) , \( a^{2} + a - 4\) , \( -213 a^{2} - 305 a + 337\) , \( -3562 a^{2} - 4967 a + 5934\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-213a^{2}-305a+337\right){x}-3562a^{2}-4967a+5934$ |
| 8.2-a2 |
8.2-a |
$2$ |
$2$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{11} \) |
$2.73678$ |
$(a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$115.0713585$ |
1.328375410 |
\( -429 a^{2} - 6543 a + 18202 \) |
\( \bigl[a\) , \( -a^{2} + a + 3\) , \( a\) , \( 0\) , \( -a - 4\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}-a-4$ |
| 11.1-a1 |
11.1-a |
$2$ |
$3$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
11.1 |
\( 11 \) |
\( 11^{3} \) |
$2.88596$ |
$(a^2-3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$0.325355384$ |
$252.3526576$ |
1.263741375 |
\( -\frac{967556}{1331} a^{2} + \frac{4496237}{1331} a - \frac{2914196}{1331} \) |
\( \bigl[a^{2} - 4\) , \( -1\) , \( 1\) , \( -3 a^{2} - 3 a + 7\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(-3a^{2}-3a+7\right){x}$ |
| 11.1-a2 |
11.1-a |
$2$ |
$3$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
11.1 |
\( 11 \) |
\( 11^{9} \) |
$2.88596$ |
$(a^2-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$0.976066152$ |
$9.346394726$ |
1.263741375 |
\( \frac{61835282694087819}{2357947691} a^{2} + \frac{86035147903815922}{2357947691} a - \frac{103429095791332024}{2357947691} \) |
\( \bigl[a^{2} - 4\) , \( -1\) , \( 1\) , \( -128 a^{2} - 178 a + 217\) , \( -1493 a^{2} - 2077 a + 2497\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(-128a^{2}-178a+217\right){x}-1493a^{2}-2077a+2497$ |
| 14.1-a1 |
14.1-a |
$2$ |
$2$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{2} \cdot 7^{5} \) |
$3.00432$ |
$(a-2), (a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$79.92868641$ |
1.845381908 |
\( -\frac{11964947}{67228} a^{2} + \frac{11957979}{67228} a + \frac{57392243}{67228} \) |
\( \bigl[1\) , \( -a^{2} + 5\) , \( a^{2} + a - 3\) , \( 6 a^{2} + 11 a - 4\) , \( -59 a^{2} - 81 a + 101\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(6a^{2}+11a-4\right){x}-59a^{2}-81a+101$ |
| 14.1-a2 |
14.1-a |
$2$ |
$2$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2 \cdot 7^{10} \) |
$3.00432$ |
$(a-2), (a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$79.92868641$ |
1.845381908 |
\( \frac{35888603105371}{564950498} a^{2} - \frac{112057680914945}{564950498} a + \frac{66962763894959}{564950498} \) |
\( \bigl[1\) , \( -a^{2} + 5\) , \( a^{2} + a - 3\) , \( -84 a^{2} - 114 a + 146\) , \( -669 a^{2} - 930 a + 1121\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-84a^{2}-114a+146\right){x}-669a^{2}-930a+1121$ |
| 14.2-a1 |
14.2-a |
$2$ |
$3$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
14.2 |
\( 2 \cdot 7 \) |
\( - 2^{9} \cdot 7^{9} \) |
$3.00432$ |
$(a-2), (-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3^{2} \) |
$1$ |
$2.777038401$ |
1.154085470 |
\( -\frac{2157224594899}{8605184} a^{2} + \frac{6840427066535}{8605184} a - \frac{4025231686117}{8605184} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{2} + a + 4\) , \( a + 1\) , \( 22 a^{2} + 7 a - 134\) , \( 177 a^{2} - 19 a - 956\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(22a^{2}+7a-134\right){x}+177a^{2}-19a-956$ |
| 14.2-a2 |
14.2-a |
$2$ |
$3$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
14.2 |
\( 2 \cdot 7 \) |
\( - 2^{3} \cdot 7^{3} \) |
$3.00432$ |
$(a-2), (-a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$74.98003682$ |
1.154085470 |
\( -\frac{90277}{392} a^{2} + \frac{50417}{392} a + \frac{538525}{392} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{2} + a + 4\) , \( a + 1\) , \( -3 a^{2} + 2 a + 21\) , \( -5 a^{2} + 4 a + 30\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-3a^{2}+2a+21\right){x}-5a^{2}+4a+30$ |
| 16.1-a1 |
16.1-a |
$1$ |
$1$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{10} \) |
$3.07193$ |
$(a-2), (-a^2-a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$30.37577428$ |
1.402622933 |
\( \frac{155923}{2} a^{2} - 17689 a - 403476 \) |
\( \bigl[a^{2} + a - 4\) , \( a^{2} - 4\) , \( a^{2} + a - 4\) , \( a^{2} + a - 4\) , \( a^{2} + 2 a - 4\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(a^{2}+a-4\right){x}+a^{2}+2a-4$ |
| 16.3-a1 |
16.3-a |
$4$ |
$6$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{15} \) |
$3.07193$ |
$(a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{2} \) |
$1$ |
$3.719507252$ |
1.545757982 |
\( \frac{87555872470048749}{8} a^{2} - \frac{277048488967881345}{8} a + \frac{161822258750058731}{8} \) |
\( \bigl[a^{2} - 4\) , \( a - 1\) , \( a\) , \( -729 a^{2} + 2343 a - 1436\) , \( -27721 a^{2} + 87627 a - 51024\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-729a^{2}+2343a-1436\right){x}-27721a^{2}+87627a-51024$ |
| 16.3-a2 |
16.3-a |
$4$ |
$6$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{21} \) |
$3.07193$ |
$(a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$33.47556527$ |
1.545757982 |
\( \frac{19279053}{512} a^{2} - \frac{63659385}{512} a + \frac{42176123}{512} \) |
\( \bigl[a^{2} - 4\) , \( a - 1\) , \( a\) , \( -9 a^{2} + 28 a - 16\) , \( -29 a^{2} + 94 a - 60\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-9a^{2}+28a-16\right){x}-29a^{2}+94a-60$ |
| 16.3-a3 |
16.3-a |
$4$ |
$6$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{18} \) |
$3.07193$ |
$(a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{2} \) |
$1$ |
$3.719507252$ |
1.545757982 |
\( -\frac{2566132861253}{64} a^{2} + \frac{2520228955985}{64} a + \frac{17449596177405}{64} \) |
\( \bigl[a\) , \( -a^{2} - a + 4\) , \( a^{2} - 4\) , \( -36 a^{2} - 193 a - 279\) , \( -2107 a^{2} - 1775 a + 5926\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-36a^{2}-193a-279\right){x}-2107a^{2}-1775a+5926$ |
| 16.3-a4 |
16.3-a |
$4$ |
$6$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{30} \) |
$3.07193$ |
$(a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$33.47556527$ |
1.545757982 |
\( -\frac{195962533}{262144} a^{2} + \frac{398930673}{262144} a + \frac{1725009309}{262144} \) |
\( \bigl[a\) , \( -a^{2} - a + 4\) , \( a^{2} - 4\) , \( -a^{2} - 3 a + 1\) , \( -a - 2\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-a^{2}-3a+1\right){x}-a-2$ |
| 16.3-b1 |
16.3-b |
$2$ |
$2$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{10} \) |
$3.07193$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.062291989$ |
$172.2139462$ |
1.486056599 |
\( -30942535 a^{2} + 7030797 a + 160150272 \) |
\( \bigl[a^{2} + a - 4\) , \( -a^{2} + a + 4\) , \( 0\) , \( -2 a^{2} - a + 9\) , \( -5 a^{2} - 6 a + 10\bigr] \) |
${y}^2+\left(a^{2}+a-4\right){x}{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-2a^{2}-a+9\right){x}-5a^{2}-6a+10$ |
| 16.3-b2 |
16.3-b |
$2$ |
$2$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{11} \) |
$3.07193$ |
$(a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.124583978$ |
$172.2139462$ |
1.486056599 |
\( -429 a^{2} - 6543 a + 18202 \) |
\( \bigl[a\) , \( a^{2} + a - 5\) , \( a^{2} + a - 4\) , \( -3 a^{2} + 8 a\) , \( 6 a^{2} - 18 a + 8\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(-3a^{2}+8a\right){x}+6a^{2}-18a+8$ |
| 16.3-c1 |
16.3-c |
$8$ |
$12$ |
3.3.469.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{21} \) |
$3.07193$ |
$(a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2 \) |
$1$ |
$27.52539682$ |
1.429880323 |
\( -\frac{2638200006150459}{512} a^{2} + \frac{599226037309295}{512} a + \frac{13654121353016131}{512} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + 3\) , \( a^{2} + a - 4\) , \( 90 a^{2} + 102 a - 200\) , \( -1072 a^{2} - 1453 a + 1876\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(90a^{2}+102a-200\right){x}-1072a^{2}-1453a+1876$ |
*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.
