| 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 |
| 2178.5-c6 |
2178.5-c |
$8$ |
$20$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2178.5 |
\( 2 \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{10} \cdot 3^{20} \cdot 11^{4} \) |
$1.72662$ |
$(a), (-a-1), (a-1), (a+3), (a-3)$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2^{5} \cdot 5^{3} \) |
$1$ |
$0.560225554$ |
3.961392883 |
\( \frac{168105213359}{228637728} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 115\) , \( 561\bigr] \) |
${y}^2+{x}{y}={x}^{3}+115{x}+561$ |
| 300.2-b4 |
300.2-b |
$8$ |
$20$ |
\(\Q(\sqrt{-15}) \) |
$2$ |
$[0, 1]$ |
300.2 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{10} \cdot 5^{6} \) |
$1.44034$ |
$(2,a), (2,a+1), (3,a+1), (5,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2Cs, 5B.1.2 |
$1$ |
\( 2^{5} \cdot 5^{3} \) |
$1$ |
$0.787497134$ |
4.066617715 |
\( -\frac{19465109}{248832} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -28\) , \( 272\bigr] \) |
${y}^2+{x}{y}={x}^3-28{x}+272$ |
| 36.1-a3 |
36.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{20} \) |
$0.78920$ |
$(-a), (-a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2^{3} \cdot 5^{2} \) |
$1$ |
$7.710672559$ |
1.069277895 |
\( \frac{476379541}{236196} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 48 a - 115\) , \( -96 a + 218\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(48a-115\right){x}-96a+218$ |
| 36.1-a4 |
36.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{4} \) |
$0.90248$ |
$(-a+2), (-a-1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2^{3} \cdot 5^{2} \) |
$1$ |
$16.24186429$ |
1.969615354 |
\( \frac{141420761}{9216} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( -174 a - 270\) , \( 1819 a + 2840\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-174a-270\right){x}+1819a+2840$ |
| 132.1-b3 |
132.1-b |
$8$ |
$20$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
132.1 |
\( 2^{2} \cdot 3 \cdot 11 \) |
\( 2^{20} \cdot 3^{10} \cdot 11^{2} \) |
$1.73996$ |
$(-a-2), (-a+3), (-2a+7), (-4a-9)$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2^{4} \cdot 5^{3} \) |
$1$ |
$5.679783475$ |
4.943616968 |
\( \frac{10091699281}{2737152} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -45\) , \( 81\bigr] \) |
${y}^2+{x}{y}={x}^{3}-45{x}+81$ |
| 450.1-bh5 |
450.1-bh |
$8$ |
$20$ |
\(\Q(\sqrt{10}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{20} \cdot 5^{6} \) |
$2.60299$ |
$(2,a), (3,a+1), (3,a+2), (5,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2^{5} \cdot 5^{3} \) |
$0.815118739$ |
$3.130278287$ |
8.068704795 |
\( \frac{502270291349}{1889568} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -828\) , \( 9072\bigr] \) |
${y}^2+{x}{y}={x}^{3}-828{x}+9072$ |
| 57.1-a7 |
57.1-a |
$8$ |
$20$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
57.1 |
\( 3 \cdot 19 \) |
\( 3^{10} \cdot 19^{2} \) |
$1.57771$ |
$(-a^2+1), (2a^2-3)$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$157.3079290$ |
0.873932938 |
\( \frac{2701680301}{29241} a^{2} + \frac{4042084009}{29241} a + \frac{1228401061}{29241} \) |
\( \bigl[a\) , \( -a^{2} - a + 2\) , \( a\) , \( -6 a^{2} - 10 a - 3\) , \( 19 a^{2} + 36 a + 10\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(-6a^{2}-10a-3\right){x}+19a^{2}+36a+10$ |
| 57.2-a3 |
57.2-a |
$8$ |
$20$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
57.2 |
\( 3 \cdot 19 \) |
\( 3^{10} \cdot 19^{2} \) |
$1.57771$ |
$(-a^2+1), (2a^2-2a-5)$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$157.3079290$ |
0.873932938 |
\( -\frac{6743764310}{29241} a^{2} + \frac{2701680301}{29241} a + \frac{20119290283}{29241} \) |
\( \bigl[a^{2} - 2\) , \( -a^{2} - a + 2\) , \( a\) , \( 15 a^{2} - 5 a - 44\) , \( -25 a^{2} + 9 a + 72\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(15a^{2}-5a-44\right){x}-25a^{2}+9a+72$ |
| 57.3-a3 |
57.3-a |
$8$ |
$20$ |
\(\Q(\zeta_{9})^+\) |
$3$ |
$[3, 0]$ |
57.3 |
\( 3 \cdot 19 \) |
\( 3^{10} \cdot 19^{2} \) |
$1.57771$ |
$(-a^2+1), (-a^2+5)$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$157.3079290$ |
0.873932938 |
\( \frac{4042084009}{29241} a^{2} - \frac{6743764310}{29241} a - \frac{1452406355}{29241} \) |
\( \bigl[a^{2} + a - 2\) , \( -a^{2} + a + 1\) , \( a^{2} + a - 2\) , \( -10 a^{2} + 14 a + 3\) , \( 36 a^{2} - 56 a - 25\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+1\right){x}^{2}+\left(-10a^{2}+14a+3\right){x}+36a^{2}-56a-25$ |
| 44.2-c2 |
44.2-c |
$8$ |
$20$ |
3.3.316.1 |
$3$ |
$[3, 0]$ |
44.2 |
\( 2^{2} \cdot 11 \) |
\( 2^{20} \cdot 11^{2} \) |
$2.98463$ |
$(a), (-a+1), (a^2-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2^{3} \cdot 5^{2} \) |
$1$ |
$109.9600064$ |
3.092866821 |
\( \frac{38566610865}{123904} a^{2} - \frac{47704886211}{61952} a + \frac{18326938253}{61952} \) |
\( \bigl[a^{2} + a - 3\) , \( a^{2} - 4\) , \( a^{2} - 2\) , \( -24 a^{2} + 64 a - 25\) , \( 134 a^{2} - 378 a + 147\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-24a^{2}+64a-25\right){x}+134a^{2}-378a+147$ |
| 121.2-a7 |
121.2-a |
$8$ |
$20$ |
4.4.725.1 |
$4$ |
$[4, 0]$ |
121.2 |
\( 11^{2} \) |
\( 11^{4} \) |
$4.38183$ |
$(-a^3+2a^2+a-3), (-a^3+3a)$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$2442.592906$ |
0.907156231 |
\( -\frac{765788765}{121} a^{3} + \frac{765788765}{121} a^{2} + \frac{1531577530}{121} a + \frac{490956721}{121} \) |
\( \bigl[a^{2}\) , \( a^{3} - a^{2} - 2 a + 1\) , \( a^{3} - a^{2} - a + 2\) , \( -20 a^{3} + 31 a^{2} + 45 a - 46\) , \( 50 a^{3} - 75 a^{2} - 114 a + 108\bigr] \) |
${y}^2+a^{2}{x}{y}+\left(a^{3}-a^{2}-a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-2a+1\right){x}^{2}+\left(-20a^{3}+31a^{2}+45a-46\right){x}+50a^{3}-75a^{2}-114a+108$ |
| 324.1-a4 |
324.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{2}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
324.1 |
\( 2^{2} \cdot 3^{4} \) |
\( 2^{4} \cdot 3^{8} \) |
$7.36235$ |
$(1/2a^3-2a), (-1/2a^3-1/2a^2+2a), (-1/2a^3-1/2a^2+3a+1)$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2Cs, 5B.1.1[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$1962.456482$ |
0.981228241 |
\( \frac{131872229}{18} \) |
\( \bigl[\frac{1}{2} a^{2} - 1\) , \( \frac{1}{2} a^{2} - 2\) , \( \frac{1}{2} a^{2} - 1\) , \( 5 a^{2} - 31\) , \( -\frac{31}{2} a^{2} + 82\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-1\right){x}{y}+\left(\frac{1}{2}a^{2}-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-2\right){x}^{2}+\left(5a^{2}-31\right){x}-\frac{31}{2}a^{2}+82$ |
| 399.1-b4 |
399.1-b |
$8$ |
$20$ |
4.4.1957.1 |
$4$ |
$[4, 0]$ |
399.1 |
\( 3 \cdot 7 \cdot 19 \) |
\( 3^{10} \cdot 7^{10} \cdot 19^{2} \) |
$8.35710$ |
$(a^3-4a), (a^2-2), (a^3-a^2-4a)$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2^{3} \cdot 5^{2} \) |
$1$ |
$175.3848865$ |
1.982288026 |
\( \frac{87366888160239823279}{316917738585819} a^{3} + \frac{182831225481752826673}{316917738585819} a^{2} + \frac{9138440044292447044}{105639246195273} a - \frac{36715850509804879036}{316917738585819} \) |
\( \bigl[a^{3} - 4 a - 1\) , \( a^{2} - a - 3\) , \( a + 1\) , \( 15 a^{3} - 5 a^{2} - 94 a - 67\) , \( -72 a^{3} + 38 a^{2} + 454 a + 287\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(15a^{3}-5a^{2}-94a-67\right){x}-72a^{3}+38a^{2}+454a+287$ |
| 1.1-a3 |
1.1-a |
$12$ |
$40$ |
\(\Q(\zeta_{16})^+\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$4.04393$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$4075.671888$ |
0.225151189 |
\( -55168 a^{2} + 190144 \) |
\( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( -a^{3} - a^{2} + 4 a + 2\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -2 a^{3} - 2 a^{2} + 4 a + 3\) , \( -a^{3} - 2 a^{2} + a + 2\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{3}+a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+2\right){x}^{2}+\left(-2a^{3}-2a^{2}+4a+3\right){x}-a^{3}-2a^{2}+a+2$ |
| 1.1-a5 |
1.1-a |
$12$ |
$40$ |
\(\Q(\zeta_{16})^+\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$4.04393$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$4075.671888$ |
0.225151189 |
\( 55168 a^{2} - 30528 \) |
\( \bigl[a^{2} - 2\) , \( a^{3} - a^{2} - 2 a + 3\) , \( a + 1\) , \( -2 a^{2} - 3 a + 4\) , \( a^{3} - 3 a\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-2a+3\right){x}^{2}+\left(-2a^{2}-3a+4\right){x}+a^{3}-3a$ |
| 1922.1-f5 |
1922.1-f |
$8$ |
$20$ |
\(\Q(\zeta_{16})^+\) |
$4$ |
$[4, 0]$ |
1922.1 |
\( 2 \cdot 31^{2} \) |
\( 2^{10} \cdot 31^{4} \) |
$10.40573$ |
$(a), (a^3+a^2-2a-3), (a^3-a^2-2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.807664433$ |
$824.6738696$ |
5.887192104 |
\( -\frac{384791731767}{7688} a^{2} + \frac{166284967743}{961} \) |
\( \bigl[a^{2} - 1\) , \( a^{2} - 2\) , \( 0\) , \( 22 a^{2} - 85\) , \( -94 a^{2} + 327\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(22a^{2}-85\right){x}-94a^{2}+327$ |
| 1922.4-f4 |
1922.4-f |
$8$ |
$20$ |
\(\Q(\zeta_{16})^+\) |
$4$ |
$[4, 0]$ |
1922.4 |
\( 2 \cdot 31^{2} \) |
\( 2^{10} \cdot 31^{4} \) |
$10.40573$ |
$(a), (a^3-a^2-4a+1), (a^3+a^2-4a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.807664433$ |
$824.6738696$ |
5.887192104 |
\( \frac{384791731767}{7688} a^{2} - \frac{52221796281}{1922} \) |
\( \bigl[a^{2} - 1\) , \( a^{2} - 2\) , \( a^{2} - 2\) , \( -21 a^{2}\) , \( 52 a^{2} - 8\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}-21a^{2}{x}+52a^{2}-8$ |
| 16.1-b7 |
16.1-b |
$8$ |
$20$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$5.96099$ |
$(-a), (-1/2a^3+1/2a^2+5/2a-1)$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$3439.250798$ |
0.729119711 |
\( \frac{1790195}{8} a^{3} - \frac{1790195}{8} a^{2} - \frac{5370585}{8} a + \frac{2926869}{4} \) |
\( \bigl[a + 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 4\) , \( a^{2} - 2\) , \( 2 a^{3} - 11 a - 8\) , \( -10 a^{3} - 2 a^{2} + 48 a + 36\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-4\right){x}^{2}+\left(2a^{3}-11a-8\right){x}-10a^{3}-2a^{2}+48a+36$ |
| 9.1-b6 |
9.1-b |
$8$ |
$20$ |
\(\Q(\sqrt{2}, \sqrt{3})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$5.64495$ |
$(a^2-2)$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$4012.736889$ |
0.417993425 |
\( \frac{85184}{3} \) |
\( \bigl[a^{3} - 3 a\) , \( a^{3} - 3 a\) , \( a^{3} - 3 a + 1\) , \( -2 a^{3} + 6 a - 3\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{3}-3a\right){x}^{2}+\left(-2a^{3}+6a-3\right){x}$ |
| 22.1-b3 |
22.1-b |
$8$ |
$20$ |
4.4.2777.1 |
$4$ |
$[4, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( 2^{10} \cdot 11^{2} \) |
$6.92994$ |
$(-a), (-a^3+2a^2+2a-1)$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$1697.894796$ |
1.610989990 |
\( \frac{189687996477}{123904} a^{3} + \frac{252879329025}{123904} a^{2} - \frac{75995630703}{61952} a - \frac{153356764887}{123904} \) |
\( \bigl[a^{3} - 4 a - 1\) , \( -a^{3} + 2 a^{2} + 3 a - 4\) , \( a^{2} - 2\) , \( 4 a^{3} - 7 a^{2} - 9 a + 5\) , \( -a^{3} + 2 a^{2} + a - 3\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-4\right){x}^{2}+\left(4a^{3}-7a^{2}-9a+5\right){x}-a^{3}+2a^{2}+a-3$ |
| 196.6-c6 |
196.6-c |
$8$ |
$20$ |
4.4.7232.1 |
$4$ |
$[4, 0]$ |
196.6 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{4} \) |
$14.69941$ |
$(-1/2a^3+a^2+5/2a-3), (-a-1), (-a^3+2a^2+3a-1)$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2^{3} \cdot 5^{2} \) |
$1$ |
$924.4085466$ |
5.435065066 |
\( -\frac{42265721}{784} a^{3} + \frac{42265721}{392} a^{2} + \frac{126797163}{784} a + \frac{83839757}{1568} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a - 2\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{5}{2} a\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a - 2\) , \( -\frac{2231}{2} a^{3} + 2955 a^{2} + \frac{7315}{2} a - 6833\) , \( 34041 a^{3} - 90285 a^{2} - 111322 a + 208789\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a-2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+\frac{5}{2}a\right){x}^{2}+\left(-\frac{2231}{2}a^{3}+2955a^{2}+\frac{7315}{2}a-6833\right){x}+34041a^{3}-90285a^{2}-111322a+208789$ |
| 6.1-b6 |
6.1-b |
$8$ |
$20$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{20} \cdot 3^{10} \) |
$9.70525$ |
$(a^3+a^2-3a-1), (-a^3+a^2+4a-3)$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2^{3} \cdot 5^{2} \) |
$1$ |
$388.0186227$ |
2.234721032 |
\( \frac{137453854619383}{61917364224} a^{3} - \frac{69119317227029}{30958682112} a^{2} - \frac{694491025501121}{61917364224} a + \frac{967236366550849}{61917364224} \) |
\( \bigl[a^{2} - 2\) , \( a^{2} - 3\) , \( a^{2} - 3\) , \( 26 a^{3} + 11 a^{2} - 117 a - 62\) , \( -11 a^{3} - 5 a^{2} + 49 a + 27\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(26a^{3}+11a^{2}-117a-62\right){x}-11a^{3}-5a^{2}+49a+27$ |
| 108.1-a5 |
108.1-a |
$8$ |
$20$ |
4.4.8112.1 |
$4$ |
$[4, 0]$ |
108.1 |
\( 2^{2} \cdot 3^{3} \) |
\( 2^{8} \cdot 3^{40} \) |
$14.45042$ |
$(a), (-a^3+4a+1), (a^2-2)$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2^{4} \cdot 5^{2} \) |
$1$ |
$59.45447132$ |
0.660116442 |
\( \frac{476379541}{236196} \) |
\( \bigl[a^{2} - 2\) , \( -a^{2} + 3\) , \( a^{2} - 2\) , \( -50 a^{2} + 35\) , \( 95 a^{2} - 67\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-50a^{2}+35\right){x}+95a^{2}-67$ |
| 174.1-n6 |
174.1-n |
$8$ |
$20$ |
4.4.10273.1 |
$4$ |
$[4, 0]$ |
174.1 |
\( 2 \cdot 3 \cdot 29 \) |
\( 2^{10} \cdot 3^{10} \cdot 29^{2} \) |
$17.26060$ |
$(a), (-a^2+1), (a^3-2a^2-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2^{3} \cdot 5^{2} \) |
$1$ |
$613.3294192$ |
3.025625397 |
\( -\frac{58678474085203571}{50852054016} a^{3} + \frac{4862016425002697}{3178253376} a^{2} + \frac{115315397569577845}{16950684672} a + \frac{174637849428858235}{50852054016} \) |
\( \bigl[2 a^{3} - 5 a^{2} - 6 a + 3\) , \( a^{2} - 2 a - 4\) , \( a^{3} - 2 a^{2} - 3 a\) , \( 204 a^{3} - 271 a^{2} - 1204 a - 607\) , \( -3232 a^{3} + 4287 a^{2} + 19047 a + 9597\bigr] \) |
${y}^2+\left(2a^{3}-5a^{2}-6a+3\right){x}{y}+\left(a^{3}-2a^{2}-3a\right){y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(204a^{3}-271a^{2}-1204a-607\right){x}-3232a^{3}+4287a^{2}+19047a+9597$ |
| 40.1-i8 |
40.1-i |
$8$ |
$20$ |
4.4.11324.1 |
$4$ |
$[4, 0]$ |
40.1 |
\( 2^{3} \cdot 5 \) |
\( 2^{14} \cdot 5^{10} \) |
$15.07981$ |
$(a^3-5a), (a+1), (-a^2+a+3)$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2^{3} \cdot 5^{2} \) |
$1$ |
$443.3766907$ |
2.083257392 |
\( \frac{576761237679}{78125000} a^{3} + \frac{3173134996933}{312500000} a^{2} - \frac{5280932976143}{312500000} a - \frac{1547503816013}{312500000} \) |
\( \bigl[a + 1\) , \( -a^{3} - a^{2} + 5 a + 2\) , \( a^{2} - 2\) , \( 10 a^{3} - 2 a^{2} - 57 a - 19\) , \( 45 a^{3} + 18 a^{2} - 196 a - 71\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}-a^{2}+5a+2\right){x}^{2}+\left(10a^{3}-2a^{2}-57a-19\right){x}+45a^{3}+18a^{2}-196a-71$ |
| 16.1-a4 |
16.1-a |
$8$ |
$20$ |
4.4.15317.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{28} \) |
$15.64013$ |
$(-a), (a-1), (-a^2+a+1)$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2^{3} \cdot 5^{2} \) |
$1$ |
$954.7137071$ |
3.857059212 |
\( \frac{91653023}{1024} a^{2} - \frac{91653023}{1024} a - \frac{37932201}{1024} \) |
\( \bigl[a^{3} - 5 a - 1\) , \( -a^{3} + 5 a + 3\) , \( 1\) , \( 158 a^{3} - 106 a^{2} - 772 a - 238\) , \( -231 a^{3} + 155 a^{2} + 1130 a + 347\bigr] \) |
${y}^2+\left(a^{3}-5a-1\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+5a+3\right){x}^{2}+\left(158a^{3}-106a^{2}-772a-238\right){x}-231a^{3}+155a^{2}+1130a+347$ |
| 81.1-h3 |
81.1-h |
$8$ |
$20$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
81.1 |
\( 3^{4} \) |
\( 3^{24} \) |
$20.22103$ |
$(a), (-a^2+2a+5), (-a^3+2a^2+5a-1)$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$4$ |
\( 2^{3} \cdot 5^{2} \) |
$1$ |
$261.5510059$ |
4.003891969 |
\( -\frac{2662612328525}{59049} a^{3} + \frac{5325224657050}{59049} a^{2} + \frac{13313061642625}{59049} a + \frac{3469114365379}{59049} \) |
\( \bigl[a^{3} - a^{2} - 7 a - 3\) , \( -a^{3} + 2 a^{2} + 4 a + 1\) , \( a + 1\) , \( -14 a^{3} - 21 a^{2} + 19 a + 29\) , \( -89 a^{3} - 216 a^{2} - 60 a + 85\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-7a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a+1\right){x}^{2}+\left(-14a^{3}-21a^{2}+19a+29\right){x}-89a^{3}-216a^{2}-60a+85$ |
| 295.2-b4 |
295.2-b |
$8$ |
$20$ |
5.5.24217.1 |
$5$ |
$[5, 0]$ |
295.2 |
\( 5 \cdot 59 \) |
\( 5^{10} \cdot 59^{2} \) |
$24.55732$ |
$(2a^4-a^3-9a^2+2a+3), (a^4-4a^2-1)$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$5176.159087$ |
1.66309650 |
\( \frac{2549162660973014}{33994140625} a^{4} + \frac{3662435434123583}{33994140625} a^{3} + \frac{1191712071776931}{33994140625} a^{2} - \frac{4952909667883307}{33994140625} a - \frac{470207069547662}{33994140625} \) |
\( \bigl[a\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 7 a - 3\) , \( a^{4} - 4 a^{2} + a\) , \( 35 a^{4} + 33 a^{3} - 148 a^{2} - 177 a - 47\) , \( 90 a^{4} + 77 a^{3} - 382 a^{2} - 416 a - 98\bigr] \) |
${y}^2+a{x}{y}+\left(a^{4}-4a^{2}+a\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-7a-3\right){x}^{2}+\left(35a^{4}+33a^{3}-148a^{2}-177a-47\right){x}+90a^{4}+77a^{3}-382a^{2}-416a-98$ |
| 303.1-b2 |
303.1-b |
$8$ |
$20$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
303.1 |
\( 3 \cdot 101 \) |
\( 3^{10} \cdot 101^{2} \) |
$30.22814$ |
$(a^2-1), (-a^4+a^3+4a^2-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.538421157$ |
$5771.356967$ |
4.06641294 |
\( -\frac{127681896807587810}{602358849} a^{4} + \frac{27632460513332713}{200786283} a^{3} + \frac{167064171108200050}{200786283} a^{2} + \frac{24882548773576451}{602358849} a - \frac{96722808769508467}{602358849} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 2\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 1\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 2\) , \( 34 a^{4} - 84 a^{3} - 62 a^{2} + 196 a - 65\) , \( -94 a^{4} + 235 a^{3} + 164 a^{2} - 552 a + 182\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+6a+2\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+6a+2\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+4a+1\right){x}^{2}+\left(34a^{4}-84a^{3}-62a^{2}+196a-65\right){x}-94a^{4}+235a^{3}+164a^{2}-552a+182$ |
| 18.1-b5 |
18.1-b |
$8$ |
$20$ |
5.5.81509.1 |
$5$ |
$[5, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{4} \) |
$34.06188$ |
$(a^2-2), (a^2-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$12039.46357$ |
2.10850366 |
\( \frac{118685917645}{9216} a^{4} + \frac{151007782241}{9216} a^{3} - \frac{251898679003}{9216} a^{2} - \frac{72188751049}{3072} a + \frac{105055722559}{9216} \) |
\( \bigl[1\) , \( a^{4} - 4 a^{2} - a + 1\) , \( 1\) , \( 48 a^{4} + 12 a^{3} - 228 a^{2} - 136 a + 78\) , \( 170 a^{4} + 36 a^{3} - 804 a^{2} - 467 a + 279\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{4}-4a^{2}-a+1\right){x}^{2}+\left(48a^{4}+12a^{3}-228a^{2}-136a+78\right){x}+170a^{4}+36a^{3}-804a^{2}-467a+279$ |
| 22.1-d3 |
22.1-d |
$12$ |
$40$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( 2^{10} \cdot 11^{2} \) |
$34.76935$ |
$(-a^3+3a), (a^4-5a^2-a+4)$ |
$1$ |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.371850371$ |
$12052.62246$ |
3.92259957 |
\( -\frac{3628139006189}{123904} a^{4} - \frac{4661034067567}{123904} a^{3} + \frac{15710811524105}{123904} a^{2} + \frac{20201587498915}{123904} a - \frac{2796655538087}{123904} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a + 3\) , \( a^{3} - a^{2} - 3 a + 1\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 3\) , \( 23 a^{4} + 22 a^{3} - 107 a^{2} - 117 a + 15\) , \( -151 a^{4} - 194 a^{3} + 647 a^{2} + 830 a - 116\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+4a+3\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+3a+3\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+1\right){x}^{2}+\left(23a^{4}+22a^{3}-107a^{2}-117a+15\right){x}-151a^{4}-194a^{3}+647a^{2}+830a-116$ |
| 22.1-d6 |
22.1-d |
$12$ |
$40$ |
5.5.81589.1 |
$5$ |
$[5, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( 2^{20} \cdot 11^{4} \) |
$34.76935$ |
$(-a^3+3a), (a^4-5a^2-a+4)$ |
$1$ |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2^{4} \cdot 5 \) |
$0.185925185$ |
$6026.311234$ |
3.92259957 |
\( \frac{13229274773910643}{15352201216} a^{4} - \frac{20739047300800335}{15352201216} a^{3} - \frac{37270695561414103}{15352201216} a^{2} + \frac{47299204188218115}{15352201216} a + \frac{9197738213488761}{15352201216} \) |
\( \bigl[a^{4} - 3 a^{2} + 1\) , \( a^{4} - 4 a^{2} - a + 2\) , \( a^{4} - 4 a^{2} + 3\) , \( 6 a^{4} - 2 a^{3} - 22 a^{2} + 3 a - 1\) , \( -8 a^{4} - 10 a^{3} + 36 a^{2} + 42 a - 8\bigr] \) |
${y}^2+\left(a^{4}-3a^{2}+1\right){x}{y}+\left(a^{4}-4a^{2}+3\right){y}={x}^{3}+\left(a^{4}-4a^{2}-a+2\right){x}^{2}+\left(6a^{4}-2a^{3}-22a^{2}+3a-1\right){x}-8a^{4}-10a^{3}+36a^{2}+42a-8$ |
| 87.1-a4 |
87.1-a |
$8$ |
$20$ |
5.5.126032.1 |
$5$ |
$[5, 0]$ |
87.1 |
\( 3 \cdot 29 \) |
\( 3^{10} \cdot 29^{2} \) |
$49.58278$ |
$(-a^4+5a^2+a-3), (-2a^4+10a^2+2a-5)$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$7838.695184$ |
1.10401092 |
\( \frac{794907065683376}{49660209} a^{4} + \frac{318574341108256}{49660209} a^{3} - \frac{4654830721140352}{49660209} a^{2} - \frac{1853644605066752}{49660209} a + \frac{4086783782063168}{49660209} \) |
\( \bigl[a^{2} - 2\) , \( a^{4} - 4 a^{2}\) , \( a^{4} + a^{3} - 6 a^{2} - 4 a + 5\) , \( 13 a^{4} + 11 a^{3} - 69 a^{2} - 54 a + 33\) , \( -41 a^{4} - 26 a^{3} + 214 a^{2} + 153 a - 92\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{4}+a^{3}-6a^{2}-4a+5\right){y}={x}^{3}+\left(a^{4}-4a^{2}\right){x}^{2}+\left(13a^{4}+11a^{3}-69a^{2}-54a+33\right){x}-41a^{4}-26a^{3}+214a^{2}+153a-92$ |
| 88.2-f3 |
88.2-f |
$8$ |
$20$ |
5.5.135076.1 |
$5$ |
$[5, 0]$ |
88.2 |
\( 2^{3} \cdot 11 \) |
\( 2^{14} \cdot 11^{2} \) |
$51.38968$ |
$(a), (-a^2+3), (-a^4+a^3+4a^2-3a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.361876231$ |
$13209.36351$ |
6.50313635 |
\( \frac{87345859}{1936} a^{4} - \frac{920665645}{1936} a^{3} + \frac{1195659695}{1936} a^{2} + \frac{26331995}{44} a - \frac{314011585}{968} \) |
\( \bigl[a^{4} + a^{3} - 5 a^{2} - 4 a + 3\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 1\) , \( a^{4} + a^{3} - 4 a^{2} - 4 a + 1\) , \( a^{4} - 6 a^{2} - 3 a + 1\) , \( a^{4} - 5 a^{2} - 2 a + 1\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-5a^{2}-4a+3\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-4a+1\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+3a+1\right){x}^{2}+\left(a^{4}-6a^{2}-3a+1\right){x}+a^{4}-5a^{2}-2a+1$ |
| 81.2-g3 |
81.2-g |
$8$ |
$20$ |
5.5.161121.1 |
$5$ |
$[5, 0]$ |
81.2 |
\( 3^{4} \) |
\( 3^{28} \) |
$55.66255$ |
$(a^4-a^3-6a^2+3a+4), (-2a^4+3a^3+10a^2-10a-4), (2a^4-3a^3-11a^2+12a+5)$ |
$1$ |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2^{3} \cdot 5^{2} \) |
$0.425415831$ |
$2593.662690$ |
6.87212541 |
\( -\frac{500293596235}{59049} a^{4} - \frac{59074988062}{59049} a^{3} + \frac{2767717264669}{59049} a^{2} + \frac{1631546666948}{59049} a + \frac{239242631816}{59049} \) |
\( \bigl[-a^{4} + 2 a^{3} + 5 a^{2} - 7 a - 2\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a\) , \( 0\) , \( -4 a^{4} + 16 a^{3} - 8 a^{2} - 16 a - 4\) , \( -11 a^{4} + 19 a^{3} + 21 a^{2} + 5 a + 1\bigr] \) |
${y}^2+\left(-a^{4}+2a^{3}+5a^{2}-7a-2\right){x}{y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+3a\right){x}^{2}+\left(-4a^{4}+16a^{3}-8a^{2}-16a-4\right){x}-11a^{4}+19a^{3}+21a^{2}+5a+1$ |
| 33.1-d4 |
33.1-d |
$8$ |
$20$ |
5.5.179024.1 |
$5$ |
$[5, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( 3^{10} \cdot 11^{2} \) |
$53.63467$ |
$(2a^4+a^3-15a^2-7a+7), (2a^4+a^3-16a^2-9a+9)$ |
$1$ |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.377249886$ |
$11481.55143$ |
2.55925803 |
\( \frac{386859684656}{7144929} a^{4} + \frac{178455835040}{7144929} a^{3} - \frac{3000647529152}{7144929} a^{2} - \frac{1404317445824}{7144929} a + \frac{1710344682304}{7144929} \) |
\( \bigl[-2 a^{4} - a^{3} + 15 a^{2} + 8 a - 6\) , \( -3 a^{4} - a^{3} + 23 a^{2} + 10 a - 11\) , \( 2 a^{4} + a^{3} - 16 a^{2} - 7 a + 11\) , \( -2 a^{4} - 2 a^{3} + 14 a^{2} + 10 a - 8\) , \( -5 a^{4} - 2 a^{3} + 40 a^{2} + 19 a - 22\bigr] \) |
${y}^2+\left(-2a^{4}-a^{3}+15a^{2}+8a-6\right){x}{y}+\left(2a^{4}+a^{3}-16a^{2}-7a+11\right){y}={x}^{3}+\left(-3a^{4}-a^{3}+23a^{2}+10a-11\right){x}^{2}+\left(-2a^{4}-2a^{3}+14a^{2}+10a-8\right){x}-5a^{4}-2a^{3}+40a^{2}+19a-22$ |
| 1.1-b3 |
1.1-b |
$8$ |
$20$ |
6.6.810448.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$80.44538$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
✓ |
$2, 3, 5$ |
2Cs, 3Ns, 5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$313671.8586$ |
0.871070 |
\( 4096 \) |
\( \bigl[0\) , \( -2 a^{5} + 5 a^{4} + 4 a^{3} - 11 a^{2} - a\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 8 a^{2} + 7 a - 3\) , \( -12 a^{5} + 25 a^{4} + 52 a^{3} - 73 a^{2} - 74 a + 19\) , \( 54 a^{5} - 119 a^{4} - 205 a^{3} + 327 a^{2} + 265 a - 71\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-5a^{3}+8a^{2}+7a-3\right){y}={x}^{3}+\left(-2a^{5}+5a^{4}+4a^{3}-11a^{2}-a\right){x}^{2}+\left(-12a^{5}+25a^{4}+52a^{3}-73a^{2}-74a+19\right){x}+54a^{5}-119a^{4}-205a^{3}+327a^{2}+265a-71$ |
| 1.1-b3 |
1.1-b |
$12$ |
$40$ |
6.6.905177.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$85.01691$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 5$ |
2Cs, 5B.1.1 |
$4$ |
\( 1 \) |
$1$ |
$71384.66692$ |
0.750306 |
\( -7385317374 a^{5} - 4750114813 a^{4} + 46947106805 a^{3} + 8979939317 a^{2} - 54332424179 a - 5690031348 \) |
\( \bigl[a^{5} + a^{4} - 5 a^{3} - a^{2} + 4 a - 1\) , \( 2 a^{5} - a^{4} - 14 a^{3} + 9 a^{2} + 13 a - 2\) , \( a^{5} - 6 a^{3} + 3 a^{2} + 5 a - 2\) , \( -9 a^{5} - 4 a^{4} + 63 a^{3} + 10 a^{2} - 82 a - 28\) , \( 17 a^{5} + 3 a^{4} - 112 a^{3} + 24 a^{2} + 125 a - 6\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-5a^{3}-a^{2}+4a-1\right){x}{y}+\left(a^{5}-6a^{3}+3a^{2}+5a-2\right){y}={x}^{3}+\left(2a^{5}-a^{4}-14a^{3}+9a^{2}+13a-2\right){x}^{2}+\left(-9a^{5}-4a^{4}+63a^{3}+10a^{2}-82a-28\right){x}+17a^{5}+3a^{4}-112a^{3}+24a^{2}+125a-6$ |
| 1.1-b4 |
1.1-b |
$12$ |
$40$ |
6.6.905177.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$85.01691$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$285538.6677$ |
0.750306 |
\( -69527 a^{5} - 44884 a^{4} + 441805 a^{3} + 85366 a^{2} - 511332 a - 51787 \) |
\( \bigl[a^{5} + a^{4} - 6 a^{3} - 3 a^{2} + 8 a + 3\) , \( -3 a^{5} - a^{4} + 20 a^{3} - 24 a - 3\) , \( a^{5} + a^{4} - 6 a^{3} - 3 a^{2} + 7 a + 2\) , \( 9 a^{5} - 4 a^{4} - 60 a^{3} + 51 a^{2} + 58 a - 47\) , \( -a^{5} + 2 a^{4} + 8 a^{3} - 13 a^{2} - 8 a + 11\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-6a^{3}-3a^{2}+8a+3\right){x}{y}+\left(a^{5}+a^{4}-6a^{3}-3a^{2}+7a+2\right){y}={x}^{3}+\left(-3a^{5}-a^{4}+20a^{3}-24a-3\right){x}^{2}+\left(9a^{5}-4a^{4}-60a^{3}+51a^{2}+58a-47\right){x}-a^{5}+2a^{4}+8a^{3}-13a^{2}-8a+11$ |
| 169.3-h5 |
169.3-h |
$8$ |
$20$ |
6.6.905177.1 |
$6$ |
$[6, 0]$ |
169.3 |
\( 13^{2} \) |
\( 13^{4} \) |
$130.36546$ |
$(a^4+a^3-5a^2-a+2)$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$165264.3999$ |
0.868526 |
\( \frac{158504673}{169} a^{5} + \frac{147137633}{169} a^{4} - \frac{962395078}{169} a^{3} - \frac{32206063}{13} a^{2} + \frac{1120899751}{169} a + \frac{553883240}{169} \) |
\( \bigl[2 a^{5} - 13 a^{3} + 5 a^{2} + 13 a - 3\) , \( a^{5} + a^{4} - 6 a^{3} - 3 a^{2} + 6 a + 3\) , \( 3 a^{5} + a^{4} - 19 a^{3} + 2 a^{2} + 21 a\) , \( 7 a^{5} + 9 a^{4} - 37 a^{3} - 29 a^{2} + 27 a + 14\) , \( -40 a^{5} - 25 a^{4} + 239 a^{3} + 31 a^{2} - 222 a - 13\bigr] \) |
${y}^2+\left(2a^{5}-13a^{3}+5a^{2}+13a-3\right){x}{y}+\left(3a^{5}+a^{4}-19a^{3}+2a^{2}+21a\right){y}={x}^{3}+\left(a^{5}+a^{4}-6a^{3}-3a^{2}+6a+3\right){x}^{2}+\left(7a^{5}+9a^{4}-37a^{3}-29a^{2}+27a+14\right){x}-40a^{5}-25a^{4}+239a^{3}+31a^{2}-222a-13$ |
| 275.1-b6 |
275.1-b |
$8$ |
$20$ |
6.6.966125.1 |
$6$ |
$[6, 0]$ |
275.1 |
\( 5^{2} \cdot 11 \) |
\( 5^{8} \cdot 11^{2} \) |
$140.25971$ |
$(a-1), (a^3-3a)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2Cs, 5B.1.1[2] |
|
\( 2^{3} \) |
$1$ |
$40581.32300$ |
5.15675 |
\( \frac{21838250235646}{605} a^{5} + \frac{25831740895029}{605} a^{4} - \frac{75032376564272}{605} a^{3} - \frac{77600017324692}{605} a^{2} + \frac{4549087554333}{605} a + \frac{9970413090037}{605} \) |
\( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 9 a^{2} - 2\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 9 a^{2} + 4 a - 4\) , \( a^{4} - 4 a^{2} + 1\) , \( -12 a^{5} + 23 a^{4} + 48 a^{3} - 100 a^{2} + 13 a + 2\) , \( -7 a^{5} + 2 a^{4} + 54 a^{3} - 5 a^{2} - 131 a + 48\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-4a^{3}+9a^{2}-2\right){x}{y}+\left(a^{4}-4a^{2}+1\right){y}={x}^{3}+\left(a^{5}-2a^{4}-5a^{3}+9a^{2}+4a-4\right){x}^{2}+\left(-12a^{5}+23a^{4}+48a^{3}-100a^{2}+13a+2\right){x}-7a^{5}+2a^{4}+54a^{3}-5a^{2}-131a+48$ |
| 62.1-c3 |
62.1-c |
$8$ |
$20$ |
6.6.1868969.1 |
$6$ |
$[6, 0]$ |
62.1 |
\( 2 \cdot 31 \) |
\( 2^{10} \cdot 31^{2} \) |
$172.30805$ |
$(a), (-a^5+a^4+6a^3-5a^2-7a+5)$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$63006.14726$ |
2.30437 |
\( -\frac{418914723402083}{984064} a^{5} + \frac{131249766965505}{492032} a^{4} + \frac{1166817873961875}{492032} a^{3} - \frac{1051601350136545}{984064} a^{2} - \frac{1307600442535073}{492032} a + \frac{1269963889315657}{984064} \) |
\( \bigl[a^{5} + a^{4} - 5 a^{3} - 5 a^{2} + 3 a + 1\) , \( -a^{3} + 3 a + 2\) , \( a^{3} - 2 a\) , \( -11 a^{5} + 7 a^{4} + 44 a^{3} - 17 a^{2} - 2 a + 4\) , \( 22 a^{5} - 40 a^{4} - 89 a^{3} + 146 a^{2} + 36 a - 40\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-5a^{3}-5a^{2}+3a+1\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(-a^{3}+3a+2\right){x}^{2}+\left(-11a^{5}+7a^{4}+44a^{3}-17a^{2}-2a+4\right){x}+22a^{5}-40a^{4}-89a^{3}+146a^{2}+36a-40$ |
| 118.1-h5 |
118.1-h |
$8$ |
$20$ |
6.6.1868969.1 |
$6$ |
$[6, 0]$ |
118.1 |
\( 2 \cdot 59 \) |
\( 2^{20} \cdot 59^{2} \) |
$181.80107$ |
$(a), (-2a^5+a^4+10a^3-2a^2-9a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.472569467$ |
$34993.18019$ |
7.25770 |
\( \frac{1151545463258179757}{3650093056} a^{5} + \frac{1257575881109545553}{1825046528} a^{4} - \frac{707296380172006269}{1825046528} a^{3} - \frac{4237354053879891505}{3650093056} a^{2} - \frac{20626059288305137}{1825046528} a + \frac{1056302337569405721}{3650093056} \) |
\( \bigl[a^{4} - 5 a^{2} - a + 3\) , \( a^{5} - 4 a^{3} - 3 a^{2} + 4\) , \( -a^{4} + a^{3} + 5 a^{2} - a - 4\) , \( -115 a^{5} + 145 a^{4} + 497 a^{3} - 501 a^{2} - 241 a + 158\) , \( -977 a^{5} + 1293 a^{4} + 4158 a^{3} - 4536 a^{2} - 1850 a + 1500\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+3\right){x}{y}+\left(-a^{4}+a^{3}+5a^{2}-a-4\right){y}={x}^{3}+\left(a^{5}-4a^{3}-3a^{2}+4\right){x}^{2}+\left(-115a^{5}+145a^{4}+497a^{3}-501a^{2}-241a+158\right){x}-977a^{5}+1293a^{4}+4158a^{3}-4536a^{2}-1850a+1500$ |
*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.
