| 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 |
| 4.1-b2 |
4.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{27} \) |
$0.72596$ |
$(-a-2), (-a+3)$ |
0 |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{4} \) |
$1$ |
$13.40768290$ |
1.166989006 |
\( -\frac{5519537297}{262144} a + \frac{18610505433}{262144} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 44 a - 145\) , \( -242 a + 809\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(44a-145\right){x}-242a+809$ |
| 4.1-b5 |
4.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{27} \) |
$0.72596$ |
$(-a-2), (-a+3)$ |
0 |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{4} \) |
$1$ |
$13.40768290$ |
1.166989006 |
\( \frac{5519537297}{262144} a + \frac{1636371017}{32768} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -43 a - 101\) , \( 197 a + 467\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-43a-101\right){x}+197a+467$ |
| 56.1-a4 |
56.1-a |
$6$ |
$18$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
56.1 |
\( 2^{3} \cdot 7 \) |
\( 2^{3} \cdot 7^{6} \) |
$1.22349$ |
$(-a^2-a+2), (2)$ |
0 |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$210.0110142$ |
0.555584693 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-11{x}+12$ |
| 56.1-a5 |
56.1-a |
$6$ |
$18$ |
\(\Q(\zeta_{7})^+\) |
$3$ |
$[3, 0]$ |
56.1 |
\( 2^{3} \cdot 7 \) |
\( - 2^{6} \cdot 7^{3} \) |
$1.22349$ |
$(-a^2-a+2), (2)$ |
0 |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$210.0110142$ |
0.555584693 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}$ |
| 18.1-c3 |
18.1-c |
$6$ |
$18$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{12} \) |
$3.43550$ |
$(a-1), (a), (-a+2)$ |
0 |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{5} \) |
$1$ |
$48.31440475$ |
3.051605158 |
\( -\frac{3685599827}{1259712} a^{2} + \frac{4106644675}{629856} a + \frac{541500617}{157464} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 53088 a^{2} + 80226 a - 63675\) , \( 7673792 a^{2} + 11620135 a - 9154762\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(53088a^{2}+80226a-63675\right){x}+7673792a^{2}+11620135a-9154762$ |
| 18.1-c4 |
18.1-c |
$6$ |
$18$ |
3.3.564.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2^{9} \cdot 3^{24} \) |
$3.43550$ |
$(a-1), (a), (-a+2)$ |
0 |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{5} \) |
$1$ |
$24.15720237$ |
3.051605158 |
\( \frac{141540701768423153}{3099363912} a^{2} - \frac{436810068550773995}{3099363912} a + \frac{203544750571237595}{3099363912} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( -243952 a^{2} - 369094 a + 291685\) , \( 64337928 a^{2} + 97422455 a - 76758826\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-243952a^{2}-369094a+291685\right){x}+64337928a^{2}+97422455a-76758826$ |
| 16.1-a3 |
16.1-a |
$6$ |
$18$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{18} \) |
$5.96099$ |
$(-a), (-1/2a^3+1/2a^2+5/2a-1)$ |
0 |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$955.6704461$ |
1.125565163 |
\( \frac{546880529}{128} a^{3} - \frac{995601459}{128} a^{2} - \frac{1917966475}{128} a + \frac{666851395}{32} \) |
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 3\) , \( a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( -a^{3} + 2 a^{2} + 4 a - 4\) , \( a^{3} - 2 a^{2} - 3 a + 7\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a^{3}+2a^{2}+4a-4\right){x}+a^{3}-2a^{2}-3a+7$ |
| 16.1-a4 |
16.1-a |
$6$ |
$18$ |
4.4.2225.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{18} \) |
$5.96099$ |
$(-a), (-1/2a^3+1/2a^2+5/2a-1)$ |
0 |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$955.6704461$ |
1.125565163 |
\( \frac{45964405}{32} a^{3} + \frac{132431655}{64} a^{2} - \frac{68561993}{32} a - \frac{37780611}{16} \) |
\( \bigl[a^{2} - 3\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{1}{2} a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{1}{2} a + 1\) , \( a^{2} - 2 a\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{1}{2} a + 1\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{1}{2}a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{1}{2}a+1\right){x}^{2}+\left(a^{2}-2a\right){x}+\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{1}{2}a+1$ |
| 8.1-d2 |
8.1-d |
$6$ |
$18$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{54} \) |
$13.24736$ |
$(a+1), (a^2+a-1)$ |
0 |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{4} \) |
$1$ |
$179.7659609$ |
1.572544332 |
\( \frac{5519537297}{262144} a^{3} - \frac{5519537297}{262144} a^{2} - \frac{38636761079}{262144} a + \frac{1636371017}{32768} \) |
\( \bigl[1\) , \( a^{3} - a^{2} - 7 a - 2\) , \( a^{3} - a^{2} - 5 a\) , \( -45 a^{3} + 45 a^{2} + 314 a - 100\) , \( 241 a^{3} - 241 a^{2} - 1688 a + 569\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-a^{2}-5a\right){y}={x}^{3}+\left(a^{3}-a^{2}-7a-2\right){x}^{2}+\left(-45a^{3}+45a^{2}+314a-100\right){x}+241a^{3}-241a^{2}-1688a+569$ |
| 8.1-d5 |
8.1-d |
$6$ |
$18$ |
4.4.13068.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{54} \) |
$13.24736$ |
$(a+1), (a^2+a-1)$ |
0 |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{4} \) |
$1$ |
$179.7659609$ |
1.572544332 |
\( -\frac{5519537297}{262144} a^{3} + \frac{5519537297}{262144} a^{2} + \frac{38636761079}{262144} a + \frac{18610505433}{262144} \) |
\( \bigl[1\) , \( -a^{3} + a^{2} + 7 a + 2\) , \( a^{3} - a^{2} - 5 a\) , \( 42 a^{3} - 42 a^{2} - 295 a - 143\) , \( -198 a^{3} + 198 a^{2} + 1385 a + 666\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-a^{2}-5a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+7a+2\right){x}^{2}+\left(42a^{3}-42a^{2}-295a-143\right){x}-198a^{3}+198a^{2}+1385a+666$ |
| 4.2-f1 |
4.2-f |
$6$ |
$18$ |
4.4.13968.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{27} \) |
$12.55923$ |
$(1/2a^2+1/2a-1), (-1/2a^3+1/2a^2+4a-1)$ |
0 |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{4} \) |
$1$ |
$839.7298329$ |
3.552568606 |
\( -\frac{1533755475209}{1024} a^{3} + \frac{472673410411}{512} a^{2} + \frac{12028231718523}{1024} a + \frac{1104774680661}{256} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( -\frac{1}{2} a^{3} + \frac{7}{2} a + 1\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 1\) , \( -181 a^{3} - \frac{465}{2} a^{2} + \frac{1025}{2} a + 222\) , \( \frac{10455}{2} a^{3} + 6681 a^{2} - \frac{29421}{2} a - 6382\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{7}{2}a+1\right){x}^{2}+\left(-181a^{3}-\frac{465}{2}a^{2}+\frac{1025}{2}a+222\right){x}+\frac{10455}{2}a^{3}+6681a^{2}-\frac{29421}{2}a-6382$ |
| 4.2-f2 |
4.2-f |
$6$ |
$18$ |
4.4.13968.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{27} \) |
$12.55923$ |
$(1/2a^2+1/2a-1), (-1/2a^3+1/2a^2+4a-1)$ |
0 |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{4} \) |
$1$ |
$839.7298329$ |
3.552568606 |
\( \frac{1533755475209}{1024} a^{3} - \frac{3655919604805}{1024} a^{2} - \frac{2329414733635}{256} a + \frac{3964730446695}{256} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a + 2\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( -\frac{131}{2} a^{3} + 160 a^{2} + \frac{799}{2} a - 727\) , \( \frac{1353}{2} a^{3} - \frac{3261}{2} a^{2} - 4104 a + 7142\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+1\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-4a+2\right){x}^{2}+\left(-\frac{131}{2}a^{3}+160a^{2}+\frac{799}{2}a-727\right){x}+\frac{1353}{2}a^{3}-\frac{3261}{2}a^{2}-4104a+7142$ |
| 4.2-a2 |
4.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{54} \) |
$14.02717$ |
$(1/2a^3-7/2a+1), (-1/2a^3-a^2+1/2a)$ |
0 |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{4} \) |
$1$ |
$179.7659609$ |
2.723726681 |
\( \frac{5519537297}{262144} a^{2} - \frac{3467643755}{262144} \) |
\( \bigl[1\) , \( a^{2} - 5\) , \( a^{2} - 3\) , \( -45 a^{2} + 35\) , \( 241 a^{2} - 155\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(-45a^{2}+35\right){x}+241a^{2}-155$ |
| 4.2-a5 |
4.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{3}, \sqrt{11})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{54} \) |
$14.02717$ |
$(1/2a^3-7/2a+1), (-1/2a^3-a^2+1/2a)$ |
0 |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{4} \) |
$1$ |
$179.7659609$ |
2.723726681 |
\( -\frac{5519537297}{262144} a^{2} + \frac{8792279331}{65536} \) |
\( \bigl[1\) , \( -a^{2} + 5\) , \( a^{2} - 3\) , \( 42 a^{2} - 269\) , \( -198 a^{2} + 1259\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(42a^{2}-269\right){x}-198a^{2}+1259$ |
| 448.1-a2 |
448.1-a |
$6$ |
$18$ |
\(\Q(\zeta_{21})^+\) |
$6$ |
$[6, 0]$ |
448.1 |
\( 2^{6} \cdot 7 \) |
\( 2^{12} \cdot 7^{6} \) |
$100.11643$ |
$(a^5-6a^3+a^2+9a-4), (2)$ |
0 |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$44104.62610$ |
2.42488 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}$ |
| 448.1-a5 |
448.1-a |
$6$ |
$18$ |
\(\Q(\zeta_{21})^+\) |
$6$ |
$[6, 0]$ |
448.1 |
\( 2^{6} \cdot 7 \) |
\( 2^{6} \cdot 7^{12} \) |
$100.11643$ |
$(a^5-6a^3+a^2+9a-4), (2)$ |
0 |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$44104.62610$ |
2.42488 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-11{x}+12$ |
| 56.1-a2 |
56.1-a |
$6$ |
$18$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
56.1 |
\( 2^{3} \cdot 7 \) |
\( 2^{12} \cdot 7^{6} \) |
$129.61521$ |
$(a^5-5a^3+5a), (-a^4+a^3+4a^2-3a-2)$ |
$1$ |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.389689685$ |
$44104.62610$ |
3.68261 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}$ |
| 56.1-a5 |
56.1-a |
$6$ |
$18$ |
\(\Q(\zeta_{28})^+\) |
$6$ |
$[6, 0]$ |
56.1 |
\( 2^{3} \cdot 7 \) |
\( 2^{6} \cdot 7^{12} \) |
$129.61521$ |
$(a^5-5a^3+5a), (-a^4+a^3+4a^2-3a-2)$ |
$1$ |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.194844842$ |
$44104.62610$ |
3.68261 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-11{x}+12$ |
| 49.1-a1 |
49.1-a |
$6$ |
$18$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{9} \) |
$137.03115$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1)$ |
0 |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$39368.65074$ |
1.97264 |
\( -\frac{52672}{49} a^{5} + \frac{421376}{49} a^{3} - \frac{632064}{49} a + \frac{302912}{49} \) |
\( \bigl[\frac{1}{4} a^{5} - 2 a^{3} + 3 a\) , \( -\frac{1}{4} a^{5} + 2 a^{3} - 3 a + 1\) , \( 1\) , \( -\frac{1}{4} a^{5} + 2 a^{3} - 3 a + 1\) , \( 0\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}-2a^{3}+3a\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{4}a^{5}+2a^{3}-3a+1\right){x}^{2}+\left(-\frac{1}{4}a^{5}+2a^{3}-3a+1\right){x}$ |
| 49.1-a2 |
49.1-a |
$6$ |
$18$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{9} \) |
$137.03115$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1)$ |
0 |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$39368.65074$ |
1.97264 |
\( \frac{52672}{49} a^{5} - \frac{421376}{49} a^{3} + \frac{632064}{49} a + \frac{302912}{49} \) |
\( \bigl[\frac{1}{4} a^{5} - 2 a^{3} + 3 a\) , \( \frac{1}{4} a^{5} - 2 a^{3} + 3 a + 1\) , \( 1\) , \( 1\) , \( 0\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{5}-2a^{3}+3a\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{4}a^{5}-2a^{3}+3a+1\right){x}^{2}+{x}$ |
| 392.1-k2 |
392.1-k |
$12$ |
$36$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$162.95841$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1), (1/4a^5-2a^3+3a)$ |
0 |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$44104.62610$ |
2.20992 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}$ |
| 392.1-k9 |
392.1-k |
$12$ |
$36$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{3} \cdot 7^{15} \) |
$162.95841$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1), (1/4a^5-2a^3+3a)$ |
0 |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$5513.078263$ |
2.20992 |
\( -\frac{2928743223192875}{19208} a^{5} + \frac{2928743223192875}{2401} a^{3} - \frac{8786229669578625}{4802} a + \frac{2070934198465000}{2401} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( \frac{55}{4} a^{5} - 110 a^{3} + 165 a - 91\) , \( -\frac{145}{2} a^{5} + 580 a^{3} - 870 a + 416\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(\frac{55}{4}a^{5}-110a^{3}+165a-91\right){x}-\frac{145}{2}a^{5}+580a^{3}-870a+416$ |
| 392.1-k10 |
392.1-k |
$12$ |
$36$ |
6.6.1229312.1 |
$6$ |
$[6, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{3} \cdot 7^{15} \) |
$162.95841$ |
$(-1/4a^5+2a^3-1/2a^2-3a+1), (-1/2a^3+3a+1), (1/4a^5-2a^3+3a)$ |
0 |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$5513.078263$ |
2.20992 |
\( \frac{2928743223192875}{19208} a^{5} - \frac{2928743223192875}{2401} a^{3} + \frac{8786229669578625}{4802} a + \frac{2070934198465000}{2401} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -\frac{55}{4} a^{5} + 110 a^{3} - 165 a - 91\) , \( \frac{145}{2} a^{5} - 580 a^{3} + 870 a + 416\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-\frac{55}{4}a^{5}+110a^{3}-165a-91\right){x}+\frac{145}{2}a^{5}-580a^{3}+870a+416$ |
| 9.1-a4 |
9.1-a |
$6$ |
$18$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{3} \) |
$120.44656$ |
$(a^5-5a^3+4a)$ |
0 |
$\Z/18\Z$ |
$\textsf{potential}$ |
$-36$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$232262.9069$ |
1.27741 |
\( 44330496 a^{3} - 132991488 a + 76771008 \) |
\( \bigl[a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 5 a + 2\) , \( -a^{5} - a^{4} + 6 a^{3} + 5 a^{2} - 8 a - 4\) , \( a^{4} + a^{3} - 4 a^{2} - 3 a + 2\) , \( 27 a^{5} - 19 a^{4} - 152 a^{3} + 99 a^{2} + 176 a - 113\) , \( -104 a^{5} + 75 a^{4} + 579 a^{3} - 408 a^{2} - 674 a + 468\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-5a^{3}-4a^{2}+5a+2\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{5}-a^{4}+6a^{3}+5a^{2}-8a-4\right){x}^{2}+\left(27a^{5}-19a^{4}-152a^{3}+99a^{2}+176a-113\right){x}-104a^{5}+75a^{4}+579a^{3}-408a^{2}-674a+468$ |
| 9.1-a5 |
9.1-a |
$6$ |
$18$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{3} \) |
$120.44656$ |
$(a^5-5a^3+4a)$ |
0 |
$\Z/18\Z$ |
$\textsf{potential}$ |
$-36$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$232262.9069$ |
1.27741 |
\( -44330496 a^{3} + 132991488 a + 76771008 \) |
\( \bigl[a^{5} - 5 a^{3} + a^{2} + 4 a - 2\) , \( a^{4} - a^{3} - 4 a^{2} + 4 a + 2\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 18 a^{5} + 25 a^{4} - 73 a^{3} - 105 a^{2} + 12 a + 31\) , \( -81 a^{5} - 108 a^{4} + 346 a^{3} + 465 a^{2} - 124 a - 180\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+a^{2}+4a-2\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+4a+2\right){x}^{2}+\left(18a^{5}+25a^{4}-73a^{3}-105a^{2}+12a+31\right){x}-81a^{5}-108a^{4}+346a^{3}+465a^{2}-124a-180$ |
| 124.1-a3 |
124.1-a |
$6$ |
$18$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
124.1 |
\( 2^{2} \cdot 31 \) |
\( - 2^{12} \cdot 31^{3} \) |
$185.12584$ |
$(-2a^5+3a^4+15a^3-4a^2-22a-6), (3a^5-4a^4-23a^3+5a^2+36a+11)$ |
0 |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$26886.08527$ |
1.07740 |
\( \frac{1585885}{62} a^{5} - \frac{4757655}{124} a^{4} - \frac{11101195}{62} a^{3} + \frac{1585885}{31} a^{2} + \frac{7929425}{31} a + \frac{2656595}{31} \) |
\( \bigl[2 a^{5} - 3 a^{4} - 14 a^{3} + 4 a^{2} + 20 a + 6\) , \( 2 a^{5} - 3 a^{4} - 14 a^{3} + 4 a^{2} + 20 a + 7\) , \( 1\) , \( 1\) , \( 0\bigr] \) |
${y}^2+\left(2a^{5}-3a^{4}-14a^{3}+4a^{2}+20a+6\right){x}{y}+{y}={x}^{3}+\left(2a^{5}-3a^{4}-14a^{3}+4a^{2}+20a+7\right){x}^{2}+{x}$ |
| 124.1-a5 |
124.1-a |
$6$ |
$18$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
124.1 |
\( 2^{2} \cdot 31 \) |
\( 2^{6} \cdot 31^{6} \) |
$185.12584$ |
$(-2a^5+3a^4+15a^3-4a^2-22a-6), (3a^5-4a^4-23a^3+5a^2+36a+11)$ |
0 |
$\Z/18\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$26886.08527$ |
1.07740 |
\( \frac{718051522545}{961} a^{5} - \frac{2154154567635}{1922} a^{4} - \frac{5026360657815}{961} a^{3} + \frac{1436103045090}{961} a^{2} + \frac{7180515225450}{961} a + \frac{4752094637335}{1922} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 16 a^{5} - 24 a^{4} - 112 a^{3} + 32 a^{2} + 160 a + 31\) , \( -12 a^{5} + 18 a^{4} + 84 a^{3} - 24 a^{2} - 120 a - 25\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(16a^{5}-24a^{4}-112a^{3}+32a^{2}+160a+31\right){x}-12a^{5}+18a^{4}+84a^{3}-24a^{2}-120a-25$ |
*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.
