| 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 |
| 405.1-a1 |
405.1-a |
$2$ |
$2$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
405.1 |
\( 3^{4} \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$8.46419$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.123068789$ |
$478.0754711$ |
2.631233489 |
\( \frac{775424}{15} a^{2} - \frac{357184}{5} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{2} + a + 3\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -a^{3} - 2 a^{2} + 3 a + 7\) , \( -14 a^{3} - 17 a^{2} + 50 a + 60\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-a^{3}-2a^{2}+3a+7\right){x}-14a^{3}-17a^{2}+50a+60$ |
| 405.1-a2 |
405.1-a |
$2$ |
$2$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
405.1 |
\( 3^{4} \cdot 5 \) |
\( 3^{8} \cdot 5^{2} \) |
$8.46419$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.061534394$ |
$478.0754711$ |
2.631233489 |
\( -\frac{641792}{45} a^{2} + \frac{464320}{9} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{2} - 3\) , \( 1\) , \( a^{3} + a^{2} - 3 a - 4\) , \( -2 a^{3} + a^{2} + 5 a + 1\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(a^{3}+a^{2}-3a-4\right){x}-2a^{3}+a^{2}+5a+1$ |
| 405.1-b1 |
405.1-b |
$2$ |
$2$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
405.1 |
\( 3^{4} \cdot 5 \) |
\( 3^{8} \cdot 5^{2} \) |
$8.46419$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.061534394$ |
$478.0754711$ |
2.631233489 |
\( \frac{641792}{45} a^{2} - \frac{177472}{9} \) |
\( \bigl[a^{2} + a - 3\) , \( a^{2} - 4\) , \( a^{3} - 2 a\) , \( -3 a^{2} + a + 5\) , \( -a^{3} + 5 a - 5\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-3a^{2}+a+5\right){x}-a^{3}+5a-5$ |
| 405.1-b2 |
405.1-b |
$2$ |
$2$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
405.1 |
\( 3^{4} \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$8.46419$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.123068789$ |
$478.0754711$ |
2.631233489 |
\( -\frac{775424}{15} a^{2} + \frac{2805568}{15} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{2} + a - 2\) , \( 2\) , \( 8 a^{3} + 17 a^{2} - 10 a - 25\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-2\right){x}^{2}+2{x}+8a^{3}+17a^{2}-10a-25$ |
| 405.1-c1 |
405.1-c |
$10$ |
$32$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
405.1 |
\( 3^{4} \cdot 5 \) |
\( 3^{8} \cdot 5^{2} \) |
$8.46419$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4096$ |
\( 2^{2} \) |
$1$ |
$0.015032122$ |
1.376782212 |
\( \frac{152409672113485069453847362}{45} a^{2} - \frac{42124997329321868998968185}{9} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + 4\) , \( 1\) , \( 4363 a^{2} - 20828\) , \( 255406 a^{2} - 1062683\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(4363a^{2}-20828\right){x}+255406a^{2}-1062683$ |
| 405.1-c2 |
405.1-c |
$10$ |
$32$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
405.1 |
\( 3^{4} \cdot 5 \) |
\( 3^{8} \cdot 5^{2} \) |
$8.46419$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4096$ |
\( 2^{2} \) |
$1$ |
$0.015032122$ |
1.376782212 |
\( -\frac{152409672113485069453847362}{45} a^{2} + \frac{110284674784163200454879177}{9} \) |
\( \bigl[a^{2} - 2\) , \( a^{2} - 4\) , \( a^{2} - 3\) , \( -4366 a^{2} + 993\) , \( -251041 a^{2} + 213356\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-4366a^{2}+993\right){x}-251041a^{2}+213356$ |
| 405.1-c3 |
405.1-c |
$10$ |
$32$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
405.1 |
\( 3^{4} \cdot 5 \) |
\( 3^{16} \cdot 5^{4} \) |
$8.46419$ |
$(a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$256$ |
\( 2^{4} \) |
$1$ |
$0.240513954$ |
1.376782212 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-2160{x}-39540$ |
| 405.1-c4 |
405.1-c |
$10$ |
$32$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
405.1 |
\( 3^{4} \cdot 5 \) |
\( 3^{32} \cdot 5^{8} \) |
$8.46419$ |
$(a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{6} \) |
$1$ |
$3.848223270$ |
1.376782212 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-135{x}-660$ |
| 405.1-c5 |
405.1-c |
$10$ |
$32$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
405.1 |
\( 3^{4} \cdot 5 \) |
\( 3^{64} \cdot 5^{4} \) |
$8.46419$ |
$(a), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$64$ |
\( 2^{6} \) |
$1$ |
$0.240513954$ |
1.376782212 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-110{x}-880$ |
| 405.1-c6 |
405.1-c |
$10$ |
$32$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
405.1 |
\( 3^{4} \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$8.46419$ |
$(a), (3)$ |
0 |
$\Z/16\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$985.1451572$ |
1.376782212 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-80{x}+242$ |
| 405.1-c7 |
405.1-c |
$10$ |
$32$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
405.1 |
\( 3^{4} \cdot 5 \) |
\( 3^{16} \cdot 5^{16} \) |
$8.46419$ |
$(a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{6} \) |
$1$ |
$61.57157232$ |
1.376782212 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-10{x}-10$ |
| 405.1-c8 |
405.1-c |
$10$ |
$32$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
405.1 |
\( 3^{4} \cdot 5 \) |
\( 3^{8} \cdot 5^{8} \) |
$8.46419$ |
$(a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$985.1451572$ |
1.376782212 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-5{x}+2$ |
| 405.1-c9 |
405.1-c |
$10$ |
$32$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
405.1 |
\( 3^{4} \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$8.46419$ |
$(a), (3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$985.1451572$ |
1.376782212 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}$ |
| 405.1-c10 |
405.1-c |
$10$ |
$32$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
405.1 |
\( 3^{4} \cdot 5 \) |
\( 3^{8} \cdot 5^{32} \) |
$8.46419$ |
$(a), (3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{6} \) |
$1$ |
$3.848223270$ |
1.376782212 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+35{x}-28$ |
| 405.1-d1 |
405.1-d |
$10$ |
$32$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
405.1 |
\( 3^{4} \cdot 5 \) |
\( 3^{8} \cdot 5^{2} \) |
$8.46419$ |
$(a), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$25.96899649$ |
2.322737659 |
\( -\frac{152409672113485069453847362}{45} a^{2} + \frac{110284674784163200454879177}{9} \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{2} + 3\) , \( a\) , \( -4367 a^{2} + 996\) , \( 251041 a^{2} - 213357\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-4367a^{2}+996\right){x}+251041a^{2}-213357$ |
| 405.1-d2 |
405.1-d |
$10$ |
$32$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
405.1 |
\( 3^{4} \cdot 5 \) |
\( 3^{16} \cdot 5^{4} \) |
$8.46419$ |
$(a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$103.8759859$ |
2.322737659 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[a^{3} - 2 a\) , \( -a^{2} + 3\) , \( 0\) , \( -2159\) , \( 37380\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}-2159{x}+37380$ |
| 405.1-d3 |
405.1-d |
$10$ |
$32$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
405.1 |
\( 3^{4} \cdot 5 \) |
\( 3^{32} \cdot 5^{8} \) |
$8.46419$ |
$(a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$103.8759859$ |
2.322737659 |
\( \frac{272223782641}{164025} \) |
\( \bigl[a^{3} - 2 a\) , \( -a^{2} + 3\) , \( 0\) , \( -134\) , \( 525\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}-134{x}+525$ |
| 405.1-d4 |
405.1-d |
$10$ |
$32$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
405.1 |
\( 3^{4} \cdot 5 \) |
\( 3^{64} \cdot 5^{4} \) |
$8.46419$ |
$(a), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{6} \) |
$1$ |
$6.492249124$ |
2.322737659 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[a^{3} - 2 a\) , \( -a^{2} + 3\) , \( 0\) , \( -109\) , \( 770\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}-109{x}+770$ |
| 405.1-d5 |
405.1-d |
$10$ |
$32$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
405.1 |
\( 3^{4} \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$8.46419$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$6.492249124$ |
2.322737659 |
\( \frac{56667352321}{15} \) |
\( \bigl[a^{3} - 2 a\) , \( -a^{2} + 3\) , \( 0\) , \( -79\) , \( -322\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}-79{x}-322$ |
| 405.1-d6 |
405.1-d |
$10$ |
$32$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
405.1 |
\( 3^{4} \cdot 5 \) |
\( 3^{16} \cdot 5^{16} \) |
$8.46419$ |
$(a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$103.8759859$ |
2.322737659 |
\( \frac{111284641}{50625} \) |
\( \bigl[a^{3} - 2 a\) , \( -a^{2} + 3\) , \( 0\) , \( -9\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}-9{x}$ |
| 405.1-d7 |
405.1-d |
$10$ |
$32$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
405.1 |
\( 3^{4} \cdot 5 \) |
\( 3^{8} \cdot 5^{8} \) |
$8.46419$ |
$(a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$103.8759859$ |
2.322737659 |
\( \frac{13997521}{225} \) |
\( \bigl[a^{3} - 2 a\) , \( -a^{2} + 3\) , \( 0\) , \( -4\) , \( -7\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}-4{x}-7$ |
| 405.1-d8 |
405.1-d |
$10$ |
$32$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
405.1 |
\( 3^{4} \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$8.46419$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$103.8759859$ |
2.322737659 |
\( -\frac{1}{15} \) |
\( \bigl[a^{3} - 2 a\) , \( -a^{2} + 3\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+{x}$ |
| 405.1-d9 |
405.1-d |
$10$ |
$32$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
405.1 |
\( 3^{4} \cdot 5 \) |
\( 3^{8} \cdot 5^{32} \) |
$8.46419$ |
$(a), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{6} \) |
$1$ |
$6.492249124$ |
2.322737659 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[a^{3} - 2 a\) , \( -a^{2} + 3\) , \( 0\) , \( 36\) , \( 63\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+36{x}+63$ |
| 405.1-d10 |
405.1-d |
$10$ |
$32$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
405.1 |
\( 3^{4} \cdot 5 \) |
\( 3^{8} \cdot 5^{2} \) |
$8.46419$ |
$(a), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$25.96899649$ |
2.322737659 |
\( \frac{152409672113485069453847362}{45} a^{2} - \frac{42124997329321868998968185}{9} \) |
\( \bigl[a\) , \( a^{2} - 2\) , \( a^{3} - 3 a\) , \( 4365 a^{2} - 20834\) , \( -251041 a^{2} + 1041848\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(4365a^{2}-20834\right){x}-251041a^{2}+1041848$ |
| 405.1-e1 |
405.1-e |
$2$ |
$2$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
405.1 |
\( 3^{4} \cdot 5 \) |
\( 3^{8} \cdot 5^{2} \) |
$8.46419$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.061534394$ |
$478.0754711$ |
2.631233489 |
\( \frac{641792}{45} a^{2} - \frac{177472}{9} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{3} - a^{2} + 3 a + 2\) , \( 1\) , \( -2 a^{2} + a + 4\) , \( a^{3} - a^{2} - 5 a + 6\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+{y}={x}^{3}+\left(-a^{3}-a^{2}+3a+2\right){x}^{2}+\left(-2a^{2}+a+4\right){x}+a^{3}-a^{2}-5a+6$ |
| 405.1-e2 |
405.1-e |
$2$ |
$2$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
405.1 |
\( 3^{4} \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$8.46419$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.123068789$ |
$478.0754711$ |
2.631233489 |
\( -\frac{775424}{15} a^{2} + \frac{2805568}{15} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{3} - a^{2} + 3 a + 3\) , \( 1\) , \( -2 a^{3} - a^{2} + 8 a + 5\) , \( -9 a^{3} - 17 a^{2} + 14 a + 26\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+{y}={x}^{3}+\left(-a^{3}-a^{2}+3a+3\right){x}^{2}+\left(-2a^{3}-a^{2}+8a+5\right){x}-9a^{3}-17a^{2}+14a+26$ |
| 405.1-f1 |
405.1-f |
$2$ |
$2$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
405.1 |
\( 3^{4} \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$8.46419$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.123068789$ |
$478.0754711$ |
2.631233489 |
\( \frac{775424}{15} a^{2} - \frac{357184}{5} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{3} - a^{2} + 2 a + 3\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{3} - 2 a^{2} - 4 a + 7\) , \( 15 a^{3} - 17 a^{2} - 54 a + 60\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(-a^{3}-a^{2}+2a+3\right){x}^{2}+\left(a^{3}-2a^{2}-4a+7\right){x}+15a^{3}-17a^{2}-54a+60$ |
| 405.1-f2 |
405.1-f |
$2$ |
$2$ |
\(\Q(\zeta_{20})^+\) |
$4$ |
$[4, 0]$ |
405.1 |
\( 3^{4} \cdot 5 \) |
\( 3^{8} \cdot 5^{2} \) |
$8.46419$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.061534394$ |
$478.0754711$ |
2.631233489 |
\( -\frac{641792}{45} a^{2} + \frac{464320}{9} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{2} - a + 4\) , \( a^{2} + a - 2\) , \( a^{3} - 2 a^{2} - 5 a + 5\) , \( 3 a^{3} - a^{2} - 9 a - 3\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(a^{3}-2a^{2}-5a+5\right){x}+3a^{3}-a^{2}-9a-3$ |
*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.
