| 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 |
| 9.1-a1 |
9.1-a |
$2$ |
$5$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{6} \) |
$119.55466$ |
$(2a^5-a^4-14a^3+2a^2+23a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$1226.536094$ |
1.10096 |
\( \frac{79572442844}{27} a^{5} + \frac{179028656408}{27} a^{4} - \frac{154197900412}{27} a^{3} - \frac{506013769217}{27} a^{2} - \frac{263202231980}{27} a - \frac{35350337779}{27} \) |
\( \bigl[-a^{5} + 7 a^{3} + 2 a^{2} - 11 a - 5\) , \( 4 a^{5} - 2 a^{4} - 27 a^{3} + 3 a^{2} + 41 a + 15\) , \( -a^{5} + a^{4} + 6 a^{3} - 3 a^{2} - 8 a - 3\) , \( 18 a^{5} + 6 a^{4} - 105 a^{3} - 50 a^{2} + 97 a + 43\) , \( 47 a^{5} + 62 a^{4} - 218 a^{3} - 338 a^{2} - 56 a + 22\bigr] \) |
${y}^2+\left(-a^{5}+7a^{3}+2a^{2}-11a-5\right){x}{y}+\left(-a^{5}+a^{4}+6a^{3}-3a^{2}-8a-3\right){y}={x}^{3}+\left(4a^{5}-2a^{4}-27a^{3}+3a^{2}+41a+15\right){x}^{2}+\left(18a^{5}+6a^{4}-105a^{3}-50a^{2}+97a+43\right){x}+47a^{5}+62a^{4}-218a^{3}-338a^{2}-56a+22$ |
| 9.1-a2 |
9.1-a |
$2$ |
$5$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{30} \) |
$119.55466$ |
$(2a^5-a^4-14a^3+2a^2+23a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 1 \) |
$1$ |
$1226.536094$ |
1.10096 |
\( -\frac{47946476284126}{14348907} a^{5} - \frac{21211156063675}{14348907} a^{4} + \frac{404669473071680}{14348907} a^{3} + \frac{98469557612671}{14348907} a^{2} - \frac{670666419604364}{14348907} a - \frac{290449774050121}{14348907} \) |
\( \bigl[-2 a^{5} + a^{4} + 14 a^{3} - a^{2} - 22 a - 10\) , \( -a^{5} + a^{4} + 7 a^{3} - 4 a^{2} - 11 a - 1\) , \( -4 a^{5} + 2 a^{4} + 27 a^{3} - 4 a^{2} - 42 a - 12\) , \( -77 a^{5} + 37 a^{4} + 522 a^{3} - 95 a^{2} - 804 a - 158\) , \( -354 a^{5} + 162 a^{4} + 2399 a^{3} - 399 a^{2} - 3697 a - 758\bigr] \) |
${y}^2+\left(-2a^{5}+a^{4}+14a^{3}-a^{2}-22a-10\right){x}{y}+\left(-4a^{5}+2a^{4}+27a^{3}-4a^{2}-42a-12\right){y}={x}^{3}+\left(-a^{5}+a^{4}+7a^{3}-4a^{2}-11a-1\right){x}^{2}+\left(-77a^{5}+37a^{4}+522a^{3}-95a^{2}-804a-158\right){x}-354a^{5}+162a^{4}+2399a^{3}-399a^{2}-3697a-758$ |
| 9.1-b1 |
9.1-b |
$2$ |
$5$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{2} \) |
$119.55466$ |
$(2a^5-a^4-14a^3+2a^2+23a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 1 \) |
$0.016952447$ |
$26721.26522$ |
2.43968 |
\( -\frac{961893898216}{3} a^{5} + \frac{211583061698}{3} a^{4} + \frac{6688850789906}{3} a^{3} + \frac{455704107955}{3} a^{2} - \frac{10690384702193}{3} a - \frac{4398914300311}{3} \) |
\( \bigl[-4 a^{5} + 2 a^{4} + 27 a^{3} - 3 a^{2} - 41 a - 15\) , \( a^{5} - 6 a^{3} - a^{2} + 6 a + 1\) , \( -a^{5} + a^{4} + 6 a^{3} - 3 a^{2} - 8 a - 2\) , \( 22 a^{5} + 2 a^{4} - 126 a^{3} - 50 a^{2} + 137 a + 62\) , \( -20 a^{5} - 105 a^{4} + 48 a^{3} + 445 a^{2} + 407 a + 102\bigr] \) |
${y}^2+\left(-4a^{5}+2a^{4}+27a^{3}-3a^{2}-41a-15\right){x}{y}+\left(-a^{5}+a^{4}+6a^{3}-3a^{2}-8a-2\right){y}={x}^{3}+\left(a^{5}-6a^{3}-a^{2}+6a+1\right){x}^{2}+\left(22a^{5}+2a^{4}-126a^{3}-50a^{2}+137a+62\right){x}-20a^{5}-105a^{4}+48a^{3}+445a^{2}+407a+102$ |
| 9.1-b2 |
9.1-b |
$2$ |
$5$ |
6.6.1241125.1 |
$6$ |
$[6, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{10} \) |
$119.55466$ |
$(2a^5-a^4-14a^3+2a^2+23a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 5 \) |
$0.003390489$ |
$26721.26522$ |
2.43968 |
\( \frac{17522450}{243} a^{5} + \frac{39783650}{243} a^{4} - \frac{33141304}{243} a^{3} - \frac{112323782}{243} a^{2} - \frac{60359501}{243} a - \frac{8259061}{243} \) |
\( \bigl[-3 a^{5} + 2 a^{4} + 20 a^{3} - 5 a^{2} - 31 a - 10\) , \( -4 a^{5} + 2 a^{4} + 27 a^{3} - 4 a^{2} - 42 a - 12\) , \( -3 a^{5} + a^{4} + 20 a^{3} - 30 a - 11\) , \( -8 a^{5} + 2 a^{4} + 54 a^{3} + a^{2} - 82 a - 26\) , \( 2 a^{5} - 14 a^{3} - 4 a^{2} + 22 a + 14\bigr] \) |
${y}^2+\left(-3a^{5}+2a^{4}+20a^{3}-5a^{2}-31a-10\right){x}{y}+\left(-3a^{5}+a^{4}+20a^{3}-30a-11\right){y}={x}^{3}+\left(-4a^{5}+2a^{4}+27a^{3}-4a^{2}-42a-12\right){x}^{2}+\left(-8a^{5}+2a^{4}+54a^{3}+a^{2}-82a-26\right){x}+2a^{5}-14a^{3}-4a^{2}+22a+14$ |
*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.
