| 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 |
| 42483.2-a1 |
42483.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
42483.2 |
\( 3 \cdot 7^{2} \cdot 17^{2} \) |
\( 3^{34} \cdot 7^{8} \cdot 17^{2} \) |
$2.22205$ |
$(-2a+1), (-3a+1), (3a-2), (17)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$0.104805898$ |
0.968155418 |
\( \frac{5009339741732864}{5271114033171} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 3565\) , \( 72914\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}+3565{x}+72914$ |
| 42483.2-b1 |
42483.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
42483.2 |
\( 3 \cdot 7^{2} \cdot 17^{2} \) |
\( 3^{2} \cdot 7^{8} \cdot 17^{2} \) |
$2.22205$ |
$(-2a+1), (-3a+1), (3a-2), (17)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2^{5} \) |
$0.010455521$ |
$1.976299793$ |
3.054062238 |
\( -\frac{16777216}{122451} \) |
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( 5 a\) , \( -16\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+5a{x}-16$ |
| 42483.2-c1 |
42483.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
42483.2 |
\( 3 \cdot 7^{2} \cdot 17^{2} \) |
\( 3^{6} \cdot 7^{12} \cdot 17^{2} \) |
$2.22205$ |
$(-2a+1), (-3a+1), (3a-2), (17)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \cdot 5 \) |
$0.049981145$ |
$0.622217189$ |
2.872814360 |
\( \frac{205512830885888}{129656139291} a + \frac{2108123474022400}{129656139291} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -181 a - 38\) , \( 1243 a - 326\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}+\left(-181a-38\right){x}+1243a-326$ |
| 42483.2-d1 |
42483.2-d |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
42483.2 |
\( 3 \cdot 7^{2} \cdot 17^{2} \) |
\( 3^{6} \cdot 7^{12} \cdot 17^{2} \) |
$2.22205$ |
$(-2a+1), (-3a+1), (3a-2), (17)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \cdot 5 \) |
$0.049981145$ |
$0.622217189$ |
2.872814360 |
\( -\frac{205512830885888}{129656139291} a + \frac{771212101636096}{43218713097} \) |
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( 38 a + 181\) , \( -1243 a + 917\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(38a+181\right){x}-1243a+917$ |
| 42483.2-e1 |
42483.2-e |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
42483.2 |
\( 3 \cdot 7^{2} \cdot 17^{2} \) |
\( 3^{2} \cdot 7^{4} \cdot 17^{6} \) |
$2.22205$ |
$(-2a+1), (-3a+1), (3a-2), (17)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2^{3} \cdot 3 \) |
$0.049501407$ |
$1.457177004$ |
3.997978591 |
\( \frac{841232384}{722211} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -20 a\) , \( -17\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}-20a{x}-17$ |
| 42483.2-f1 |
42483.2-f |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
42483.2 |
\( 3 \cdot 7^{2} \cdot 17^{2} \) |
\( 3^{14} \cdot 7^{4} \cdot 17^{2} \) |
$2.22205$ |
$(-2a+1), (-3a+1), (3a-2), (17)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2^{3} \cdot 7 \) |
$0.029120331$ |
$1.168373965$ |
4.400130743 |
\( -\frac{8390176768}{1821771} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 42 a\) , \( 110\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+42a{x}+110$ |
*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.
