| 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 |
| 32.2-a2 |
32.2-a |
$2$ |
$5$ |
\(\Q(\sqrt{-79}) \) |
$2$ |
$[0, 1]$ |
32.2 |
\( 2^{5} \) |
\( 2^{24} \cdot 5^{12} \) |
$1.88903$ |
$(2,a), (2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.125088747$ |
$3.435235081$ |
3.867685449 |
\( -\frac{179945}{1024} a + \frac{111409}{256} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 2 a + 72\) , \( -60 a - 208\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(a-1\right){x}^2+\left(2a+72\right){x}-60a-208$ |
| 32.5-a2 |
32.5-a |
$2$ |
$5$ |
\(\Q(\sqrt{-79}) \) |
$2$ |
$[0, 1]$ |
32.5 |
\( 2^{5} \) |
\( 2^{24} \) |
$1.88903$ |
$(2,a), (2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2^{2} \) |
$0.625443736$ |
$3.435235081$ |
3.867685449 |
\( -\frac{179945}{1024} a + \frac{111409}{256} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -4 a - 11\) , \( -a + 17\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+a{x}^2+\left(-4a-11\right){x}-a+17$ |
| 128.2-d2 |
128.2-d |
$2$ |
$5$ |
\(\Q(\sqrt{-79}) \) |
$2$ |
$[0, 1]$ |
128.2 |
\( 2^{7} \) |
\( 2^{30} \) |
$2.67150$ |
$(2,a), (2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.287555632$ |
$2.429078021$ |
6.286946782 |
\( -\frac{179945}{1024} a + \frac{111409}{256} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -2 a + 12\) , \( 4 a - 16\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(-2a+12\right){x}+4a-16$ |
| 128.7-d2 |
128.7-d |
$2$ |
$5$ |
\(\Q(\sqrt{-79}) \) |
$2$ |
$[0, 1]$ |
128.7 |
\( 2^{7} \) |
\( 2^{30} \cdot 5^{12} \) |
$2.67150$ |
$(2,a), (2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2^{2} \) |
$1.437778161$ |
$2.429078021$ |
6.286946782 |
\( -\frac{179945}{1024} a + \frac{111409}{256} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 30 a - 98\) , \( 152 a + 712\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3-a{x}^2+\left(30a-98\right){x}+152a+712$ |
| 484.4-a2 |
484.4-a |
$2$ |
$5$ |
\(\Q(\sqrt{-79}) \) |
$2$ |
$[0, 1]$ |
484.4 |
\( 2^{2} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{6} \) |
$3.72532$ |
$(2,a), (2,a+1), (11,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.196922204$ |
$2.071524696$ |
7.343299505 |
\( -\frac{179945}{1024} a + \frac{111409}{256} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 10 a\) , \( -12 a - 64\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(-a+1\right){x}^2+10a{x}-12a-64$ |
| 484.6-a2 |
484.6-a |
$2$ |
$5$ |
\(\Q(\sqrt{-79}) \) |
$2$ |
$[0, 1]$ |
484.6 |
\( 2^{2} \cdot 11^{2} \) |
\( 2^{12} \cdot 5^{12} \cdot 11^{6} \) |
$3.72532$ |
$(2,a), (2,a+1), (11,a+9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2^{3} \) |
$0.984611023$ |
$2.071524696$ |
7.343299505 |
\( -\frac{179945}{1024} a + \frac{111409}{256} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -6 a - 220\) , \( 275 a - 1647\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2+\left(-6a-220\right){x}+275a-1647$ |
| 800.13-c2 |
800.13-c |
$2$ |
$5$ |
\(\Q(\sqrt{-79}) \) |
$2$ |
$[0, 1]$ |
800.13 |
\( 2^{5} \cdot 5^{2} \) |
\( 2^{36} \cdot 5^{6} \) |
$4.22401$ |
$(2,a), (2,a+1), (5,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2^{2} \) |
$3.034220434$ |
$1.536283832$ |
8.391218424 |
\( -\frac{179945}{1024} a + \frac{111409}{256} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -8 a - 48\) , \( -12 a - 272\bigr] \) |
${y}^2={x}^3+{x}^2+\left(-8a-48\right){x}-12a-272$ |
| 800.15-a2 |
800.15-a |
$2$ |
$5$ |
\(\Q(\sqrt{-79}) \) |
$2$ |
$[0, 1]$ |
800.15 |
\( 2^{5} \cdot 5^{2} \) |
\( 2^{36} \cdot 5^{6} \) |
$4.22401$ |
$(2,a), (2,a+1), (5,a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.536283832$ |
1.382763481 |
\( -\frac{179945}{1024} a + \frac{111409}{256} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -18 a - 35\) , \( 46 a + 377\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a-1\right){x}^2+\left(-18a-35\right){x}+46a+377$ |
| 800.4-a2 |
800.4-a |
$2$ |
$5$ |
\(\Q(\sqrt{-79}) \) |
$2$ |
$[0, 1]$ |
800.4 |
\( 2^{5} \cdot 5^{2} \) |
\( 2^{36} \cdot 5^{6} \) |
$4.22401$ |
$(2,a), (2,a+1), (5,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.536283832$ |
1.382763481 |
\( -\frac{179945}{1024} a + \frac{111409}{256} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -8 a - 48\) , \( 12 a + 272\bigr] \) |
${y}^2={x}^3-{x}^2+\left(-8a-48\right){x}+12a+272$ |
| 800.6-c2 |
800.6-c |
$2$ |
$5$ |
\(\Q(\sqrt{-79}) \) |
$2$ |
$[0, 1]$ |
800.6 |
\( 2^{5} \cdot 5^{2} \) |
\( 2^{24} \cdot 5^{18} \) |
$4.22401$ |
$(2,a), (2,a+1), (5,a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.606844086$ |
$1.536283832$ |
8.391218424 |
\( -\frac{179945}{1024} a + \frac{111409}{256} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 75 a + 177\) , \( 546 a - 3674\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(75a+177\right){x}+546a-3674$ |
*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.
