| 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 |
| 73.2-a3 |
73.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
73.2 |
\( 73 \) |
\( 73 \) |
$0.45241$ |
$(9a-8)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 1 \) |
$1$ |
$9.727002267$ |
0.311993743 |
\( -\frac{9927}{73} a + \frac{30887}{73} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -a - 1\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a-1\right){x}$ |
| 5329.3-a3 |
5329.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
5329.3 |
\( 73^{2} \) |
\( 73^{7} \) |
$1.32239$ |
$(9a-8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$0.828937186$ |
$1.138459504$ |
2.179408166 |
\( -\frac{9927}{73} a + \frac{30887}{73} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -26 a + 9\) , \( -72 a - 24\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-26a+9\right){x}-72a-24$ |
| 12337.2-c4 |
12337.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12337.2 |
\( 13^{2} \cdot 73 \) |
\( 13^{6} \cdot 73 \) |
$1.63118$ |
$(-4a+1), (9a-8)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$2.697785033$ |
3.115133830 |
\( -\frac{9927}{73} a + \frac{30887}{73} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 5 a - 1\) , \( 9 a - 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(5a-1\right){x}+9a-7$ |
| 12337.6-a4 |
12337.6-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12337.6 |
\( 13^{2} \cdot 73 \) |
\( 13^{6} \cdot 73 \) |
$1.63118$ |
$(4a-3), (9a-8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2 \) |
$1.034235357$ |
$2.697785033$ |
3.221781549 |
\( -\frac{9927}{73} a + \frac{30887}{73} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 2 a - 4\) , \( 5\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(2a-4\right){x}+5$ |
| 18688.2-e4 |
18688.2-e |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
18688.2 |
\( 2^{8} \cdot 73 \) |
\( 2^{24} \cdot 73 \) |
$1.80963$ |
$(9a-8), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$2.431750566$ |
2.807943688 |
\( -\frac{9927}{73} a + \frac{30887}{73} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 3 a - 6\) , \( -9 a - 1\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(3a-6\right){x}-9a-1$ |
| 32193.2-b4 |
32193.2-b |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32193.2 |
\( 3^{2} \cdot 7^{2} \cdot 73 \) |
\( 3^{6} \cdot 7^{6} \cdot 73 \) |
$2.07319$ |
$(-2a+1), (-3a+1), (9a-8)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$2.122605913$ |
2.450974190 |
\( -\frac{9927}{73} a + \frac{30887}{73} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 2 a + 5\) , \( -2 a - 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+5\right){x}-2a-7$ |
| 32193.6-a4 |
32193.6-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32193.6 |
\( 3^{2} \cdot 7^{2} \cdot 73 \) |
\( 3^{6} \cdot 7^{6} \cdot 73 \) |
$2.07319$ |
$(-2a+1), (3a-2), (9a-8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$0.349859445$ |
$2.122605913$ |
3.429985888 |
\( -\frac{9927}{73} a + \frac{30887}{73} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 5 a + 1\) , \( -14 a + 10\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(5a+1\right){x}-14a+10$ |
| 45625.2-a4 |
45625.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
45625.2 |
\( 5^{4} \cdot 73 \) |
\( 5^{12} \cdot 73 \) |
$2.26204$ |
$(9a-8), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2 \) |
$2.072711932$ |
$1.945400453$ |
4.656046711 |
\( -\frac{9927}{73} a + \frac{30887}{73} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 4 a - 9\) , \( 13 a + 1\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(4a-9\right){x}+13a+1$ |
| 99937.2-a4 |
99937.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99937.2 |
\( 37^{2} \cdot 73 \) |
\( 37^{6} \cdot 73 \) |
$2.75189$ |
$(-7a+4), (9a-8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2 \) |
$1.878939471$ |
$1.599109322$ |
3.469447446 |
\( -\frac{9927}{73} a + \frac{30887}{73} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -8 a - 4\) , \( -17 a + 33\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-8a-4\right){x}-17a+33$ |
| 99937.6-a4 |
99937.6-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99937.6 |
\( 37^{2} \cdot 73 \) |
\( 37^{6} \cdot 73 \) |
$2.75189$ |
$(-7a+3), (9a-8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2 \) |
$1.831328087$ |
$1.599109322$ |
3.381533386 |
\( -\frac{9927}{73} a + \frac{30887}{73} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -5 a - 8\) , \( 24 a - 32\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-5a-8\right){x}+24a-32$ |
*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.
