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-a2 |
73.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
73.2 |
\( 73 \) |
\( 73^{2} \) |
$0.45241$ |
$(9a-8)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2 \) |
$1$ |
$4.863501133$ |
0.311993743 |
\( \frac{927841113}{5329} a - \frac{1323774856}{5329} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -6 a - 1\) , \( 4 a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-6a-1\right){x}+4a$ |
5329.3-a2 |
5329.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
5329.3 |
\( 73^{2} \) |
\( 73^{8} \) |
$1.32239$ |
$(9a-8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1.657874373$ |
$0.569229752$ |
2.179408166 |
\( \frac{927841113}{5329} a - \frac{1323774856}{5329} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -341 a - 76\) , \( -3390 a + 857\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-341a-76\right){x}-3390a+857$ |
12337.2-c2 |
12337.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12337.2 |
\( 13^{2} \cdot 73 \) |
\( 13^{6} \cdot 73^{2} \) |
$1.63118$ |
$(-4a+1), (9a-8)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$1.348892516$ |
3.115133830 |
\( \frac{927841113}{5329} a - \frac{1323774856}{5329} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 40 a + 39\) , \( 226 a - 266\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(40a+39\right){x}+226a-266$ |
12337.6-a2 |
12337.6-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12337.6 |
\( 13^{2} \cdot 73 \) |
\( 13^{6} \cdot 73^{2} \) |
$1.63118$ |
$(4a-3), (9a-8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$0.517117678$ |
$1.348892516$ |
3.221781549 |
\( \frac{927841113}{5329} a - \frac{1323774856}{5329} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 77 a - 44\) , \( 178 a + 34\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(77a-44\right){x}+178a+34$ |
18688.2-e2 |
18688.2-e |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
18688.2 |
\( 2^{8} \cdot 73 \) |
\( 2^{24} \cdot 73^{2} \) |
$1.80963$ |
$(9a-8), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$1.215875283$ |
2.807943688 |
\( \frac{927841113}{5329} a - \frac{1323774856}{5329} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 83 a - 86\) , \( -345 a + 159\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(83a-86\right){x}-345a+159$ |
32193.2-b2 |
32193.2-b |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32193.2 |
\( 3^{2} \cdot 7^{2} \cdot 73 \) |
\( 3^{6} \cdot 7^{6} \cdot 73^{2} \) |
$2.07319$ |
$(-2a+1), (-3a+1), (9a-8)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$1.061302956$ |
2.450974190 |
\( \frac{927841113}{5329} a - \frac{1323774856}{5329} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -43 a + 125\) , \( -416 a + 68\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-43a+125\right){x}-416a+68$ |
32193.6-a2 |
32193.6-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32193.6 |
\( 3^{2} \cdot 7^{2} \cdot 73 \) |
\( 3^{6} \cdot 7^{6} \cdot 73^{2} \) |
$2.07319$ |
$(-2a+1), (3a-2), (9a-8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$0.699718891$ |
$1.061302956$ |
3.429985888 |
\( \frac{927841113}{5329} a - \frac{1323774856}{5329} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 50 a + 76\) , \( -443 a + 520\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(50a+76\right){x}-443a+520$ |
45625.2-a2 |
45625.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
45625.2 |
\( 5^{4} \cdot 73 \) |
\( 5^{12} \cdot 73^{2} \) |
$2.26204$ |
$(9a-8), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1.036355966$ |
$0.972700226$ |
4.656046711 |
\( \frac{927841113}{5329} a - \frac{1323774856}{5329} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 129 a - 134\) , \( 638 a - 374\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(129a-134\right){x}+638a-374$ |
99937.2-a2 |
99937.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99937.2 |
\( 37^{2} \cdot 73 \) |
\( 37^{6} \cdot 73^{2} \) |
$2.75189$ |
$(-7a+4), (9a-8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$0.939469735$ |
$0.799554661$ |
3.469447446 |
\( \frac{927841113}{5329} a - \frac{1323774856}{5329} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -43 a - 169\) , \( 264 a + 771\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-43a-169\right){x}+264a+771$ |
99937.6-a2 |
99937.6-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99937.6 |
\( 37^{2} \cdot 73 \) |
\( 37^{6} \cdot 73^{2} \) |
$2.75189$ |
$(-7a+3), (9a-8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$0.915664043$ |
$0.799554661$ |
3.381533386 |
\( \frac{927841113}{5329} a - \frac{1323774856}{5329} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 30 a - 208\) , \( 253 a - 1145\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(30a-208\right){x}+253a-1145$ |
*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.