| 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 |
| 73.1-a2 |
73.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
73.1 |
\( 73 \) |
\( 73^{2} \) |
$0.45241$ |
$(-9a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2 \) |
$1$ |
$4.863501133$ |
0.311993743 |
\( -\frac{927841113}{5329} a - \frac{395933743}{5329} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 5\) , \( -4 a + 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+5{x}-4a+4$ |
| 5329.1-a2 |
5329.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
5329.1 |
\( 73^{2} \) |
\( 73^{8} \) |
$1.32239$ |
$(-9a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1.657874373$ |
$0.569229752$ |
2.179408166 |
\( -\frac{927841113}{5329} a - \frac{395933743}{5329} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 75 a + 341\) , \( 3389 a - 2532\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(75a+341\right){x}+3389a-2532$ |
| 12337.1-a2 |
12337.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12337.1 |
\( 13^{2} \cdot 73 \) |
\( 13^{6} \cdot 73^{2} \) |
$1.63118$ |
$(-4a+1), (-9a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$0.517117678$ |
$1.348892516$ |
3.221781549 |
\( -\frac{927841113}{5329} a - \frac{395933743}{5329} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -79 a + 35\) , \( -179 a + 213\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-79a+35\right){x}-179a+213$ |
| 12337.5-c2 |
12337.5-c |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12337.5 |
\( 13^{2} \cdot 73 \) |
\( 13^{6} \cdot 73^{2} \) |
$1.63118$ |
$(4a-3), (-9a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$1.348892516$ |
3.115133830 |
\( -\frac{927841113}{5329} a - \frac{395933743}{5329} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -40 a + 79\) , \( -147 a - 80\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-40a+79\right){x}-147a-80$ |
| 18688.1-e2 |
18688.1-e |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
18688.1 |
\( 2^{8} \cdot 73 \) |
\( 2^{24} \cdot 73^{2} \) |
$1.80963$ |
$(-9a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$1.215875283$ |
2.807943688 |
\( -\frac{927841113}{5329} a - \frac{395933743}{5329} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 86 a - 83\) , \( 345 a - 186\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(86a-83\right){x}+345a-186$ |
| 32193.1-a2 |
32193.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32193.1 |
\( 3^{2} \cdot 7^{2} \cdot 73 \) |
\( 3^{6} \cdot 7^{6} \cdot 73^{2} \) |
$2.07319$ |
$(-2a+1), (-3a+1), (-9a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$0.699718891$ |
$1.061302956$ |
3.429985888 |
\( -\frac{927841113}{5329} a - \frac{395933743}{5329} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 128 a - 76\) , \( 494 a - 50\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(128a-76\right){x}+494a-50$ |
| 32193.5-b2 |
32193.5-b |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32193.5 |
\( 3^{2} \cdot 7^{2} \cdot 73 \) |
\( 3^{6} \cdot 7^{6} \cdot 73^{2} \) |
$2.07319$ |
$(-2a+1), (3a-2), (-9a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$1.061302956$ |
2.450974190 |
\( -\frac{927841113}{5329} a - \frac{395933743}{5329} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 81 a - 126\) , \( 497 a - 473\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(81a-126\right){x}+497a-473$ |
| 45625.1-a2 |
45625.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
45625.1 |
\( 5^{4} \cdot 73 \) |
\( 5^{12} \cdot 73^{2} \) |
$2.26204$ |
$(-9a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1.036355966$ |
$0.972700226$ |
4.656046711 |
\( -\frac{927841113}{5329} a - \frac{395933743}{5329} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -5 a + 134\) , \( -638 a + 264\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-5a+134\right){x}-638a+264$ |
| 99937.1-a2 |
99937.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99937.1 |
\( 37^{2} \cdot 73 \) |
\( 37^{6} \cdot 73^{2} \) |
$2.75189$ |
$(-7a+4), (-9a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$0.915664043$ |
$0.799554661$ |
3.381533386 |
\( -\frac{927841113}{5329} a - \frac{395933743}{5329} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 208 a - 30\) , \( -253 a - 892\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(208a-30\right){x}-253a-892$ |
| 99937.5-a2 |
99937.5-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99937.5 |
\( 37^{2} \cdot 73 \) |
\( 37^{6} \cdot 73^{2} \) |
$2.75189$ |
$(-7a+3), (-9a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$0.939469735$ |
$0.799554661$ |
3.469447446 |
\( -\frac{927841113}{5329} a - \frac{395933743}{5329} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 44 a - 213\) , \( -308 a + 1248\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(44a-213\right){x}-308a+1248$ |
*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.
