| 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-a4 |
73.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
73.1 |
\( 73 \) |
\( 73^{6} \) |
$0.45241$ |
$(-9a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$1.621167044$ |
0.311993743 |
\( -\frac{55816089234767}{151334226289} a + \frac{107352826006104}{151334226289} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 11 a + 5\) , \( -20 a + 11\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(11a+5\right){x}-20a+11$ |
| 5329.1-a4 |
5329.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
5329.1 |
\( 73^{2} \) |
\( 73^{12} \) |
$1.32239$ |
$(-9a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$4.973623120$ |
$0.189743250$ |
2.179408166 |
\( -\frac{55816089234767}{151334226289} a + \frac{107352826006104}{151334226289} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 868 a + 135\) , \( 18504 a - 12861\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(868a+135\right){x}+18504a-12861$ |
| 12337.1-a4 |
12337.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12337.1 |
\( 13^{2} \cdot 73 \) |
\( 13^{6} \cdot 73^{6} \) |
$1.63118$ |
$(-4a+1), (-9a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1.551353035$ |
$0.449630838$ |
3.221781549 |
\( -\frac{55816089234767}{151334226289} a + \frac{107352826006104}{151334226289} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 181 a - 30\) , \( -1160 a + 1313\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(181a-30\right){x}-1160a+1313$ |
| 12337.5-c4 |
12337.5-c |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12337.5 |
\( 13^{2} \cdot 73 \) |
\( 13^{6} \cdot 73^{6} \) |
$1.63118$ |
$(4a-3), (-9a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.449630838$ |
3.115133830 |
\( -\frac{55816089234767}{151334226289} a + \frac{107352826006104}{151334226289} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 140 a - 186\) , \( -1021 a - 380\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(140a-186\right){x}-1021a-380$ |
| 18688.1-e4 |
18688.1-e |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
18688.1 |
\( 2^{8} \cdot 73 \) |
\( 2^{24} \cdot 73^{6} \) |
$1.80963$ |
$(-9a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.405291761$ |
2.807943688 |
\( -\frac{55816089234767}{151334226289} a + \frac{107352826006104}{151334226289} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -234 a + 157\) , \( 1849 a - 714\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-234a+157\right){x}+1849a-714$ |
| 32193.1-a4 |
32193.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32193.1 |
\( 3^{2} \cdot 7^{2} \cdot 73 \) |
\( 3^{6} \cdot 7^{6} \cdot 73^{6} \) |
$2.07319$ |
$(-2a+1), (-3a+1), (-9a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$2.099156675$ |
$0.353767652$ |
3.429985888 |
\( -\frac{55816089234767}{151334226289} a + \frac{107352826006104}{151334226289} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -307 a + 104\) , \( 2015 a + 598\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-307a+104\right){x}+2015a+598$ |
| 32193.5-b4 |
32193.5-b |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32193.5 |
\( 3^{2} \cdot 7^{2} \cdot 73 \) |
\( 3^{6} \cdot 7^{6} \cdot 73^{6} \) |
$2.07319$ |
$(-2a+1), (3a-2), (-9a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.353767652$ |
2.450974190 |
\( -\frac{55816089234767}{151334226289} a + \frac{107352826006104}{151334226289} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -264 a + 279\) , \( 2393 a - 2360\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-264a+279\right){x}+2393a-2360$ |
| 45625.1-a4 |
45625.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
45625.1 |
\( 5^{4} \cdot 73 \) |
\( 5^{12} \cdot 73^{6} \) |
$2.26204$ |
$(-9a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$3.109067898$ |
$0.324233408$ |
4.656046711 |
\( -\frac{55816089234767}{151334226289} a + \frac{107352826006104}{151334226289} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 120 a - 366\) , \( -3763 a + 1639\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(120a-366\right){x}-3763a+1639$ |
| 99937.1-a4 |
99937.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99937.1 |
\( 37^{2} \cdot 73 \) |
\( 37^{6} \cdot 73^{6} \) |
$2.75189$ |
$(-7a+4), (-9a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$2.746992131$ |
$0.266518220$ |
3.381533386 |
\( -\frac{55816089234767}{151334226289} a + \frac{107352826006104}{151334226289} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -427 a - 90\) , \( -996 a - 5177\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-427a-90\right){x}-996a-5177$ |
| 99937.5-a4 |
99937.5-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
99937.5 |
\( 37^{2} \cdot 73 \) |
\( 37^{6} \cdot 73^{6} \) |
$2.75189$ |
$(-7a+3), (-9a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$2.818409207$ |
$0.266518220$ |
3.469447446 |
\( -\frac{55816089234767}{151334226289} a + \frac{107352826006104}{151334226289} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -261 a + 552\) , \( -2215 a + 6278\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-261a+552\right){x}-2215a+6278$ |
*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.
