| 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 |
| 1536.1-a4 |
1536.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1536.1 |
\( 2^{9} \cdot 3 \) |
\( 2^{20} \cdot 3^{2} \) |
$1.93788$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.214487533$ |
1.505292890 |
\( \frac{24993664}{3} a + \frac{43299296}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -16 a - 32\) , \( -56 a - 96\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-16a-32\right){x}-56a-96$ |
| 1536.1-c4 |
1536.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1536.1 |
\( 2^{9} \cdot 3 \) |
\( 2^{20} \cdot 3^{2} \) |
$1.93788$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.171973525$ |
$5.214487533$ |
3.528326832 |
\( \frac{24993664}{3} a + \frac{43299296}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 26 a - 49\) , \( 74 a - 133\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(26a-49\right){x}+74a-133$ |
| 1536.1-v4 |
1536.1-v |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1536.1 |
\( 2^{9} \cdot 3 \) |
\( 2^{20} \cdot 3^{2} \) |
$1.93788$ |
$(a+1), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$17.42092743$ |
2.514494285 |
\( \frac{24993664}{3} a + \frac{43299296}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -16 a - 32\) , \( 56 a + 96\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-16a-32\right){x}+56a+96$ |
| 1536.1-x4 |
1536.1-x |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1536.1 |
\( 2^{9} \cdot 3 \) |
\( 2^{20} \cdot 3^{2} \) |
$1.93788$ |
$(a+1), (a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.506068181$ |
$17.42092743$ |
2.545011098 |
\( \frac{24993664}{3} a + \frac{43299296}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 26 a - 49\) , \( -74 a + 133\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(26a-49\right){x}-74a+133$ |
| 3072.1-c4 |
3072.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{14} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$9.011399049$ |
2.601366833 |
\( \frac{24993664}{3} a + \frac{43299296}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -32 a - 56\) , \( -142 a - 246\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-32a-56\right){x}-142a-246$ |
| 3072.1-h4 |
3072.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{14} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$9.011399049$ |
1.300683416 |
\( \frac{24993664}{3} a + \frac{43299296}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 2 a - 9\) , \( -3 a + 3\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a-9\right){x}-3a+3$ |
| 3072.1-bx4 |
3072.1-bx |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{14} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.274362612$ |
$20.16139966$ |
3.193632813 |
\( \frac{24993664}{3} a + \frac{43299296}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -32 a - 56\) , \( 142 a + 246\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-32a-56\right){x}+142a+246$ |
| 3072.1-cb4 |
3072.1-cb |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{14} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.732026511$ |
$20.16139966$ |
4.260463665 |
\( \frac{24993664}{3} a + \frac{43299296}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2 a - 9\) , \( 3 a - 3\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(2a-9\right){x}+3a-3$ |
| 4608.1-b4 |
4608.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4608.1 |
\( 2^{9} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{8} \) |
$2.55039$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.396249456$ |
$8.230856948$ |
3.766024158 |
\( \frac{24993664}{3} a + \frac{43299296}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 78 a - 147\) , \( 399 a - 666\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(78a-147\right){x}+399a-666$ |
| 4608.1-c4 |
4608.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4608.1 |
\( 2^{9} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{8} \) |
$2.55039$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.230856948$ |
2.376043737 |
\( \frac{24993664}{3} a + \frac{43299296}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -46 a - 99\) , \( 241 a + 406\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-46a-99\right){x}+241a+406$ |
| 4608.1-bc4 |
4608.1-bc |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4608.1 |
\( 2^{9} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{8} \) |
$2.55039$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.678888256$ |
1.062003562 |
\( \frac{24993664}{3} a + \frac{43299296}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 78 a - 147\) , \( -399 a + 666\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(78a-147\right){x}-399a+666$ |
| 4608.1-bf4 |
4608.1-bf |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4608.1 |
\( 2^{9} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{8} \) |
$2.55039$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.017672002$ |
$3.678888256$ |
4.323085168 |
\( \frac{24993664}{3} a + \frac{43299296}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -46 a - 99\) , \( -241 a - 406\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-46a-99\right){x}-241a-406$ |
*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.
