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-a1 |
1536.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1536.1 |
\( 2^{9} \cdot 3 \) |
\( - 2^{17} \cdot 3^{2} \) |
$1.93788$ |
$(a+1), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$10.42897506$ |
1.505292890 |
\( -\frac{740855896}{3} a + \frac{1283201128}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 2450 a - 4241\) , \( -86241 a + 149373\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(2450a-4241\right){x}-86241a+149373$ |
1536.1-c1 |
1536.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1536.1 |
\( 2^{9} \cdot 3 \) |
\( - 2^{17} \cdot 3^{2} \) |
$1.93788$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.171973525$ |
$10.42897506$ |
3.528326832 |
\( -\frac{740855896}{3} a + \frac{1283201128}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 34114 a - 59087\) , \( -4482861 a + 7764543\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(34114a-59087\right){x}-4482861a+7764543$ |
1536.1-v1 |
1536.1-v |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1536.1 |
\( 2^{9} \cdot 3 \) |
\( - 2^{17} \cdot 3^{2} \) |
$1.93788$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.355231857$ |
2.514494285 |
\( -\frac{740855896}{3} a + \frac{1283201128}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2450 a - 4241\) , \( 86241 a - 149373\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(2450a-4241\right){x}+86241a-149373$ |
1536.1-x1 |
1536.1-x |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1536.1 |
\( 2^{9} \cdot 3 \) |
\( - 2^{17} \cdot 3^{2} \) |
$1.93788$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.024272724$ |
$4.355231857$ |
2.545011098 |
\( -\frac{740855896}{3} a + \frac{1283201128}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 34114 a - 59087\) , \( 4482861 a - 7764543\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(34114a-59087\right){x}+4482861a-7764543$ |
3072.1-c1 |
3072.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{23} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$2.252849762$ |
2.601366833 |
\( -\frac{740855896}{3} a + \frac{1283201128}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 96 a - 160\) , \( 632 a - 1096\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(96a-160\right){x}+632a-1096$ |
3072.1-h1 |
3072.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{23} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.252849762$ |
1.300683416 |
\( -\frac{740855896}{3} a + \frac{1283201128}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 1312 a - 2272\) , \( 32872 a - 56936\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(1312a-2272\right){x}+32872a-56936$ |
3072.1-bx1 |
3072.1-bx |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{23} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.097450451$ |
$10.08069983$ |
3.193632813 |
\( -\frac{740855896}{3} a + \frac{1283201128}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 96 a - 160\) , \( -632 a + 1096\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(96a-160\right){x}-632a+1096$ |
3072.1-cb1 |
3072.1-cb |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{23} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.732026511$ |
$10.08069983$ |
4.260463665 |
\( -\frac{740855896}{3} a + \frac{1283201128}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 1312 a - 2272\) , \( -32872 a + 56936\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(1312a-2272\right){x}-32872a+56936$ |
4608.1-b1 |
4608.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4608.1 |
\( 2^{9} \cdot 3^{2} \) |
\( - 2^{17} \cdot 3^{8} \) |
$2.55039$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.396249456$ |
$8.230856948$ |
3.766024158 |
\( -\frac{740855896}{3} a + \frac{1283201128}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 102344 a - 177264\) , \( -23395972 a + 40523012\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(102344a-177264\right){x}-23395972a+40523012$ |
4608.1-c1 |
4608.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4608.1 |
\( 2^{9} \cdot 3^{2} \) |
\( - 2^{17} \cdot 3^{8} \) |
$2.55039$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.230856948$ |
2.376043737 |
\( -\frac{740855896}{3} a + \frac{1283201128}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 7348 a - 12726\) , \( -455468 a + 788894\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(7348a-12726\right){x}-455468a+788894$ |
4608.1-bc1 |
4608.1-bc |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4608.1 |
\( 2^{9} \cdot 3^{2} \) |
\( - 2^{17} \cdot 3^{8} \) |
$2.55039$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.839444128$ |
1.062003562 |
\( -\frac{740855896}{3} a + \frac{1283201128}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 102344 a - 177264\) , \( 23395972 a - 40523012\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(102344a-177264\right){x}+23395972a-40523012$ |
4608.1-bf1 |
4608.1-bf |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4608.1 |
\( 2^{9} \cdot 3^{2} \) |
\( - 2^{17} \cdot 3^{8} \) |
$2.55039$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$4.070688009$ |
$1.839444128$ |
4.323085168 |
\( -\frac{740855896}{3} a + \frac{1283201128}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 7348 a - 12726\) , \( 455468 a - 788894\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(7348a-12726\right){x}+455468a-788894$ |
*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.