| 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 |
| 1344.2-b6 |
1344.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1344.2 |
\( 2^{6} \cdot 3 \cdot 7 \) |
\( 2^{20} \cdot 3 \cdot 7^{2} \) |
$0.93713$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.063601265$ |
1.228140953 |
\( -\frac{7384301576}{147} a + \frac{25339394260}{147} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -234 a - 43\) , \( 1895 a - 638\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-234a-43\right){x}+1895a-638$ |
| 5376.2-b6 |
5376.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
5376.2 |
\( 2^{8} \cdot 3 \cdot 7 \) |
\( 2^{20} \cdot 3 \cdot 7^{2} \) |
$1.32530$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.063601265$ |
1.228140953 |
\( -\frac{7384301576}{147} a + \frac{25339394260}{147} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -234 a - 43\) , \( -1895 a + 638\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-234a-43\right){x}-1895a+638$ |
| 16128.2-e6 |
16128.2-e |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
16128.2 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{20} \cdot 3^{7} \cdot 7^{2} \) |
$1.74419$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.614070476$ |
1.418135020 |
\( -\frac{7384301576}{147} a + \frac{25339394260}{147} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 704 a + 128\) , \( 2560 a - 9328\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(704a+128\right){x}+2560a-9328$ |
| 16128.2-g6 |
16128.2-g |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
16128.2 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{20} \cdot 3^{7} \cdot 7^{2} \) |
$1.74419$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.985258728$ |
$0.614070476$ |
2.794459814 |
\( -\frac{7384301576}{147} a + \frac{25339394260}{147} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 704 a + 128\) , \( -2560 a + 9328\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(704a+128\right){x}-2560a+9328$ |
| 28224.3-d6 |
28224.3-d |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28224.3 |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{20} \cdot 3^{7} \cdot 7^{8} \) |
$2.00611$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.232096824$ |
2.144018622 |
\( -\frac{7384301576}{147} a + \frac{25339394260}{147} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -6007 a + 1469\) , \( -162985 a + 134224\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6007a+1469\right){x}-162985a+134224$ |
| 37632.3-d6 |
37632.3-d |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
37632.3 |
\( 2^{8} \cdot 3 \cdot 7^{2} \) |
\( 2^{20} \cdot 3 \cdot 7^{8} \) |
$2.15570$ |
$(-2a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.402003491$ |
0.928387296 |
\( -\frac{7384301576}{147} a + \frac{25339394260}{147} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -1513 a + 2003\) , \( -11377 a - 22477\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-1513a+2003\right){x}-11377a-22477$ |
| 37632.3-j6 |
37632.3-j |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
37632.3 |
\( 2^{8} \cdot 3 \cdot 7^{2} \) |
\( 2^{20} \cdot 3 \cdot 7^{8} \) |
$2.15570$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$4.237899947$ |
$0.402003491$ |
3.934412475 |
\( -\frac{7384301576}{147} a + \frac{25339394260}{147} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 2003 a - 490\) , \( 11377 a + 22477\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(2003a-490\right){x}+11377a+22477$ |
| 86016.2-i6 |
86016.2-i |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
86016.2 |
\( 2^{12} \cdot 3 \cdot 7 \) |
\( 2^{32} \cdot 3 \cdot 7^{2} \) |
$2.65060$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.599470554$ |
$0.531800632$ |
3.192516246 |
\( -\frac{7384301576}{147} a + \frac{25339394260}{147} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -937 a - 171\) , \( 14052 a - 4167\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-937a-171\right){x}+14052a-4167$ |
| 86016.2-bf6 |
86016.2-bf |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
86016.2 |
\( 2^{12} \cdot 3 \cdot 7 \) |
\( 2^{32} \cdot 3 \cdot 7^{2} \) |
$2.65060$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.078284816$ |
$0.531800632$ |
5.104853393 |
\( -\frac{7384301576}{147} a + \frac{25339394260}{147} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -937 a - 171\) , \( -14052 a + 4167\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-937a-171\right){x}-14052a+4167$ |
| 112896.3-q6 |
112896.3-q |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.3 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{20} \cdot 3^{7} \cdot 7^{8} \) |
$2.83706$ |
$(-2a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$2.198000371$ |
$0.232096824$ |
4.712553729 |
\( -\frac{7384301576}{147} a + \frac{25339394260}{147} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4540 a - 6008\) , \( 167524 a - 140232\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(4540a-6008\right){x}+167524a-140232$ |
*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.
