| 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 |
| 14400.1-a1 |
14400.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
14400.1 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{10} \cdot 5^{2} \) |
$1.69547$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.196275961$ |
1.381340496 |
\( \frac{556852}{45} a - \frac{327892}{45} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -44 a - 8\) , \( 188 a - 72\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-44a-8\right){x}+188a-72$ |
| 14400.1-a2 |
14400.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
14400.1 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{14} \cdot 5^{4} \) |
$1.69547$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.598137980$ |
1.381340496 |
\( -\frac{8435734}{2025} a + \frac{44288}{15} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -44 a - 128\) , \( -52 a - 648\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-44a-128\right){x}-52a-648$ |
| 14400.1-b1 |
14400.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
14400.1 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{14} \cdot 5^{4} \) |
$1.69547$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.598137980$ |
1.381340496 |
\( \frac{8435734}{2025} a - \frac{2456854}{2025} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -172 a + 128\) , \( 52 a - 700\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-172a+128\right){x}+52a-700$ |
| 14400.1-b2 |
14400.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
14400.1 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{10} \cdot 5^{2} \) |
$1.69547$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.196275961$ |
1.381340496 |
\( -\frac{556852}{45} a + 5088 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -52 a + 8\) , \( -188 a + 116\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-52a+8\right){x}-188a+116$ |
| 14400.1-c1 |
14400.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
14400.1 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{6} \cdot 5^{4} \) |
$1.69547$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.483700806$ |
$1.195535861$ |
2.670968580 |
\( \frac{1293836}{25} a - \frac{1028876}{25} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 65 a + 5\) , \( -25 a - 200\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(65a+5\right){x}-25a-200$ |
| 14400.1-c2 |
14400.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
14400.1 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{6} \cdot 5^{2} \) |
$1.69547$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.241850403$ |
$2.391071723$ |
2.670968580 |
\( -\frac{5776}{5} a + 1728 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 5 a + 5\) , \( -13 a + 4\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(5a+5\right){x}-13a+4$ |
| 14400.1-d1 |
14400.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
14400.1 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{6} \cdot 5^{2} \) |
$1.69547$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.241850403$ |
$2.391071723$ |
2.670968580 |
\( \frac{5776}{5} a + \frac{2864}{5} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 10 a - 5\) , \( 13 a - 9\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(10a-5\right){x}+13a-9$ |
| 14400.1-d2 |
14400.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
14400.1 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{6} \cdot 5^{4} \) |
$1.69547$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.483700806$ |
$1.195535861$ |
2.670968580 |
\( -\frac{1293836}{25} a + \frac{52992}{5} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 70 a - 5\) , \( 25 a - 225\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(70a-5\right){x}+25a-225$ |
| 14400.1-e1 |
14400.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
14400.1 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{6} \cdot 5^{2} \) |
$1.69547$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.948709202$ |
2.250175564 |
\( -\frac{108}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3\) , \( -18\bigr] \) |
${y}^2={x}^{3}-3{x}-18$ |
| 14400.1-e2 |
14400.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
14400.1 |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{6} \cdot 5^{4} \) |
$1.69547$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.974354601$ |
2.250175564 |
\( \frac{3721734}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -123\) , \( -522\bigr] \) |
${y}^2={x}^{3}-123{x}-522$ |
*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.
