| 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 |
| 1600.2-a1 |
1600.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
1600.2 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{3} \) |
$1.87441$ |
$(-a-1), (a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.288732634$ |
$4.931078164$ |
1.717123012 |
\( \frac{384256}{25} a - \frac{397312}{25} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -2 a - 2\) , \( -a - 2\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a-2\right){x}-a-2$ |
| 1600.2-a2 |
1600.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
1600.2 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{6} \) |
$1.87441$ |
$(-a-1), (a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.144366317$ |
$2.465539082$ |
1.717123012 |
\( \frac{60592}{625} a - \frac{118864}{625} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -2 a + 3\) , \( -5 a - 5\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a+3\right){x}-5a-5$ |
| 1600.2-b1 |
1600.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
1600.2 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{3} \) |
$1.87441$ |
$(-a-1), (a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.288732634$ |
$4.931078164$ |
1.717123012 |
\( -\frac{384256}{25} a - \frac{13056}{25} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 2 a - 4\) , \( a - 3\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(2a-4\right){x}+a-3$ |
| 1600.2-b2 |
1600.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
1600.2 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{6} \) |
$1.87441$ |
$(-a-1), (a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.144366317$ |
$2.465539082$ |
1.717123012 |
\( -\frac{60592}{625} a - \frac{58272}{625} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 2 a + 1\) , \( 5 a - 10\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(2a+1\right){x}+5a-10$ |
| 1600.2-c1 |
1600.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
1600.2 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{8} \) |
$1.87441$ |
$(-a-1), (a-2), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.498444490$ |
1.807192052 |
\( \frac{237276}{625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \) |
${y}^2={x}^{3}+13{x}-34$ |
| 1600.2-c2 |
1600.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
1600.2 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{4} \) |
$1.87441$ |
$(-a-1), (a-2), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.996888981$ |
1.807192052 |
\( \frac{148176}{25} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( -6\bigr] \) |
${y}^2={x}^{3}-7{x}-6$ |
| 1600.2-c3 |
1600.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
1600.2 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{2} \) |
$1.87441$ |
$(-a-1), (a-2), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$5.993777963$ |
1.807192052 |
\( \frac{55296}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( 1\bigr] \) |
${y}^2={x}^{3}-2{x}+1$ |
| 1600.2-c4 |
1600.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
1600.2 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{2} \) |
$1.87441$ |
$(-a-1), (a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$1.498444490$ |
1.807192052 |
\( \frac{132304644}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -107\) , \( -426\bigr] \) |
${y}^2={x}^{3}-107{x}-426$ |
*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.
