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 |
600.1-o1 |
600.1-o |
$8$ |
$16$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
600.1 |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( - 2^{11} \cdot 3 \cdot 5^{2} \) |
$2.16662$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1.520929017$ |
$5.822038123$ |
3.615000532 |
\( -\frac{1705382858958144777649}{15} a + 278487854702414976744 \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 2450 a - 6801\) , \( -109970 a + 277443\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(2450a-6801\right){x}-109970a+277443$ |
600.1-p1 |
600.1-p |
$8$ |
$16$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
600.1 |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( - 2^{11} \cdot 3 \cdot 5^{2} \) |
$2.16662$ |
$(-a+2), (a+3), (-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$256$ |
\( 1 \) |
$1$ |
$0.201451965$ |
2.631757453 |
\( -\frac{1705382858958144777649}{15} a + 278487854702414976744 \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -15950 a - 39200\) , \( -1756612 a - 4303380\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-15950a-39200\right){x}-1756612a-4303380$ |
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*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.