| 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 |
| 11858.2-a1 |
11858.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11858.2 |
\( 2 \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{12} \cdot 7^{2} \cdot 11^{4} \) |
$2.63746$ |
$(a), (a+3), (a-3), (7)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.390271149$ |
$1.816873982$ |
4.011125434 |
\( -\frac{2749884201}{54208} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -29\) , \( 69\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-29{x}+69$ |
| 11858.2-a2 |
11858.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11858.2 |
\( 2 \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{6} \cdot 7^{4} \cdot 11^{2} \) |
$2.63746$ |
$(a), (a+3), (a-3), (7)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.561084599$ |
$0.908436991$ |
4.011125434 |
\( \frac{11422548526761}{4312} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -469\) , \( 4029\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-469{x}+4029$ |
| 11858.2-b1 |
11858.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11858.2 |
\( 2 \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{8} \cdot 7^{2} \cdot 11^{4} \) |
$2.63746$ |
$(a), (a+3), (a-3), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.405544247$ |
3.401953300 |
\( -\frac{338608873}{13552} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -14\) , \( -28\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-14{x}-28$ |
| 11858.2-b2 |
11858.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11858.2 |
\( 2 \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{4} \cdot 7^{4} \cdot 11^{2} \) |
$2.63746$ |
$(a), (a+3), (a-3), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.202772123$ |
3.401953300 |
\( \frac{1426487591593}{2156} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -234\) , \( -1480\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-234{x}-1480$ |
| 11858.2-c1 |
11858.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11858.2 |
\( 2 \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{24} \cdot 7^{2} \cdot 11^{4} \) |
$2.63746$ |
$(a), (a+3), (a-3), (7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \cdot 3 \) |
$0.564696259$ |
$1.141049216$ |
5.467459015 |
\( -\frac{5545233}{3469312} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -4\) , \( -89\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-4{x}-89$ |
| 11858.2-c2 |
11858.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11858.2 |
\( 2 \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{6} \cdot 7^{2} \cdot 11^{16} \) |
$2.63746$ |
$(a), (a+3), (a-3), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$2.258785036$ |
$0.285262304$ |
5.467459015 |
\( \frac{24331017010833}{12004097336} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -604\) , \( 2343\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-604{x}+2343$ |
| 11858.2-c3 |
11858.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11858.2 |
\( 2 \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{12} \cdot 7^{4} \cdot 11^{8} \) |
$2.63746$ |
$(a), (a+3), (a-3), (7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \cdot 3 \) |
$1.129392518$ |
$0.570524608$ |
5.467459015 |
\( \frac{3750606459153}{45914176} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -324\) , \( -2137\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-324{x}-2137$ |
| 11858.2-c4 |
11858.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11858.2 |
\( 2 \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{6} \cdot 7^{8} \cdot 11^{4} \) |
$2.63746$ |
$(a), (a+3), (a-3), (7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \cdot 3 \) |
$2.258785036$ |
$0.285262304$ |
5.467459015 |
\( \frac{15226621995131793}{2324168} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -5164\) , \( -141529\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-5164{x}-141529$ |
*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.
