| 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 |
| 19600.1-a1 |
19600.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
19600.1 |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 5^{2} \cdot 7^{10} \) |
$2.99053$ |
$(a), (5), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 5 \) |
$0.128582376$ |
$1.674108353$ |
1.522123934 |
\( \frac{14155776}{84035} \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( 8\) , \( 27\bigr] \) |
${y}^2+a{y}={x}^{3}+8{x}+27$ |
| 19600.1-b1 |
19600.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
19600.1 |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 5^{2} \cdot 7^{6} \) |
$2.99053$ |
$(a), (5), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.337321606$ |
$1.194888048$ |
1.710045356 |
\( -\frac{225637236736}{1715} \) |
\( \bigl[0\) , \( -1\) , \( a\) , \( -201\) , \( -1032\bigr] \) |
${y}^2+a{y}={x}^{3}-{x}^{2}-201{x}-1032$ |
| 19600.1-b2 |
19600.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
19600.1 |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 5^{6} \cdot 7^{2} \) |
$2.99053$ |
$(a), (5), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.112440535$ |
$3.584664146$ |
1.710045356 |
\( -\frac{65536}{875} \) |
\( \bigl[0\) , \( -1\) , \( a\) , \( -1\) , \( -2\bigr] \) |
${y}^2+a{y}={x}^{3}-{x}^{2}-{x}-2$ |
| 19600.1-c1 |
19600.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
19600.1 |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 5^{18} \cdot 7^{2} \) |
$2.99053$ |
$(a), (5), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 3^{2} \) |
$0.631888037$ |
$0.387487601$ |
3.116416187 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -525\) , \( -4673\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-525{x}-4673$ |
| 19600.1-c2 |
19600.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
19600.1 |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 5^{2} \cdot 7^{2} \) |
$2.99053$ |
$(a), (5), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.631888037$ |
$3.487388410$ |
3.116416187 |
\( -\frac{262144}{35} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -5\) , \( 7\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-5{x}+7$ |
| 19600.1-c3 |
19600.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
19600.1 |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 5^{6} \cdot 7^{6} \) |
$2.99053$ |
$(a), (5), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs |
$1$ |
\( 3^{2} \) |
$0.210629345$ |
$1.162462803$ |
3.116416187 |
\( \frac{71991296}{42875} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 35\) , \( -25\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+35{x}-25$ |
| 19600.1-d1 |
19600.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
19600.1 |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{20} \cdot 5^{4} \cdot 7^{2} \) |
$2.99053$ |
$(a), (5), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.613941328$ |
$1.849974466$ |
3.212459027 |
\( \frac{1367631}{2800} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 10\) , \( -22\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+10{x}-22$ |
| 19600.1-d2 |
19600.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
19600.1 |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 5^{8} \cdot 7^{4} \) |
$2.99053$ |
$(a), (5), (7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.227882656$ |
$0.924987233$ |
3.212459027 |
\( \frac{611960049}{122500} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -70\) , \( -150\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-70{x}-150$ |
| 19600.1-d3 |
19600.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
19600.1 |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{14} \cdot 5^{16} \cdot 7^{2} \) |
$2.99053$ |
$(a), (5), (7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$2.455765312$ |
$0.462493616$ |
3.212459027 |
\( \frac{74565301329}{5468750} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -350\) , \( 2538\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-350{x}+2538$ |
| 19600.1-d4 |
19600.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
19600.1 |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{14} \cdot 5^{4} \cdot 7^{8} \) |
$2.99053$ |
$(a), (5), (7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$0.613941328$ |
$0.462493616$ |
3.212459027 |
\( \frac{2121328796049}{120050} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -1070\) , \( -12950\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-1070{x}-12950$ |
| 19600.1-e1 |
19600.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
19600.1 |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
$2.99053$ |
$(a), (5), (7)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$6.146050106$ |
4.345913707 |
\( -\frac{1024}{35} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( 0\) , \( 1\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}+1$ |
| 19600.1-f1 |
19600.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
19600.1 |
\( 2^{4} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 5^{10} \cdot 7^{6} \) |
$2.99053$ |
$(a), (5), (7)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 3 \cdot 5 \) |
$1$ |
$0.914120687$ |
9.695714049 |
\( -\frac{30211716096}{1071875} \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( -103\) , \( 415\bigr] \) |
${y}^2+a{y}={x}^{3}-103{x}+415$ |
*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.
