| 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 |
| 450.1-a1 |
450.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{2} \cdot 5^{6} \) |
$2.73003$ |
$(a+3), (a-4), (-a-4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$5.367489134$ |
4.855076597 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -11\) , \( 51\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-11{x}+51$ |
| 450.1-a2 |
450.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \) |
$2.73003$ |
$(a+3), (a-4), (-a-4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$5.367489134$ |
4.855076597 |
\( \frac{357911}{2160} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 4\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+4{x}$ |
| 450.1-a3 |
450.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{2} \cdot 5^{24} \) |
$2.73003$ |
$(a+3), (a-4), (-a-4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.341872283$ |
4.855076597 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -451\) , \( 91\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-451{x}+91$ |
| 450.1-a4 |
450.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{24} \cdot 5^{2} \) |
$2.73003$ |
$(a+3), (a-4), (-a-4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$5.367489134$ |
4.855076597 |
\( \frac{35578826569}{5314410} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -66\) , \( 126\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-66{x}+126$ |
| 450.1-a5 |
450.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 5^{4} \) |
$2.73003$ |
$(a+3), (a-4), (-a-4), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$5.367489134$ |
4.855076597 |
\( \frac{702595369}{72900} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -16\) , \( -44\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-16{x}-44$ |
| 450.1-a6 |
450.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{12} \) |
$2.73003$ |
$(a+3), (a-4), (-a-4), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$5.367489134$ |
4.855076597 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -331\) , \( 2035\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-331{x}+2035$ |
| 450.1-a7 |
450.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{8} \) |
$2.73003$ |
$(a+3), (a-4), (-a-4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.341872283$ |
4.855076597 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -286\) , \( -2150\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-286{x}-2150$ |
| 450.1-a8 |
450.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{8} \cdot 5^{6} \) |
$2.73003$ |
$(a+3), (a-4), (-a-4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$5.367489134$ |
4.855076597 |
\( \frac{16778985534208729}{81000} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -5331\) , \( 145035\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-5331{x}+145035$ |
| 450.1-b1 |
450.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{2} \cdot 5^{6} \) |
$2.73003$ |
$(a+3), (a-4), (-a-4), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$7.516152357$ |
$1.248395236$ |
1.414559890 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -14\) , \( -64\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-14{x}-64$ |
| 450.1-b2 |
450.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \) |
$2.73003$ |
$(a+3), (a-4), (-a-4), (3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$2.505384119$ |
$11.23555713$ |
1.414559890 |
\( \frac{357911}{2160} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 1\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}+2$ |
| 450.1-b3 |
450.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{2} \cdot 5^{24} \) |
$2.73003$ |
$(a+3), (a-4), (-a-4), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1.879038089$ |
$1.248395236$ |
1.414559890 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -454\) , \( -544\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-454{x}-544$ |
| 450.1-b4 |
450.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{24} \cdot 5^{2} \) |
$2.73003$ |
$(a+3), (a-4), (-a-4), (3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$2.505384119$ |
$2.808889283$ |
1.414559890 |
\( \frac{35578826569}{5314410} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -69\) , \( -194\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-69{x}-194$ |
| 450.1-b5 |
450.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 5^{4} \) |
$2.73003$ |
$(a+3), (a-4), (-a-4), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3 \) |
$1.252692059$ |
$11.23555713$ |
1.414559890 |
\( \frac{702595369}{72900} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -19\) , \( 26\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-19{x}+26$ |
| 450.1-b6 |
450.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{12} \) |
$2.73003$ |
$(a+3), (a-4), (-a-4), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$3.758076178$ |
$1.248395236$ |
1.414559890 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -334\) , \( -2368\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-334{x}-2368$ |
| 450.1-b7 |
450.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{8} \) |
$2.73003$ |
$(a+3), (a-4), (-a-4), (3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.626346029$ |
$11.23555713$ |
1.414559890 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-289{x}+1862$ |
| 450.1-b8 |
450.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
450.1 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{8} \cdot 5^{6} \) |
$2.73003$ |
$(a+3), (a-4), (-a-4), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$7.516152357$ |
$0.312098809$ |
1.414559890 |
\( \frac{16778985534208729}{81000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -5334\) , \( -150368\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-5334{x}-150368$ |
*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.
