| 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 |
| 4050.3-a1 |
4050.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
4050.3 |
\( 2 \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{18} \cdot 5^{2} \) |
$2.01626$ |
$(a), (-a-1), (a-1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$0.939987363$ |
1.329342877 |
\( -\frac{1860867}{320} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -69\) , \( -235\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-69{x}-235$ |
| 4050.3-a2 |
4050.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
4050.3 |
\( 2 \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 5^{6} \) |
$2.01626$ |
$(a), (-a-1), (a-1), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$2.819962089$ |
1.329342877 |
\( \frac{804357}{500} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 6\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+6{x}$ |
| 4050.3-a3 |
4050.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
4050.3 |
\( 2 \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{12} \) |
$2.01626$ |
$(a), (-a-1), (a-1), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$1.409981044$ |
1.329342877 |
\( \frac{57960603}{31250} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -24\) , \( 18\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-24{x}+18$ |
| 4050.3-a4 |
4050.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
4050.3 |
\( 2 \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{18} \cdot 5^{4} \) |
$2.01626$ |
$(a), (-a-1), (a-1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$1$ |
$0.469993681$ |
1.329342877 |
\( \frac{8527173507}{200} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -1149\) , \( -14707\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-1149{x}-14707$ |
| 4050.3-b1 |
4050.3-b |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
4050.3 |
\( 2 \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{6} \cdot 5^{2} \) |
$2.01626$ |
$(a), (-a-1), (a-1), (5)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.822902419$ |
$2.819962089$ |
4.375677880 |
\( -\frac{1860867}{320} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -8\) , \( 11\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-8{x}+11$ |
| 4050.3-b2 |
4050.3-b |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
4050.3 |
\( 2 \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{18} \cdot 5^{6} \) |
$2.01626$ |
$(a), (-a-1), (a-1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.274300806$ |
$0.939987363$ |
4.375677880 |
\( \frac{804357}{500} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 52\) , \( -53\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+52{x}-53$ |
| 4050.3-b3 |
4050.3-b |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
4050.3 |
\( 2 \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{18} \cdot 5^{12} \) |
$2.01626$ |
$(a), (-a-1), (a-1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.548601612$ |
$0.469993681$ |
4.375677880 |
\( \frac{57960603}{31250} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -218\) , \( -269\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-218{x}-269$ |
| 4050.3-b4 |
4050.3-b |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
4050.3 |
\( 2 \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{6} \cdot 5^{4} \) |
$2.01626$ |
$(a), (-a-1), (a-1), (5)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3 \) |
$1.645804838$ |
$1.409981044$ |
4.375677880 |
\( \frac{8527173507}{200} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -128\) , \( 587\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-128{x}+587$ |
| 4050.3-c1 |
4050.3-c |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
4050.3 |
\( 2 \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{14} \cdot 5^{6} \) |
$2.01626$ |
$(a), (-a-1), (a-1), (5)$ |
$1$ |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{7} \cdot 3^{2} \) |
$0.940639818$ |
$0.431430046$ |
4.591332359 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -122\) , \( 1721\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-122{x}+1721$ |
| 4050.3-c2 |
4050.3-c |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
4050.3 |
\( 2 \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{18} \cdot 5^{2} \) |
$2.01626$ |
$(a), (-a-1), (a-1), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{7} \) |
$0.313546606$ |
$1.294290140$ |
4.591332359 |
\( \frac{357911}{2160} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 13\) , \( -61\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+13{x}-61$ |
| 4050.3-c3 |
4050.3-c |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
4050.3 |
\( 2 \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{14} \cdot 5^{24} \) |
$2.01626$ |
$(a), (-a-1), (a-1), (5)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$3.762559272$ |
$0.107857511$ |
4.591332359 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -4082\) , \( 14681\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-4082{x}+14681$ |
| 4050.3-c4 |
4050.3-c |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
4050.3 |
\( 2 \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{36} \cdot 5^{2} \) |
$2.01626$ |
$(a), (-a-1), (a-1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{5} \) |
$1.254186424$ |
$0.323572535$ |
4.591332359 |
\( \frac{35578826569}{5314410} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -617\) , \( 5231\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-617{x}+5231$ |
| 4050.3-c5 |
4050.3-c |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
4050.3 |
\( 2 \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{24} \cdot 5^{4} \) |
$2.01626$ |
$(a), (-a-1), (a-1), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{7} \) |
$0.627093212$ |
$0.647145070$ |
4.591332359 |
\( \frac{702595369}{72900} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -167\) , \( -709\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-167{x}-709$ |
| 4050.3-c6 |
4050.3-c |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
4050.3 |
\( 2 \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{16} \cdot 5^{12} \) |
$2.01626$ |
$(a), (-a-1), (a-1), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{7} \cdot 3^{2} \) |
$1.881279636$ |
$0.215715023$ |
4.591332359 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3002\) , \( 63929\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-3002{x}+63929$ |
| 4050.3-c7 |
4050.3-c |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
4050.3 |
\( 2 \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{18} \cdot 5^{8} \) |
$2.01626$ |
$(a), (-a-1), (a-1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{5} \) |
$1.254186424$ |
$0.323572535$ |
4.591332359 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -2597\) , \( -50281\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-2597{x}-50281$ |
| 4050.3-c8 |
4050.3-c |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
4050.3 |
\( 2 \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{20} \cdot 5^{6} \) |
$2.01626$ |
$(a), (-a-1), (a-1), (5)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$3.762559272$ |
$0.107857511$ |
4.591332359 |
\( \frac{16778985534208729}{81000} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -48002\) , \( 4059929\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-48002{x}+4059929$ |
*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.
