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 |
1458.4-a1 |
1458.4-a |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1458.4 |
\( 2 \cdot 3^{6} \) |
\( 2^{3} \cdot 3^{12} \) |
$1.56179$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$1$ |
$3.688791195$ |
0.869456422 |
\( \frac{4725}{4} a + 3753 \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -3 a\) , \( 2 a - 2\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-3a{x}+2a-2$ |
1458.4-a2 |
1458.4-a |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1458.4 |
\( 2 \cdot 3^{6} \) |
\( 2^{9} \cdot 3^{20} \) |
$1.56179$ |
$(a), (-a-1), (a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$1.229597065$ |
0.869456422 |
\( -\frac{90933}{32} a + \frac{32829}{8} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 27 a - 15\) , \( 54 a + 35\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(27a-15\right){x}+54a+35$ |
1458.4-a3 |
1458.4-a |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1458.4 |
\( 2 \cdot 3^{6} \) |
\( 2 \cdot 3^{8} \) |
$1.56179$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$3.688791195$ |
0.869456422 |
\( -\frac{2245317}{2} a + 1184658 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 6 a + 9\) , \( -a + 11\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6a+9\right){x}-a+11$ |
1458.4-b1 |
1458.4-b |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1458.4 |
\( 2 \cdot 3^{6} \) |
\( 2^{2} \cdot 3^{6} \) |
$1.56179$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1.015681695$ |
$5.635135226$ |
1.798723678 |
\( -\frac{132651}{2} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-3{x}+3$ |
1458.4-b2 |
1458.4-b |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1458.4 |
\( 2 \cdot 3^{6} \) |
\( 2^{18} \cdot 3^{22} \) |
$1.56179$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1.015681695$ |
$0.626126136$ |
1.798723678 |
\( -\frac{1167051}{512} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -123\) , \( -667\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-123{x}-667$ |
1458.4-b3 |
1458.4-b |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1458.4 |
\( 2 \cdot 3^{6} \) |
\( 2^{6} \cdot 3^{18} \) |
$1.56179$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.338560565$ |
$1.878378408$ |
1.798723678 |
\( \frac{9261}{8} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 12\) , \( 8\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+12{x}+8$ |
1458.4-c1 |
1458.4-c |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1458.4 |
\( 2 \cdot 3^{6} \) |
\( 2^{3} \cdot 3^{12} \) |
$1.56179$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$1$ |
$3.688791195$ |
0.869456422 |
\( -\frac{4725}{4} a + 3753 \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 3 a\) , \( -2 a - 2\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+3a{x}-2a-2$ |
1458.4-c2 |
1458.4-c |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1458.4 |
\( 2 \cdot 3^{6} \) |
\( 2^{9} \cdot 3^{20} \) |
$1.56179$ |
$(a), (-a-1), (a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$1.229597065$ |
0.869456422 |
\( \frac{90933}{32} a + \frac{32829}{8} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -27 a - 15\) , \( -54 a + 35\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-27a-15\right){x}-54a+35$ |
1458.4-c3 |
1458.4-c |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1458.4 |
\( 2 \cdot 3^{6} \) |
\( 2 \cdot 3^{8} \) |
$1.56179$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$3.688791195$ |
0.869456422 |
\( \frac{2245317}{2} a + 1184658 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -5 a + 10\) , \( 11 a + 22\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-5a+10\right){x}+11a+22$ |
1458.4-d1 |
1458.4-d |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1458.4 |
\( 2 \cdot 3^{6} \) |
\( 2^{3} \cdot 3^{12} \) |
$1.56179$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$3.688791195$ |
2.608369268 |
\( -\frac{4725}{4} a + 3753 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -2 a + 1\) , \( a + 5\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a+1\right){x}+a+5$ |
1458.4-d2 |
1458.4-d |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1458.4 |
\( 2 \cdot 3^{6} \) |
\( 2^{9} \cdot 3^{8} \) |
$1.56179$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$3.688791195$ |
2.608369268 |
\( \frac{90933}{32} a + \frac{32829}{8} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3 a - 2\) , \( 3 a - 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-3a-2\right){x}+3a-1$ |
1458.4-d3 |
1458.4-d |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1458.4 |
\( 2 \cdot 3^{6} \) |
\( 2 \cdot 3^{20} \) |
$1.56179$ |
$(a), (-a-1), (a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$1.229597065$ |
2.608369268 |
\( \frac{2245317}{2} a + 1184658 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -47 a + 91\) , \( -163 a - 309\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-47a+91\right){x}-163a-309$ |
1458.4-e1 |
1458.4-e |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1458.4 |
\( 2 \cdot 3^{6} \) |
\( 2^{2} \cdot 3^{18} \) |
$1.56179$ |
$(a), (-a-1), (a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$1.878378408$ |
2.656428221 |
\( -\frac{132651}{2} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -29\) , \( -53\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-29{x}-53$ |
1458.4-e2 |
1458.4-e |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1458.4 |
\( 2 \cdot 3^{6} \) |
\( 2^{18} \cdot 3^{10} \) |
$1.56179$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{4} \) |
$1$ |
$1.878378408$ |
2.656428221 |
\( -\frac{1167051}{512} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -14\) , \( 29\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-14{x}+29$ |
1458.4-e3 |
1458.4-e |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1458.4 |
\( 2 \cdot 3^{6} \) |
\( 2^{6} \cdot 3^{6} \) |
$1.56179$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$5.635135226$ |
2.656428221 |
\( \frac{9261}{8} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 1\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+{x}-1$ |
1458.4-f1 |
1458.4-f |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1458.4 |
\( 2 \cdot 3^{6} \) |
\( 2^{3} \cdot 3^{12} \) |
$1.56179$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$3.688791195$ |
2.608369268 |
\( \frac{4725}{4} a + 3753 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 2 a + 2\) , \( a + 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+2\right){x}+a+1$ |
1458.4-f2 |
1458.4-f |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1458.4 |
\( 2 \cdot 3^{6} \) |
\( 2^{9} \cdot 3^{8} \) |
$1.56179$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$3.688791195$ |
2.608369268 |
\( -\frac{90933}{32} a + \frac{32829}{8} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 3 a - 2\) , \( -3 a - 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(3a-2\right){x}-3a-1$ |
1458.4-f3 |
1458.4-f |
$3$ |
$9$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1458.4 |
\( 2 \cdot 3^{6} \) |
\( 2 \cdot 3^{20} \) |
$1.56179$ |
$(a), (-a-1), (a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$1.229597065$ |
2.608369268 |
\( -\frac{2245317}{2} a + 1184658 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 47 a + 92\) , \( 255 a - 403\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(47a+92\right){x}+255a-403$ |
*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.