| 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 |
| 2304.3-a1 |
2304.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2304.3 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{8} \) |
$1.75107$ |
$(a), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.389095587$ |
$2.397245973$ |
2.638237549 |
\( \frac{9472}{9} a - \frac{71552}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 10\) , \( 8 a - 12\bigr] \) |
${y}^2={x}^{3}+\left(4a-10\right){x}+8a-12$ |
| 2304.3-a2 |
2304.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2304.3 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{19} \cdot 3^{14} \) |
$1.75107$ |
$(a), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.389095587$ |
$1.198622986$ |
2.638237549 |
\( -\frac{15609244}{6561} a - \frac{20009248}{6561} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -14 a + 35\) , \( -50 a - 86\bigr] \) |
${y}^2={x}^{3}+\left(-14a+35\right){x}-50a-86$ |
| 2304.3-a3 |
2304.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2304.3 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{10} \) |
$1.75107$ |
$(a), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.778191175$ |
$2.397245973$ |
2.638237549 |
\( \frac{39872}{81} a - \frac{110368}{81} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a - 5\) , \( -8 a - 2\bigr] \) |
${y}^2={x}^{3}+\left(-4a-5\right){x}-8a-2$ |
| 2304.3-a4 |
2304.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2304.3 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{19} \cdot 3^{8} \) |
$1.75107$ |
$(a), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.389095587$ |
$1.198622986$ |
2.638237549 |
\( -\frac{18653188}{9} a + \frac{32152304}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -74 a - 85\) , \( -414 a - 142\bigr] \) |
${y}^2={x}^{3}+\left(-74a-85\right){x}-414a-142$ |
| 2304.3-b1 |
2304.3-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2304.3 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.75107$ |
$(a), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$3.969390382$ |
1.403391428 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a - 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-2a-1\right){x}$ |
| 2304.3-b2 |
2304.3-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2304.3 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.75107$ |
$(a), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$3.969390382$ |
1.403391428 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a + 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(2a+1\right){x}$ |
| 2304.3-b3 |
2304.3-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2304.3 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{6} \) |
$1.75107$ |
$(a), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$1.984695191$ |
1.403391428 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 22 a + 11\) , \( -14 a - 70\bigr] \) |
${y}^2={x}^{3}+\left(22a+11\right){x}-14a-70$ |
| 2304.3-b4 |
2304.3-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2304.3 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{6} \) |
$1.75107$ |
$(a), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$1.984695191$ |
1.403391428 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 22 a + 11\) , \( 14 a + 70\bigr] \) |
${y}^2={x}^{3}+\left(22a+11\right){x}+14a+70$ |
| 2304.3-c1 |
2304.3-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2304.3 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{8} \) |
$1.75107$ |
$(a), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.397245973$ |
1.695108884 |
\( \frac{9472}{9} a - \frac{71552}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 10\) , \( -8 a + 12\bigr] \) |
${y}^2={x}^{3}+\left(4a-10\right){x}-8a+12$ |
| 2304.3-c2 |
2304.3-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2304.3 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{19} \cdot 3^{14} \) |
$1.75107$ |
$(a), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.198622986$ |
1.695108884 |
\( -\frac{15609244}{6561} a - \frac{20009248}{6561} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -14 a + 35\) , \( 50 a + 86\bigr] \) |
${y}^2={x}^{3}+\left(-14a+35\right){x}+50a+86$ |
| 2304.3-c3 |
2304.3-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2304.3 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{10} \) |
$1.75107$ |
$(a), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.397245973$ |
1.695108884 |
\( \frac{39872}{81} a - \frac{110368}{81} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a - 5\) , \( 8 a + 2\bigr] \) |
${y}^2={x}^{3}+\left(-4a-5\right){x}+8a+2$ |
| 2304.3-c4 |
2304.3-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2304.3 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{19} \cdot 3^{8} \) |
$1.75107$ |
$(a), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.198622986$ |
1.695108884 |
\( -\frac{18653188}{9} a + \frac{32152304}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -74 a - 85\) , \( 414 a + 142\bigr] \) |
${y}^2={x}^{3}+\left(-74a-85\right){x}+414a+142$ |
*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.
