| 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 |
| 6400.3-CMc1 |
6400.3-CMc |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6400.3 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{9} \) |
$1.59850$ |
$(a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-4$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$1$ |
$2.056160146$ |
1.028080073 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 i - 11\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-2i-11\right){x}$ |
| 6400.3-CMb1 |
6400.3-CMb |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6400.3 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{6} \) |
$1.59850$ |
$(a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-4$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$3.074676569$ |
1.537338284 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 i - 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(4i-3\right){x}$ |
| 6400.3-CMb2 |
6400.3-CMb |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6400.3 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{18} \cdot 5^{6} \) |
$1.59850$ |
$(a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-16$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$1.537338284$ |
1.537338284 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 44 i - 33\) , \( -154 i + 28\bigr] \) |
${y}^2={x}^{3}+\left(44i-33\right){x}-154i+28$ |
| 6400.3-CMa1 |
6400.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6400.3 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{3} \) |
$1.59850$ |
$(a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-4$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$1$ |
$4.597713860$ |
2.298856930 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 i + 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(2i+1\right){x}$ |
| 6400.3-a1 |
6400.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6400.3 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{21} \cdot 5^{8} \) |
$1.59850$ |
$(a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.587023073$ |
1.174046147 |
\( \frac{358400014}{25} a - \frac{1259500802}{25} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( 364 i + 660\) , \( 5580 i - 5344\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+\left(364i+660\right){x}+5580i-5344$ |
| 6400.3-a2 |
6400.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6400.3 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{7} \) |
$1.59850$ |
$(a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2.348092294$ |
1.174046147 |
\( \frac{51328}{5} a - \frac{73024}{5} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 4 i + 14\) , \( -18 i + 14\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(4i+14\right){x}-18i+14$ |
| 6400.3-a3 |
6400.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6400.3 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{8} \) |
$1.59850$ |
$(a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$2.348092294$ |
1.174046147 |
\( \frac{11136}{25} a - \frac{10048}{25} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( -6 i\) , \( 4 i - 12\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}-6i{x}+4i-12$ |
| 6400.3-a4 |
6400.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6400.3 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{18} \cdot 5^{10} \) |
$1.59850$ |
$(a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.174046147$ |
1.174046147 |
\( -\frac{4463256}{625} a - \frac{162592}{625} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 24 i + 40\) , \( -84 i + 72\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+\left(24i+40\right){x}-84i+72$ |
| 6400.3-a5 |
6400.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6400.3 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{21} \cdot 5^{14} \) |
$1.59850$ |
$(a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.587023073$ |
1.174046147 |
\( \frac{2033300354}{390625} a + \frac{130878178}{390625} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 164 i + 60\) , \( -348 i - 880\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+\left(164i+60\right){x}-348i-880$ |
| 6400.3-a6 |
6400.3-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6400.3 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{18} \cdot 5^{7} \) |
$1.59850$ |
$(a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.174046147$ |
1.174046147 |
\( -\frac{5120008}{5} a + \frac{3690224}{5} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( -116 i + 20\) , \( 240 i - 464\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+\left(-116i+20\right){x}+240i-464$ |
| 6400.3-b1 |
6400.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6400.3 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{3} \) |
$1.59850$ |
$(a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.337192776$ |
$3.590202120$ |
2.421180444 |
\( 6112 a - 15616 \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( -4 i + 5\) , \( -i - 5\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(-4i+5\right){x}-i-5$ |
| 6400.3-b2 |
6400.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6400.3 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{3} \) |
$1.59850$ |
$(a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.168596388$ |
$3.590202120$ |
2.421180444 |
\( -1408 a - 256 \) |
\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( 4 i\) , \( 4\bigr] \) |
${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+4i{x}+4$ |
| 6400.3-c1 |
6400.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6400.3 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{9} \) |
$1.59850$ |
$(a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.605587198$ |
1.605587198 |
\( 6112 a - 15616 \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( 30 i - 2\) , \( 52 i + 52\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+\left(30i-2\right){x}+52i+52$ |
| 6400.3-c2 |
6400.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6400.3 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{9} \) |
$1.59850$ |
$(a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.605587198$ |
1.605587198 |
\( -1408 a - 256 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -10 i - 13\) , \( -22 i - 33\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-10i-13\right){x}-22i-33$ |
| 6400.3-d1 |
6400.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6400.3 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{19} \cdot 5^{7} \) |
$1.59850$ |
$(a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.032999837$ |
2.065999675 |
\( -\frac{7495692}{5} a - \frac{10604804}{5} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( -138 i - 97\) , \( 845 i + 193\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(-138i-97\right){x}+845i+193$ |
| 6400.3-d2 |
6400.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6400.3 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{19} \cdot 5^{10} \) |
$1.59850$ |
$(a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.032999837$ |
2.065999675 |
\( -\frac{7953316}{625} a - \frac{11486012}{625} \) |
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 2 i - 77\) , \( 7 i + 243\bigr] \) |
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(2i-77\right){x}+7i+243$ |
| 6400.3-d3 |
6400.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6400.3 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{8} \) |
$1.59850$ |
$(a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.065999675$ |
2.065999675 |
\( \frac{35616}{25} a + \frac{5312}{25} \) |
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( -8 i - 7\) , \( -15 i - 3\bigr] \) |
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(-8i-7\right){x}-15i-3$ |
| 6400.3-d4 |
6400.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6400.3 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{7} \) |
$1.59850$ |
$(a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.065999675$ |
2.065999675 |
\( -\frac{12928}{5} a + \frac{3584}{5} \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( -12\) , \( -8 i + 12\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}-12{x}-8i+12$ |
*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.
