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 |
98000.3-a1 |
98000.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98000.3 |
\( 2^{4} \cdot 5^{3} \cdot 7^{2} \) |
\( 2^{4} \cdot 5^{16} \cdot 7^{6} \) |
$3.16210$ |
$(a+1), (-a-2), (2a+1), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$0.408807199$ |
1.635228796 |
\( -\frac{30211716096}{1071875} \) |
\( \bigl[0\) , \( 0\) , \( i + 1\) , \( 412 i - 309\) , \( -4560 i + 829\bigr] \) |
${y}^2+\left(i+1\right){y}={x}^{3}+\left(412i-309\right){x}-4560i+829$ |
98000.3-b1 |
98000.3-b |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98000.3 |
\( 2^{4} \cdot 5^{3} \cdot 7^{2} \) |
\( 2^{4} \cdot 5^{14} \cdot 7^{2} \) |
$3.16210$ |
$(a+1), (-a-2), (2a+1), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$1.179301087$ |
2.358602174 |
\( -\frac{25191424}{21875} a + \frac{52359168}{21875} \) |
\( \bigl[0\) , \( i + 1\) , \( i + 1\) , \( 11 i + 36\) , \( 77 i + 1\bigr] \) |
${y}^2+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(11i+36\right){x}+77i+1$ |
98000.3-c1 |
98000.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98000.3 |
\( 2^{4} \cdot 5^{3} \cdot 7^{2} \) |
\( 2^{4} \cdot 5^{5} \cdot 7^{2} \) |
$3.16210$ |
$(a+1), (-a-2), (2a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.647958766$ |
2.647958766 |
\( \frac{95935712}{175} a - \frac{64291184}{175} \) |
\( \bigl[i + 1\) , \( 1\) , \( i + 1\) , \( 18 i + 10\) , \( 5 i - 37\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(18i+10\right){x}+5i-37$ |
98000.3-c2 |
98000.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98000.3 |
\( 2^{4} \cdot 5^{3} \cdot 7^{2} \) |
\( 2^{8} \cdot 5^{4} \cdot 7^{4} \) |
$3.16210$ |
$(a+1), (-a-2), (2a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.647958766$ |
2.647958766 |
\( \frac{116736}{245} a + \frac{299008}{245} \) |
\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( -4 i - 4\) , \( 6 i - 3\bigr] \) |
${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(-4i-4\right){x}+6i-3$ |
98000.3-d1 |
98000.3-d |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98000.3 |
\( 2^{4} \cdot 5^{3} \cdot 7^{2} \) |
\( 2^{4} \cdot 5^{20} \cdot 7^{2} \) |
$3.16210$ |
$(a+1), (-a-2), (2a+1), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$0.502073263$ |
1.004146527 |
\( \frac{2040723769344}{341796875} a - \frac{423142340608}{341796875} \) |
\( \bigl[0\) , \( -i - 1\) , \( i + 1\) , \( -229 i + 91\) , \( 188 i - 1663\bigr] \) |
${y}^2+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-229i+91\right){x}+188i-1663$ |
98000.3-e1 |
98000.3-e |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98000.3 |
\( 2^{4} \cdot 5^{3} \cdot 7^{2} \) |
\( 2^{4} \cdot 5^{8} \cdot 7^{6} \) |
$3.16210$ |
$(a+1), (-a-2), (2a+1), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1.156757163$ |
$0.534370180$ |
4.945092273 |
\( -\frac{225637236736}{1715} \) |
\( \bigl[0\) , \( i + 1\) , \( i + 1\) , \( 806 i - 604\) , \( 12162 i - 2669\bigr] \) |
${y}^2+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(806i-604\right){x}+12162i-2669$ |
98000.3-e2 |
98000.3-e |
$2$ |
$3$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98000.3 |
\( 2^{4} \cdot 5^{3} \cdot 7^{2} \) |
\( 2^{4} \cdot 5^{12} \cdot 7^{2} \) |
$3.16210$ |
$(a+1), (-a-2), (2a+1), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.385585721$ |
$1.603110541$ |
4.945092273 |
\( -\frac{65536}{875} \) |
\( \bigl[0\) , \( i + 1\) , \( i + 1\) , \( 6 i - 4\) , \( 32 i - 9\bigr] \) |
${y}^2+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(6i-4\right){x}+32i-9$ |
98000.3-f1 |
98000.3-f |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98000.3 |
\( 2^{4} \cdot 5^{3} \cdot 7^{2} \) |
\( 2^{4} \cdot 5^{8} \cdot 7^{10} \) |
$3.16210$ |
$(a+1), (-a-2), (2a+1), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$0.748684016$ |
1.497368032 |
\( \frac{14155776}{84035} \) |
\( \bigl[0\) , \( 0\) , \( i + 1\) , \( -32 i + 24\) , \( -292 i + 53\bigr] \) |
${y}^2+\left(i+1\right){y}={x}^{3}+\left(-32i+24\right){x}-292i+53$ |
98000.3-g1 |
98000.3-g |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98000.3 |
\( 2^{4} \cdot 5^{3} \cdot 7^{2} \) |
\( 2^{4} \cdot 5^{4} \cdot 7^{2} \) |
$3.16210$ |
$(a+1), (-a-2), (2a+1), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.293571801$ |
$4.202879954$ |
4.935388156 |
\( -\frac{149504}{35} a - \frac{264192}{35} \) |
\( \bigl[0\) , \( i\) , \( i + 1\) , \( 3 i + 2\) , \( i - 4\bigr] \) |
${y}^2+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(3i+2\right){x}+i-4$ |
98000.3-h1 |
98000.3-h |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98000.3 |
\( 2^{4} \cdot 5^{3} \cdot 7^{2} \) |
\( 2^{4} \cdot 5^{8} \cdot 7^{2} \) |
$3.16210$ |
$(a+1), (-a-2), (2a+1), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 2 \) |
$0.526913406$ |
$2.748597166$ |
5.793090781 |
\( -\frac{1024}{35} \) |
\( \bigl[0\) , \( -i - 1\) , \( i + 1\) , \( 2 i - 1\) , \( -7 i + 2\bigr] \) |
${y}^2+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(2i-1\right){x}-7i+2$ |
98000.3-i1 |
98000.3-i |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98000.3 |
\( 2^{4} \cdot 5^{3} \cdot 7^{2} \) |
\( 2^{12} \cdot 5^{24} \cdot 7^{2} \) |
$3.16210$ |
$(a+1), (-a-2), (2a+1), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.173289723$ |
3.119215019 |
\( -\frac{250523582464}{13671875} \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( 2102 i - 1576\) , \( 53504 i - 10922\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(2102i-1576\right){x}+53504i-10922$ |
98000.3-i2 |
98000.3-i |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98000.3 |
\( 2^{4} \cdot 5^{3} \cdot 7^{2} \) |
\( 2^{12} \cdot 5^{8} \cdot 7^{2} \) |
$3.16210$ |
$(a+1), (-a-2), (2a+1), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$1.559607509$ |
3.119215019 |
\( -\frac{262144}{35} \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( 22 i - 16\) , \( -56 i - 2\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(22i-16\right){x}-56i-2$ |
98000.3-i3 |
98000.3-i |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98000.3 |
\( 2^{4} \cdot 5^{3} \cdot 7^{2} \) |
\( 2^{12} \cdot 5^{12} \cdot 7^{6} \) |
$3.16210$ |
$(a+1), (-a-2), (2a+1), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3Cs |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$0.519869169$ |
3.119215019 |
\( \frac{71991296}{42875} \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( -138 i + 104\) , \( 136 i + 54\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(-138i+104\right){x}+136i+54$ |
98000.3-j1 |
98000.3-j |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98000.3 |
\( 2^{4} \cdot 5^{3} \cdot 7^{2} \) |
\( 2^{20} \cdot 5^{10} \cdot 7^{2} \) |
$3.16210$ |
$(a+1), (-a-2), (2a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.827333732$ |
3.309334931 |
\( \frac{1367631}{2800} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( -37 i + 27\) , \( -176 i + 53\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-37i+27\right){x}-176i+53$ |
98000.3-j2 |
98000.3-j |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98000.3 |
\( 2^{4} \cdot 5^{3} \cdot 7^{2} \) |
\( 2^{16} \cdot 5^{14} \cdot 7^{4} \) |
$3.16210$ |
$(a+1), (-a-2), (2a+1), (7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.413666866$ |
3.309334931 |
\( \frac{611960049}{122500} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 283 i - 213\) , \( -2144 i + 229\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(283i-213\right){x}-2144i+229$ |
98000.3-j3 |
98000.3-j |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98000.3 |
\( 2^{4} \cdot 5^{3} \cdot 7^{2} \) |
\( 2^{14} \cdot 5^{22} \cdot 7^{2} \) |
$3.16210$ |
$(a+1), (-a-2), (2a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.206833433$ |
3.309334931 |
\( \frac{74565301329}{5468750} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 1403 i - 1053\) , \( 25464 i - 5427\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(1403i-1053\right){x}+25464i-5427$ |
98000.3-j4 |
98000.3-j |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
98000.3 |
\( 2^{4} \cdot 5^{3} \cdot 7^{2} \) |
\( 2^{14} \cdot 5^{10} \cdot 7^{8} \) |
$3.16210$ |
$(a+1), (-a-2), (2a+1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.206833433$ |
3.309334931 |
\( \frac{2121328796049}{120050} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 4283 i - 3213\) , \( -149944 i + 24829\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(4283i-3213\right){x}-149944i+24829$ |
*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.