| 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 |
| 8100.2-a1 |
8100.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8100.2 |
\( 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{8} \) |
$1.69547$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$0.400741926$ |
$1.635871764$ |
2.622249606 |
\( -\frac{42660324}{15625} a + \frac{45166032}{15625} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( -21 i + 3\) , \( -20 i + 35\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-21i+3\right){x}-20i+35$ |
| 8100.2-a2 |
8100.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8100.2 |
\( 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{18} \cdot 5^{8} \) |
$1.69547$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1.202225778$ |
$0.545290588$ |
2.622249606 |
\( \frac{42660324}{15625} a + \frac{45166032}{15625} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 189 i + 33\) , \( 604 i + 567\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(189i+33\right){x}+604i+567$ |
| 8100.2-a3 |
8100.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8100.2 |
\( 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{18} \cdot 5^{4} \) |
$1.69547$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$2.404451556$ |
$1.090581176$ |
2.622249606 |
\( -\frac{1556928}{125} a + \frac{930096}{125} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( 53 i + 33\) , \( -4 i + 162\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(53i+33\right){x}-4i+162$ |
| 8100.2-a4 |
8100.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8100.2 |
\( 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 5^{4} \) |
$1.69547$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.801483852$ |
$3.271743528$ |
2.622249606 |
\( \frac{1556928}{125} a + \frac{930096}{125} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -7 i + 3\) , \( 2 i + 10\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-7i+3\right){x}+2i+10$ |
| 8100.2-b1 |
8100.2-b |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8100.2 |
\( 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{18} \cdot 5^{8} \) |
$1.69547$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1.202225778$ |
$0.545290588$ |
2.622249606 |
\( -\frac{42660324}{15625} a + \frac{45166032}{15625} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -190 i + 33\) , \( -571 i + 756\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-190i+33\right){x}-571i+756$ |
| 8100.2-b2 |
8100.2-b |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8100.2 |
\( 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{8} \) |
$1.69547$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$0.400741926$ |
$1.635871764$ |
2.622249606 |
\( \frac{42660324}{15625} a + \frac{45166032}{15625} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( 20 i + 3\) , \( 23 i + 14\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(20i+3\right){x}+23i+14$ |
| 8100.2-b3 |
8100.2-b |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8100.2 |
\( 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 5^{4} \) |
$1.69547$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.801483852$ |
$3.271743528$ |
2.622249606 |
\( -\frac{1556928}{125} a + \frac{930096}{125} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 6 i + 3\) , \( i + 4\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(6i+3\right){x}+i+4$ |
| 8100.2-b4 |
8100.2-b |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8100.2 |
\( 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{18} \cdot 5^{4} \) |
$1.69547$ |
$(a+1), (-a-2), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$2.404451556$ |
$1.090581176$ |
2.622249606 |
\( \frac{1556928}{125} a + \frac{930096}{125} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( -54 i + 33\) , \( 37 i + 216\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-54i+33\right){x}+37i+216$ |
| 8100.2-c1 |
8100.2-c |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8100.2 |
\( 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 5^{5} \) |
$1.69547$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$1.070515942$ |
2.141031885 |
\( -\frac{59648644}{625} a - \frac{119744792}{625} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( 44 i - 99\) , \( -311 i + 324\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(44i-99\right){x}-311i+324$ |
| 8100.2-c2 |
8100.2-c |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8100.2 |
\( 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 5^{5} \) |
$1.69547$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$1.070515942$ |
2.141031885 |
\( \frac{59648644}{625} a - \frac{119744792}{625} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( -45 i - 99\) , \( 212 i + 369\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-45i-99\right){x}+212i+369$ |
| 8100.2-c3 |
8100.2-c |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8100.2 |
\( 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 5^{15} \) |
$1.69547$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{3} \) |
$1$ |
$0.356838647$ |
2.141031885 |
\( -\frac{893935595564}{244140625} a - \frac{1336401187352}{244140625} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( 494 i - 9\) , \( 3199 i + 3186\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(494i-9\right){x}+3199i+3186$ |
| 8100.2-c4 |
8100.2-c |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8100.2 |
\( 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 5^{15} \) |
$1.69547$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{3} \) |
$1$ |
$0.356838647$ |
2.141031885 |
\( \frac{893935595564}{244140625} a - \frac{1336401187352}{244140625} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( -495 i - 9\) , \( -3208 i + 3681\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(-495i-9\right){x}-3208i+3681$ |
| 8100.2-c5 |
8100.2-c |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8100.2 |
\( 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 5^{12} \) |
$1.69547$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{3} \) |
$1$ |
$0.713677295$ |
2.141031885 |
\( -\frac{20720464}{15625} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 81\) , \( -391 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+81{x}-391i$ |
| 8100.2-c6 |
8100.2-c |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8100.2 |
\( 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 5^{4} \) |
$1.69547$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$1$ |
$2.141031885$ |
2.141031885 |
\( \frac{21296}{25} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( -9\) , \( 5 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}-9{x}+5i$ |
| 8100.2-c7 |
8100.2-c |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8100.2 |
\( 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 5^{2} \) |
$1.69547$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$2.141031885$ |
2.141031885 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -12\) , \( -11\bigr] \) |
${y}^2={x}^{3}-12{x}-11$ |
| 8100.2-c8 |
8100.2-c |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8100.2 |
\( 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 5^{6} \) |
$1.69547$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$1$ |
$0.713677295$ |
2.141031885 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -372\) , \( 2761\bigr] \) |
${y}^2={x}^{3}-372{x}+2761$ |
*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.
