| 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 |
| 19200.1-a1 |
19200.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{2} \cdot 5^{2} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.083452188$ |
$3.481586885$ |
2.683949384 |
\( \frac{21296}{15} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 4\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+4{x}$ |
| 19200.1-a2 |
19200.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{4} \cdot 5^{4} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.333808752$ |
$1.740793442$ |
2.683949384 |
\( \frac{470596}{225} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -16\) , \( 16\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-16{x}+16$ |
| 19200.1-a3 |
19200.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{2} \cdot 5^{8} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.333808752$ |
$0.870396721$ |
2.683949384 |
\( \frac{136835858}{1875} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -136\) , \( -560\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-136{x}-560$ |
| 19200.1-a4 |
19200.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{8} \cdot 5^{2} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.333808752$ |
$0.870396721$ |
2.683949384 |
\( \frac{546718898}{405} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -216\) , \( 1296\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-216{x}+1296$ |
| 19200.1-b1 |
19200.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{8} \cdot 5^{4} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.506476365$ |
$1.036005372$ |
2.423542006 |
\( \frac{8435734}{2025} a - \frac{2456854}{2025} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 58 a - 43\) , \( -159 a + 42\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(58a-43\right){x}-159a+42$ |
| 19200.1-b2 |
19200.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{4} \cdot 5^{2} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.253238182$ |
$2.072010745$ |
2.423542006 |
\( -\frac{556852}{45} a + 5088 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 18 a - 3\) , \( 9 a + 18\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(18a-3\right){x}+9a+18$ |
| 19200.1-c1 |
19200.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{2} \cdot 5^{16} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.382893755$ |
1.768510500 |
\( -\frac{27995042}{1171875} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -80\) , \( 2400\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-80{x}+2400$ |
| 19200.1-c2 |
19200.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{16} \cdot 5^{2} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.765787510$ |
1.768510500 |
\( \frac{54607676}{32805} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 80\) , \( -80\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+80{x}-80$ |
| 19200.1-c3 |
19200.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{8} \cdot 5^{4} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.531575020$ |
1.768510500 |
\( \frac{3631696}{2025} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -20\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-20{x}$ |
| 19200.1-c4 |
19200.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{4} \cdot 5^{8} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$1$ |
$0.765787510$ |
1.768510500 |
\( \frac{868327204}{5625} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -200\) , \( 1152\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-200{x}+1152$ |
| 19200.1-c5 |
19200.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{2} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.063150040$ |
1.768510500 |
\( \frac{24918016}{45} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -15\) , \( -18\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-15{x}-18$ |
| 19200.1-c6 |
19200.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{2} \cdot 5^{4} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.382893755$ |
1.768510500 |
\( \frac{1770025017602}{75} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -3200\) , \( 70752\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-3200{x}+70752$ |
| 19200.1-d1 |
19200.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{4} \cdot 5^{2} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.253238182$ |
$2.072010745$ |
2.423542006 |
\( \frac{556852}{45} a - \frac{327892}{45} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 3 a - 18\) , \( -9 a + 27\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(3a-18\right){x}-9a+27$ |
| 19200.1-d2 |
19200.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{8} \cdot 5^{4} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.506476365$ |
$1.036005372$ |
2.423542006 |
\( -\frac{8435734}{2025} a + \frac{44288}{15} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 43 a - 58\) , \( 159 a - 117\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(43a-58\right){x}+159a-117$ |
| 19200.1-e1 |
19200.1-e |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{48} \cdot 3^{2} \cdot 5^{6} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.323572535$ |
2.241776282 |
\( -\frac{273359449}{1536000} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -216\) , \( 4080\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-216{x}+4080$ |
| 19200.1-e2 |
19200.1-e |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{32} \cdot 3^{6} \cdot 5^{2} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$0.970717605$ |
2.241776282 |
\( \frac{357911}{2160} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 24\) , \( -144\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+24{x}-144$ |
| 19200.1-e3 |
19200.1-e |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{30} \cdot 3^{2} \cdot 5^{24} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B[2] |
$4$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.080893133$ |
2.241776282 |
\( \frac{10316097499609}{5859375000} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -7256\) , \( 34800\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-7256{x}+34800$ |
| 19200.1-e4 |
19200.1-e |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{26} \cdot 3^{24} \cdot 5^{2} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B[2] |
$4$ |
\( 2^{3} \) |
$1$ |
$0.242679401$ |
2.241776282 |
\( \frac{35578826569}{5314410} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -1096\) , \( 12400\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-1096{x}+12400$ |
| 19200.1-e5 |
19200.1-e |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{28} \cdot 3^{12} \cdot 5^{4} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B[2] |
$4$ |
\( 2^{4} \) |
$1$ |
$0.485358802$ |
2.241776282 |
\( \frac{702595369}{72900} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -296\) , \( -1680\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-296{x}-1680$ |
| 19200.1-e6 |
19200.1-e |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{36} \cdot 3^{4} \cdot 5^{12} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B[2] |
$4$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.161786267$ |
2.241776282 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -5336\) , \( 151536\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-5336{x}+151536$ |
| 19200.1-e7 |
19200.1-e |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{26} \cdot 3^{6} \cdot 5^{8} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B[2] |
$4$ |
\( 2^{5} \) |
$1$ |
$0.242679401$ |
2.241776282 |
\( \frac{2656166199049}{33750} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -4616\) , \( -119184\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-4616{x}-119184$ |
| 19200.1-e8 |
19200.1-e |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{30} \cdot 3^{8} \cdot 5^{6} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B[2] |
$4$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.080893133$ |
2.241776282 |
\( \frac{16778985534208729}{81000} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -85336\) , \( 9623536\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-85336{x}+9623536$ |
| 19200.1-f1 |
19200.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{4} \cdot 5^{2} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.171946953$ |
$2.072010745$ |
3.291136107 |
\( \frac{556852}{45} a - \frac{327892}{45} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 3 a - 18\) , \( 9 a - 27\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(3a-18\right){x}+9a-27$ |
| 19200.1-f2 |
19200.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{8} \cdot 5^{4} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.085973476$ |
$1.036005372$ |
3.291136107 |
\( -\frac{8435734}{2025} a + \frac{44288}{15} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 43 a - 58\) , \( -159 a + 117\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(43a-58\right){x}-159a+117$ |
| 19200.1-g1 |
19200.1-g |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{32} \cdot 5^{2} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1.300312843$ |
$0.139731357$ |
3.356843389 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1760\) , \( 52788\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-1760{x}+52788$ |
| 19200.1-g2 |
19200.1-g |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{2} \cdot 5^{2} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.325078210$ |
$2.235701712$ |
3.356843389 |
\( -\frac{1}{15} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 0\) , \( -12\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-12$ |
| 19200.1-g3 |
19200.1-g |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{4} \cdot 5^{16} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$0.650156421$ |
$0.279462714$ |
3.356843389 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 560\) , \( 2900\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+560{x}+2900$ |
| 19200.1-g4 |
19200.1-g |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{8} \cdot 5^{8} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1.300312843$ |
$0.558925428$ |
3.356843389 |
\( \frac{111284641}{50625} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -160\) , \( 308\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-160{x}+308$ |
| 19200.1-g5 |
19200.1-g |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{4} \cdot 5^{4} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.650156421$ |
$1.117850856$ |
3.356843389 |
\( \frac{13997521}{225} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -80\) , \( -300\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-80{x}-300$ |
| 19200.1-g6 |
19200.1-g |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{16} \cdot 5^{4} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$2.600625687$ |
$0.279462714$ |
3.356843389 |
\( \frac{272223782641}{164025} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -2160\) , \( 37908\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-2160{x}+37908$ |
| 19200.1-g7 |
19200.1-g |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{2} \cdot 5^{2} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.300312843$ |
$0.558925428$ |
3.356843389 |
\( \frac{56667352321}{15} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1280\) , \( -18060\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-1280{x}-18060$ |
| 19200.1-g8 |
19200.1-g |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{24} \cdot 3^{8} \cdot 5^{2} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$5.201251375$ |
$0.139731357$ |
3.356843389 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -34560\) , \( 2461428\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-34560{x}+2461428$ |
| 19200.1-h1 |
19200.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{22} \cdot 3^{8} \cdot 5^{4} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.085973476$ |
$1.036005372$ |
3.291136107 |
\( \frac{8435734}{2025} a - \frac{2456854}{2025} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -15 a + 58\) , \( 159 a - 42\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-15a+58\right){x}+159a-42$ |
| 19200.1-h2 |
19200.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{4} \cdot 5^{2} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.171946953$ |
$2.072010745$ |
3.291136107 |
\( -\frac{556852}{45} a + 5088 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -15 a + 18\) , \( -9 a - 18\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-15a+18\right){x}-9a-18$ |
*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.
