| 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 |
| 68450.5-a1 |
68450.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2^{2} \cdot 5^{2} \cdot 37^{8} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.604991208$ |
$0.858111294$ |
2.076599157 |
\( \frac{1689410871}{18741610} \) |
\( \bigl[i\) , \( 1\) , \( 0\) , \( 25\) , \( 209\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+{x}^{2}+25{x}+209$ |
| 68450.5-a2 |
68450.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2^{8} \cdot 5^{2} \cdot 37^{2} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.604991208$ |
$3.432445179$ |
2.076599157 |
\( \frac{15438249}{2960} \) |
\( \bigl[i\) , \( 1\) , \( 0\) , \( -5\) , \( -5\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+{x}^{2}-5{x}-5$ |
| 68450.5-a3 |
68450.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2^{4} \cdot 5^{4} \cdot 37^{4} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.302495604$ |
$1.716222589$ |
2.076599157 |
\( \frac{1767172329}{136900} \) |
\( \bigl[i\) , \( 1\) , \( 0\) , \( -25\) , \( 39\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+{x}^{2}-25{x}+39$ |
| 68450.5-a4 |
68450.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2^{2} \cdot 5^{8} \cdot 37^{2} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.604991208$ |
$0.858111294$ |
2.076599157 |
\( \frac{6825481747209}{46250} \) |
\( \bigl[i\) , \( 1\) , \( 0\) , \( -395\) , \( 2925\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+{x}^{2}-395{x}+2925$ |
| 68450.5-b1 |
68450.5-b |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2^{2} \cdot 5^{2} \cdot 37^{2} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$2.402409187$ |
$2.186771298$ |
2.334897536 |
\( -\frac{16954786009}{370} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( -53\) , \( -146\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-53{x}-146$ |
| 68450.5-b2 |
68450.5-b |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2^{6} \cdot 5^{6} \cdot 37^{6} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.800803062$ |
$0.728923766$ |
2.334897536 |
\( -\frac{702595369}{50653000} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( -18\) , \( -342\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-18{x}-342$ |
| 68450.5-b3 |
68450.5-b |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2^{18} \cdot 5^{18} \cdot 37^{2} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$2.402409187$ |
$0.242974588$ |
2.334897536 |
\( \frac{510273943271}{37000000000} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( 167\) , \( 9204\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+167{x}+9204$ |
| 68450.5-c1 |
68450.5-c |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2^{3} \cdot 5^{15} \cdot 37^{3} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$0.292829669$ |
$0.563848334$ |
4.623122610 |
\( \frac{381018345107444271}{33422851562500} a - \frac{27278761668403303}{33422851562500} \) |
\( \bigl[1\) , \( -i - 1\) , \( 1\) , \( -183 i - 132\) , \( -1226 i - 124\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-183i-132\right){x}-1226i-124$ |
| 68450.5-c2 |
68450.5-c |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2^{6} \cdot 5^{9} \cdot 37^{3} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 7 \) |
$0.073207417$ |
$1.127696669$ |
4.623122610 |
\( -\frac{2967941642509}{855625000} a + \frac{110070123389}{106953125} \) |
\( \bigl[i\) , \( i + 1\) , \( i\) , \( -13 i - 41\) , \( -42 i - 112\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-13i-41\right){x}-42i-112$ |
| 68450.5-d1 |
68450.5-d |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2^{3} \cdot 5^{15} \cdot 37^{3} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$0.292829669$ |
$0.563848334$ |
4.623122610 |
\( -\frac{381018345107444271}{33422851562500} a - \frac{27278761668403303}{33422851562500} \) |
\( \bigl[i\) , \( -i + 1\) , \( i\) , \( 183 i - 131\) , \( -1226 i + 124\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(183i-131\right){x}-1226i+124$ |
| 68450.5-d2 |
68450.5-d |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2^{6} \cdot 5^{9} \cdot 37^{3} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 7 \) |
$0.073207417$ |
$1.127696669$ |
4.623122610 |
\( \frac{2967941642509}{855625000} a + \frac{110070123389}{106953125} \) |
\( \bigl[1\) , \( i - 1\) , \( 1\) , \( 13 i - 42\) , \( -42 i + 112\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(13i-42\right){x}-42i+112$ |
| 68450.5-e1 |
68450.5-e |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2^{22} \cdot 5^{2} \cdot 37^{2} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.585252191$ |
$1.631436169$ |
3.819206376 |
\( \frac{214921799}{378880} \) |
\( \bigl[i\) , \( -1\) , \( 0\) , \( 13\) , \( 19\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-{x}^{2}+13{x}+19$ |
| 68450.5-f1 |
68450.5-f |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2^{18} \cdot 5^{3} \cdot 37^{3} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$0.134999260$ |
$1.317717944$ |
6.404074123 |
\( \frac{1346487493}{17523200} a + \frac{7432037549}{4380800} \) |
\( \bigl[i\) , \( 0\) , \( i + 1\) , \( 11 i + 25\) , \( -2 i - 14\bigr] \) |
${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+\left(11i+25\right){x}-2i-14$ |
| 68450.5-f2 |
68450.5-f |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2^{9} \cdot 5^{3} \cdot 37^{6} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$0.269998520$ |
$0.658858972$ |
6.404074123 |
\( -\frac{155462940438507}{1499328800} a + \frac{237224048385169}{1499328800} \) |
\( \bigl[i\) , \( 0\) , \( i + 1\) , \( 91 i + 265\) , \( -1586 i + 834\bigr] \) |
${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+\left(91i+265\right){x}-1586i+834$ |
| 68450.5-g1 |
68450.5-g |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2^{18} \cdot 5^{3} \cdot 37^{3} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$0.134999260$ |
$1.317717944$ |
6.404074123 |
\( -\frac{1346487493}{17523200} a + \frac{7432037549}{4380800} \) |
\( \bigl[1\) , \( 0\) , \( i + 1\) , \( -12 i + 24\) , \( -2 i + 14\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-12i+24\right){x}-2i+14$ |
| 68450.5-g2 |
68450.5-g |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2^{9} \cdot 5^{3} \cdot 37^{6} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$0.269998520$ |
$0.658858972$ |
6.404074123 |
\( \frac{155462940438507}{1499328800} a + \frac{237224048385169}{1499328800} \) |
\( \bigl[1\) , \( 0\) , \( i + 1\) , \( -92 i + 264\) , \( -1586 i - 834\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-92i+264\right){x}-1586i-834$ |
| 68450.5-h1 |
68450.5-h |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2^{6} \cdot 5^{15} \cdot 37^{5} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2^{5} \cdot 3^{3} \) |
$1$ |
$0.207070166$ |
4.969683988 |
\( -\frac{818871339068490287063}{3660470703125000} a - \frac{45099024956931216152}{457558837890625} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -920 i + 2805\) , \( 54952 i + 28239\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+\left(-920i+2805\right){x}+54952i+28239$ |
| 68450.5-h2 |
68450.5-h |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2^{6} \cdot 5^{15} \cdot 37^{5} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2^{5} \cdot 3^{3} \) |
$1$ |
$0.207070166$ |
4.969683988 |
\( \frac{818871339068490287063}{3660470703125000} a - \frac{45099024956931216152}{457558837890625} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( 920 i + 2805\) , \( -54952 i + 28239\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+\left(920i+2805\right){x}-54952i+28239$ |
| 68450.5-h3 |
68450.5-h |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2^{4} \cdot 5^{4} \cdot 37^{12} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{6} \cdot 3^{2} \) |
$1$ |
$0.138046777$ |
4.969683988 |
\( -\frac{16048965315233521}{256572640900} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -5255\) , \( 149075\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-5255{x}+149075$ |
| 68450.5-h4 |
68450.5-h |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2^{2} \cdot 5^{5} \cdot 37^{15} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2^{5} \cdot 3^{2} \) |
$1$ |
$0.069023388$ |
4.969683988 |
\( -\frac{3925596463972580570890057}{8228690007300044101250} a + \frac{1684584749749505877267688}{4114345003650022050625} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( 5030 i - 5095\) , \( 293862 i + 186619\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+\left(5030i-5095\right){x}+293862i+186619$ |
| 68450.5-h5 |
68450.5-h |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2^{2} \cdot 5^{5} \cdot 37^{15} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2^{5} \cdot 3^{2} \) |
$1$ |
$0.069023388$ |
4.969683988 |
\( \frac{3925596463972580570890057}{8228690007300044101250} a + \frac{1684584749749505877267688}{4114345003650022050625} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -5030 i - 5095\) , \( -293862 i + 186619\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+\left(-5030i-5095\right){x}-293862i+186619$ |
| 68450.5-h6 |
68450.5-h |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2^{12} \cdot 5^{12} \cdot 37^{4} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{6} \cdot 3^{3} \) |
$1$ |
$0.414140332$ |
4.969683988 |
\( \frac{1625964918479}{1369000000} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( 245\) , \( 975\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+245{x}+975$ |
| 68450.5-h7 |
68450.5-h |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2^{24} \cdot 5^{6} \cdot 37^{2} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{3} \) |
$1$ |
$0.828280664$ |
4.969683988 |
\( \frac{46694890801}{18944000} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -75\) , \( 143\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-75{x}+143$ |
| 68450.5-h8 |
68450.5-h |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2^{8} \cdot 5^{2} \cdot 37^{6} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.276093554$ |
4.969683988 |
\( \frac{16232905099479601}{4052240} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -5275\) , \( 147903\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-5275{x}+147903$ |
| 68450.5-i1 |
68450.5-i |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2^{4} \cdot 5^{5} \cdot 37^{3} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$2.278397211$ |
4.556794423 |
\( -\frac{34353674}{855625} a + \frac{2747628703}{3422500} \) |
\( \bigl[i\) , \( i\) , \( i\) , \( 4 i + 6\) , \( -5 i - 6\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(4i+6\right){x}-5i-6$ |
| 68450.5-i2 |
68450.5-i |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2^{2} \cdot 5^{4} \cdot 37^{6} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$1.139198605$ |
4.556794423 |
\( \frac{517593117}{3748322} a + \frac{160844155574}{46854025} \) |
\( \bigl[i\) , \( i\) , \( i\) , \( -26 i - 34\) , \( -73 i - 30\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(-26i-34\right){x}-73i-30$ |
| 68450.5-i3 |
68450.5-i |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2 \cdot 5^{2} \cdot 37^{9} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.569599302$ |
4.556794423 |
\( -\frac{11118569221560365}{7024958907842} a + \frac{824691791614398091}{35124794539210} \) |
\( \bigl[i\) , \( i\) , \( i\) , \( -151 i - 209\) , \( 1177 i + 980\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(-151i-209\right){x}+1177i+980$ |
| 68450.5-i4 |
68450.5-i |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2 \cdot 5^{5} \cdot 37^{6} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$1$ |
$0.569599302$ |
4.556794423 |
\( \frac{1743482895211437}{2342701250} a + \frac{15919076014245841}{2342701250} \) |
\( \bigl[i\) , \( i\) , \( i\) , \( -381 i - 499\) , \( -5155 i - 3216\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(-381i-499\right){x}-5155i-3216$ |
| 68450.5-j1 |
68450.5-j |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2^{4} \cdot 5^{5} \cdot 37^{3} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$2.278397211$ |
4.556794423 |
\( \frac{34353674}{855625} a + \frac{2747628703}{3422500} \) |
\( \bigl[1\) , \( i\) , \( 1\) , \( -4 i + 5\) , \( -5 i + 6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+i{x}^{2}+\left(-4i+5\right){x}-5i+6$ |
| 68450.5-j2 |
68450.5-j |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2^{2} \cdot 5^{4} \cdot 37^{6} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$1.139198605$ |
4.556794423 |
\( -\frac{517593117}{3748322} a + \frac{160844155574}{46854025} \) |
\( \bigl[1\) , \( i\) , \( 1\) , \( 26 i - 35\) , \( -73 i + 30\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+i{x}^{2}+\left(26i-35\right){x}-73i+30$ |
| 68450.5-j3 |
68450.5-j |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2 \cdot 5^{2} \cdot 37^{9} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.569599302$ |
4.556794423 |
\( \frac{11118569221560365}{7024958907842} a + \frac{824691791614398091}{35124794539210} \) |
\( \bigl[1\) , \( i\) , \( 1\) , \( 151 i - 210\) , \( 1177 i - 980\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+i{x}^{2}+\left(151i-210\right){x}+1177i-980$ |
| 68450.5-j4 |
68450.5-j |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
68450.5 |
\( 2 \cdot 5^{2} \cdot 37^{2} \) |
\( 2 \cdot 5^{5} \cdot 37^{6} \) |
$2.89076$ |
$(a+1), (-a-2), (2a+1), (a+6), (a-6)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$1$ |
$0.569599302$ |
4.556794423 |
\( -\frac{1743482895211437}{2342701250} a + \frac{15919076014245841}{2342701250} \) |
\( \bigl[1\) , \( i\) , \( 1\) , \( 381 i - 500\) , \( -5155 i + 3216\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+i{x}^{2}+\left(381i-500\right){x}-5155i+3216$ |
*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.
