| 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 |
| 5202.5-a1 |
5202.5-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{22} \cdot 3^{8} \cdot 17^{3} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.887997728$ |
0.627909215 |
\( -\frac{288090894583}{323606016} a + \frac{3514414555109}{1294424064} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -33 a + 50\) , \( -36 a - 134\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-33a+50\right){x}-36a-134$ |
| 5202.5-a2 |
5202.5-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{11} \cdot 3^{16} \cdot 17^{3} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.443998864$ |
0.627909215 |
\( -\frac{311615647507297603}{88465794624} a + \frac{41779045002361607}{22116448656} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -513 a + 690\) , \( -3204 a - 11142\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-513a+690\right){x}-3204a-11142$ |
| 5202.5-b1 |
5202.5-b |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{22} \cdot 3^{8} \cdot 17^{3} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$0.887997728$ |
0.627909215 |
\( \frac{288090894583}{323606016} a + \frac{3514414555109}{1294424064} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 33 a + 50\) , \( 36 a - 134\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(33a+50\right){x}+36a-134$ |
| 5202.5-b2 |
5202.5-b |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{11} \cdot 3^{16} \cdot 17^{3} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.443998864$ |
0.627909215 |
\( \frac{311615647507297603}{88465794624} a + \frac{41779045002361607}{22116448656} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 513 a + 690\) , \( 3204 a - 11142\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(513a+690\right){x}+3204a-11142$ |
| 5202.5-c1 |
5202.5-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2 \cdot 3^{10} \cdot 17^{5} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.573015571$ |
$1.151150664$ |
1.865707623 |
\( -\frac{118666603548005}{1095962562} a - \frac{91723455040024}{547981281} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -25 a + 88\) , \( 199 a + 230\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-25a+88\right){x}+199a+230$ |
| 5202.5-c2 |
5202.5-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2 \cdot 3^{10} \cdot 17^{5} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.573015571$ |
$1.151150664$ |
1.865707623 |
\( \frac{118666603548005}{1095962562} a - \frac{91723455040024}{547981281} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 25 a + 88\) , \( -199 a + 230\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(25a+88\right){x}-199a+230$ |
| 5202.5-c3 |
5202.5-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 17^{4} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.286507785$ |
$2.302301329$ |
1.865707623 |
\( \frac{46268279}{46818} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 8\) , \( 10\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+8{x}+10$ |
| 5202.5-c4 |
5202.5-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 17^{2} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.143253892$ |
$4.604602658$ |
1.865707623 |
\( \frac{1771561}{612} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -2\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-2{x}$ |
| 5202.5-d1 |
5202.5-d |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{9} \cdot 3^{10} \cdot 17^{15} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{5} \) |
$4.545067097$ |
$0.069311322$ |
3.564096622 |
\( -\frac{795638018697416056308875}{122322703950862781472} a - \frac{740752568391229768255000}{3822584498464461921} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -8560 a + 22289\) , \( -811360 a - 1058718\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-8560a+22289\right){x}-811360a-1058718$ |
| 5202.5-d2 |
5202.5-d |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{9} \cdot 3^{10} \cdot 17^{15} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{5} \) |
$4.545067097$ |
$0.069311322$ |
3.564096622 |
\( \frac{795638018697416056308875}{122322703950862781472} a - \frac{740752568391229768255000}{3822584498464461921} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 8560 a + 22289\) , \( 811360 a - 1058718\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(8560a+22289\right){x}+811360a-1058718$ |
| 5202.5-d3 |
5202.5-d |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{3} \cdot 3^{30} \cdot 17^{5} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$1.515022365$ |
$0.207933967$ |
3.564096622 |
\( -\frac{410311536960329978125}{94355189265718404} a - \frac{136155893118005119000}{23588797316429601} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1090 a + 104\) , \( -12160 a + 18366\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-1090a+104\right){x}-12160a+18366$ |
| 5202.5-d4 |
5202.5-d |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{3} \cdot 3^{30} \cdot 17^{5} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$1.515022365$ |
$0.207933967$ |
3.564096622 |
\( \frac{410311536960329978125}{94355189265718404} a - \frac{136155893118005119000}{23588797316429601} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 1090 a + 104\) , \( 12160 a + 18366\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(1090a+104\right){x}+12160a+18366$ |
| 5202.5-d5 |
5202.5-d |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{6} \cdot 3^{24} \cdot 17^{4} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{7} \cdot 3^{2} \) |
$0.757511182$ |
$0.415867934$ |
3.564096622 |
\( -\frac{1107111813625}{1228691592} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -216\) , \( 2062\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-216{x}+2062$ |
| 5202.5-d6 |
5202.5-d |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{18} \cdot 3^{8} \cdot 17^{12} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{7} \) |
$2.272533548$ |
$0.138622644$ |
3.564096622 |
\( \frac{655215969476375}{1001033261568} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 1809\) , \( -37790\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+1809{x}-37790$ |
| 5202.5-d7 |
5202.5-d |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{36} \cdot 3^{4} \cdot 17^{6} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$4.545067097$ |
$0.277245289$ |
3.564096622 |
\( \frac{46753267515625}{11591221248} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -751\) , \( -6046\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-751{x}-6046$ |
| 5202.5-d8 |
5202.5-d |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{12} \cdot 3^{12} \cdot 17^{2} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1.515022365$ |
$0.831735869$ |
3.564096622 |
\( \frac{1845026709625}{793152} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -256\) , \( 1550\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-256{x}+1550$ |
| 5202.5-e1 |
5202.5-e |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2 \cdot 3^{8} \cdot 17^{9} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.318337197$ |
1.800787128 |
\( \frac{28973973968878862165}{10170654348978} a - \frac{227019597633725057126}{5085327174489} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 1776 a - 186\) , \( -26138 a - 30473\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(1776a-186\right){x}-26138a-30473$ |
| 5202.5-e2 |
5202.5-e |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 17^{3} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.546697580$ |
1.800787128 |
\( -\frac{63405599}{7803} a - \frac{2377909445}{124848} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -9 a + 4\) , \( -15\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-9a+4\right){x}-15$ |
| 5202.5-e3 |
5202.5-e |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{8} \cdot 17^{6} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$1.273348790$ |
1.800787128 |
\( -\frac{21406940170}{60886809} a - \frac{61807844839}{243547236} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -9 a - 16\) , \( -28 a - 63\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-9a-16\right){x}-28a-63$ |
| 5202.5-e4 |
5202.5-e |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{2} \cdot 3^{16} \cdot 17^{6} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.636674395$ |
1.800787128 |
\( \frac{208995993887450}{44386483761} a + \frac{92858826184591}{88772967522} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 111 a - 6\) , \( -398 a - 431\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(111a-6\right){x}-398a-431$ |
| 5202.5-e5 |
5202.5-e |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2 \cdot 3^{32} \cdot 17^{3} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.318337197$ |
1.800787128 |
\( -\frac{689132974759173725}{163244272086018} a + \frac{92030074203444902}{81622136043009} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 366 a + 334\) , \( -738 a + 5859\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(366a+334\right){x}-738a+5859$ |
| 5202.5-e6 |
5202.5-e |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 17^{9} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.636674395$ |
1.800787128 |
\( \frac{132789029221532066}{188345450907} a + \frac{141186623119318075}{376690901814} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -129 a - 346\) , \( -1450 a - 2367\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-129a-346\right){x}-1450a-2367$ |
| 5202.5-f1 |
5202.5-f |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2 \cdot 3^{8} \cdot 17^{9} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.318337197$ |
1.800787128 |
\( -\frac{28973973968878862165}{10170654348978} a - \frac{227019597633725057126}{5085327174489} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -1777 a - 186\) , \( 26137 a - 30473\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-1777a-186\right){x}+26137a-30473$ |
| 5202.5-f2 |
5202.5-f |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 17^{3} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.546697580$ |
1.800787128 |
\( \frac{63405599}{7803} a - \frac{2377909445}{124848} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 8 a + 4\) , \( -a - 15\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(8a+4\right){x}-a-15$ |
| 5202.5-f3 |
5202.5-f |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{8} \cdot 17^{6} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$1.273348790$ |
1.800787128 |
\( \frac{21406940170}{60886809} a - \frac{61807844839}{243547236} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 8 a - 16\) , \( 27 a - 63\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(8a-16\right){x}+27a-63$ |
| 5202.5-f4 |
5202.5-f |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{2} \cdot 3^{16} \cdot 17^{6} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.636674395$ |
1.800787128 |
\( -\frac{208995993887450}{44386483761} a + \frac{92858826184591}{88772967522} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -112 a - 6\) , \( 397 a - 431\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-112a-6\right){x}+397a-431$ |
| 5202.5-f5 |
5202.5-f |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2 \cdot 3^{32} \cdot 17^{3} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.318337197$ |
1.800787128 |
\( \frac{689132974759173725}{163244272086018} a + \frac{92030074203444902}{81622136043009} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -367 a + 334\) , \( 737 a + 5859\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-367a+334\right){x}+737a+5859$ |
| 5202.5-f6 |
5202.5-f |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 17^{9} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.636674395$ |
1.800787128 |
\( -\frac{132789029221532066}{188345450907} a + \frac{141186623119318075}{376690901814} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 128 a - 346\) , \( 1449 a - 2367\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(128a-346\right){x}+1449a-2367$ |
| 5202.5-g1 |
5202.5-g |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{5} \cdot 3^{24} \cdot 17^{3} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.545397751$ |
3.856544483 |
\( -\frac{32297532210782725}{72553009816008} a + \frac{60468973557987577}{18138252454002} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 89 a - 137\) , \( -532 a + 213\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(89a-137\right){x}-532a+213$ |
| 5202.5-g2 |
5202.5-g |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{10} \cdot 3^{12} \cdot 17^{3} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$1.090795502$ |
3.856544483 |
\( \frac{2091127194353}{409563864} a + \frac{36587816460805}{1638255456} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 29 a - 57\) , \( 100 a - 131\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(29a-57\right){x}+100a-131$ |
| 5202.5-h1 |
5202.5-h |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{5} \cdot 3^{24} \cdot 17^{3} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.545397751$ |
3.856544483 |
\( \frac{32297532210782725}{72553009816008} a + \frac{60468973557987577}{18138252454002} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -90 a - 137\) , \( 531 a + 213\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-90a-137\right){x}+531a+213$ |
| 5202.5-h2 |
5202.5-h |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{10} \cdot 3^{12} \cdot 17^{3} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$1.090795502$ |
3.856544483 |
\( -\frac{2091127194353}{409563864} a + \frac{36587816460805}{1638255456} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -30 a - 57\) , \( -101 a - 131\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-30a-57\right){x}-101a-131$ |
| 5202.5-i1 |
5202.5-i |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 17^{16} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{9} \) |
$1$ |
$0.183754147$ |
4.157881714 |
\( -\frac{491411892194497}{125563633938} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -1644\) , \( -30942\bigr] \) |
${y}^2+{x}{y}={x}^{3}-1644{x}-30942$ |
| 5202.5-i2 |
5202.5-i |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2 \cdot 3^{2} \cdot 17^{20} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{6} \) |
$1$ |
$0.091877073$ |
4.157881714 |
\( -\frac{61437923106397764191713}{291967151254001210886} a - \frac{146204680417750243067160}{48661191875666868481} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 4305 a - 924\) , \( -137739 a - 127314\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(4305a-924\right){x}-137739a-127314$ |
| 5202.5-i3 |
5202.5-i |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2 \cdot 3^{2} \cdot 17^{20} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{6} \) |
$1$ |
$0.091877073$ |
4.157881714 |
\( \frac{61437923106397764191713}{291967151254001210886} a - \frac{146204680417750243067160}{48661191875666868481} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -4305 a - 924\) , \( 137739 a - 127314\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-4305a-924\right){x}+137739a-127314$ |
| 5202.5-i4 |
5202.5-i |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{32} \cdot 17^{2} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{10} \) |
$1$ |
$0.367508294$ |
4.157881714 |
\( \frac{1276229915423}{2927177028} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 226\) , \( -2232\bigr] \) |
${y}^2+{x}{y}={x}^{3}+226{x}-2232$ |
| 5202.5-i5 |
5202.5-i |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 3^{16} \cdot 17^{4} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{11} \) |
$1$ |
$0.735016588$ |
4.157881714 |
\( \frac{163936758817}{30338064} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -114\) , \( -396\bigr] \) |
${y}^2+{x}{y}={x}^{3}-114{x}-396$ |
| 5202.5-i6 |
5202.5-i |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{16} \cdot 3^{8} \cdot 17^{2} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$1$ |
$1.470033177$ |
4.157881714 |
\( \frac{4354703137}{352512} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( 68\bigr] \) |
${y}^2+{x}{y}={x}^{3}-34{x}+68$ |
| 5202.5-i7 |
5202.5-i |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{8} \cdot 17^{8} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{10} \) |
$1$ |
$0.367508294$ |
4.157881714 |
\( \frac{576615941610337}{27060804} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -1734\) , \( -27936\bigr] \) |
${y}^2+{x}{y}={x}^{3}-1734{x}-27936$ |
| 5202.5-i8 |
5202.5-i |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
5202.5 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 17^{4} \) |
$2.14648$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{5} \) |
$1$ |
$0.183754147$ |
4.157881714 |
\( \frac{2361739090258884097}{5202} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -27744\) , \( -1781010\bigr] \) |
${y}^2+{x}{y}={x}^{3}-27744{x}-1781010$ |
*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.
