| 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 |
| 12.3-a1 |
12.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
12.3 |
\( 2^{2} \cdot 3 \) |
\( 2^{27} \cdot 3^{4} \cdot 47^{12} \) |
$3.81803$ |
$(2,a), (2,a+1), (3,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$4.695298367$ |
$1.986439443$ |
1.625149089 |
\( \frac{517977641}{5308416} a + \frac{1304686267}{1327104} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 1355 a - 20184\) , \( 50256 a - 1288368\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3+\left(-a+1\right){x}^2+\left(1355a-20184\right){x}+50256a-1288368$ |
| 12.3-a2 |
12.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
12.3 |
\( 2^{2} \cdot 3 \) |
\( 2^{30} \cdot 3^{2} \cdot 19^{12} \) |
$3.81803$ |
$(2,a), (2,a+1), (3,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.347649183$ |
$1.986439443$ |
1.625149089 |
\( -\frac{4997514641}{37748736} a + \frac{59842683965}{37748736} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 170 a - 4155\) , \( 9111 a - 38619\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3+\left(-a+1\right){x}^2+\left(170a-4155\right){x}+9111a-38619$ |
| 12.3-b1 |
12.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
12.3 |
\( 2^{2} \cdot 3 \) |
\( 2^{27} \cdot 3^{16} \) |
$3.81803$ |
$(2,a), (2,a+1), (3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.986439443$ |
0.346122644 |
\( \frac{517977641}{5308416} a + \frac{1304686267}{1327104} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 8 a + 3\) , \( -35 a + 93\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3+\left(-a-1\right){x}^2+\left(8a+3\right){x}-35a+93$ |
| 12.3-b2 |
12.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
12.3 |
\( 2^{2} \cdot 3 \) |
\( 2^{30} \cdot 3^{2} \cdot 29^{12} \) |
$3.81803$ |
$(2,a), (2,a+1), (3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.986439443$ |
0.346122644 |
\( -\frac{4997514641}{37748736} a + \frac{59842683965}{37748736} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -419 a + 9425\) , \( -8542 a - 295414\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+a{x}^2+\left(-419a+9425\right){x}-8542a-295414$ |
| 12.4-a1 |
12.4-a |
$2$ |
$2$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
12.4 |
\( 2^{2} \cdot 3 \) |
\( 2^{27} \cdot 3^{4} \cdot 47^{12} \) |
$3.81803$ |
$(2,a), (2,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$4.695298367$ |
$1.986439443$ |
1.625149089 |
\( -\frac{517977641}{5308416} a + \frac{1912240903}{1769472} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -1356 a - 18829\) , \( -50257 a - 1238112\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+a{x}^2+\left(-1356a-18829\right){x}-50257a-1238112$ |
| 12.4-a2 |
12.4-a |
$2$ |
$2$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
12.4 |
\( 2^{2} \cdot 3 \) |
\( 2^{30} \cdot 3^{2} \cdot 19^{12} \) |
$3.81803$ |
$(2,a), (2,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.347649183$ |
$1.986439443$ |
1.625149089 |
\( \frac{4997514641}{37748736} a + \frac{4570430777}{3145728} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -171 a - 3985\) , \( -9112 a - 29508\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^3+a{x}^2+\left(-171a-3985\right){x}-9112a-29508$ |
| 12.4-b1 |
12.4-b |
$2$ |
$2$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
12.4 |
\( 2^{2} \cdot 3 \) |
\( 2^{27} \cdot 3^{16} \) |
$3.81803$ |
$(2,a), (2,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.986439443$ |
0.346122644 |
\( -\frac{517977641}{5308416} a + \frac{1912240903}{1769472} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -7 a + 11\) , \( 27 a + 69\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3+\left(a+1\right){x}^2+\left(-7a+11\right){x}+27a+69$ |
| 12.4-b2 |
12.4-b |
$2$ |
$2$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
12.4 |
\( 2^{2} \cdot 3 \) |
\( 2^{30} \cdot 3^{2} \cdot 29^{12} \) |
$3.81803$ |
$(2,a), (2,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.986439443$ |
0.346122644 |
\( \frac{4997514641}{37748736} a + \frac{4570430777}{3145728} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 418 a + 9007\) , \( 8541 a - 303955\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3+\left(-a+1\right){x}^2+\left(418a+9007\right){x}+8541a-303955$ |
| 17.1-a1 |
17.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 17^{20} \) |
$4.16539$ |
$(17,a+8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$3.035256177$ |
$4.247877398$ |
0.561645156 |
\( -\frac{35937}{83521} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -199\) , \( -68272\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-199{x}-68272$ |
| 17.1-a2 |
17.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 17^{14} \) |
$4.16539$ |
$(17,a+8)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$3.035256177$ |
$16.99150959$ |
0.561645156 |
\( \frac{35937}{17} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -199\) , \( 510\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-199{x}+510$ |
| 17.1-a3 |
17.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 17^{16} \) |
$4.16539$ |
$(17,a+8)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$6.070512355$ |
$8.495754796$ |
0.561645156 |
\( \frac{20346417}{289} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1644\) , \( -24922\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-1644{x}-24922$ |
| 17.1-a4 |
17.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 17^{14} \) |
$4.16539$ |
$(17,a+8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$3.035256177$ |
$4.247877398$ |
0.561645156 |
\( \frac{82483294977}{17} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -26209\) , \( -1626560\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-26209{x}-1626560$ |
| 17.1-b1 |
17.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 17^{8} \) |
$4.16539$ |
$(17,a+8)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.247877398$ |
0.092520222 |
\( -\frac{35937}{83521} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( -14\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-{x}-14$ |
| 17.1-b2 |
17.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$4.16539$ |
$(17,a+8)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$16.99150959$ |
0.092520222 |
\( \frac{35937}{17} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-{x}$ |
| 17.1-b3 |
17.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 17^{4} \) |
$4.16539$ |
$(17,a+8)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.495754796$ |
0.092520222 |
\( \frac{20346417}{289} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -6\) , \( -4\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-6{x}-4$ |
| 17.1-b4 |
17.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$4.16539$ |
$(17,a+8)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4.247877398$ |
0.092520222 |
\( \frac{82483294977}{17} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -91\) , \( -310\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-91{x}-310$ |
| 22.2-a1 |
22.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
22.2 |
\( 2 \cdot 11 \) |
\( 2^{10} \cdot 11^{2} \) |
$4.44273$ |
$(2,a), (11,a+10)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$4.302114186$ |
$9.044724343$ |
3.390017628 |
\( -\frac{161486689}{123904} a - \frac{101805945}{11264} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -a - 44\) , \( -5 a + 52\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3+\left(a-1\right){x}^2+\left(-a-44\right){x}-5a+52$ |
| 22.2-a2 |
22.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
22.2 |
\( 2 \cdot 11 \) |
\( 2^{17} \cdot 11^{4} \) |
$4.44273$ |
$(2,a), (11,a+10)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$8.604228372$ |
$9.044724343$ |
3.390017628 |
\( \frac{82955047}{468512} a + \frac{15153711}{42592} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -39 a + 251\) , \( 195 a + 57\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a-1\right){x}^2+\left(-39a+251\right){x}+195a+57$ |
| 22.2-b1 |
22.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
22.2 |
\( 2 \cdot 11 \) |
\( 2^{10} \cdot 11^{2} \cdot 17^{12} \) |
$4.44273$ |
$(2,a), (11,a+10)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$9.044724343$ |
0.393994380 |
\( -\frac{161486689}{123904} a - \frac{101805945}{11264} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -96 a - 98\) , \( 1125 a - 13064\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3+\left(-a-1\right){x}^2+\left(-96a-98\right){x}+1125a-13064$ |
| 22.2-b2 |
22.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
22.2 |
\( 2 \cdot 11 \) |
\( 2^{5} \cdot 11^{4} \cdot 23^{12} \) |
$4.44273$ |
$(2,a), (11,a+10)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$9.044724343$ |
0.393994380 |
\( \frac{82955047}{468512} a + \frac{15153711}{42592} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -55 a - 1081\) , \( -1082 a - 8007\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3+\left(-a-1\right){x}^2+\left(-55a-1081\right){x}-1082a-8007$ |
| 22.3-a1 |
22.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
22.3 |
\( 2 \cdot 11 \) |
\( 2^{10} \cdot 11^{2} \) |
$4.44273$ |
$(2,a+1), (11,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$4.302114186$ |
$9.044724343$ |
3.390017628 |
\( \frac{161486689}{123904} a - \frac{320338021}{30976} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -45\) , \( 4 a + 47\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^3-a{x}^2-45{x}+4a+47$ |
| 22.3-a2 |
22.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
22.3 |
\( 2 \cdot 11 \) |
\( 2^{17} \cdot 11^{4} \) |
$4.44273$ |
$(2,a+1), (11,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$8.604228372$ |
$9.044724343$ |
3.390017628 |
\( -\frac{82955047}{468512} a + \frac{62411467}{117128} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -26 a + 344\) , \( 122 a - 540\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(a+1\right){x}^2+\left(-26a+344\right){x}+122a-540$ |
| 22.3-b1 |
22.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
22.3 |
\( 2 \cdot 11 \) |
\( 2^{10} \cdot 11^{2} \cdot 17^{12} \) |
$4.44273$ |
$(2,a+1), (11,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$9.044724343$ |
0.393994380 |
\( \frac{161486689}{123904} a - \frac{320338021}{30976} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 97 a - 194\) , \( -1029 a - 12133\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3+\left(a+1\right){x}^2+\left(97a-194\right){x}-1029a-12133$ |
| 22.3-b2 |
22.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
22.3 |
\( 2 \cdot 11 \) |
\( 2^{5} \cdot 11^{4} \cdot 23^{12} \) |
$4.44273$ |
$(2,a+1), (11,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$9.044724343$ |
0.393994380 |
\( -\frac{82955047}{468512} a + \frac{62411467}{117128} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 56 a - 1136\) , \( 1137 a - 10225\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3+\left(a+1\right){x}^2+\left(56a-1136\right){x}+1137a-10225$ |
| 36.4-a1 |
36.4-a |
$2$ |
$2$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
36.4 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{7} \cdot 3^{42} \) |
$5.02481$ |
$(2,a), (2,a+1), (3,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$5.446735470$ |
$1.164582133$ |
5.526257210 |
\( \frac{877271516290057}{9037745167392} a + \frac{2950564876055141}{2259436291848} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 24 a + 1146\) , \( 1092 a - 12752\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(a-1\right){x}^2+\left(24a+1146\right){x}+1092a-12752$ |
| 36.4-a2 |
36.4-a |
$2$ |
$2$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
36.4 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{30} \) |
$5.02481$ |
$(2,a), (2,a+1), (3,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$2.723367735$ |
$2.329164266$ |
5.526257210 |
\( -\frac{54702997655}{544195584} a + \frac{199235612291}{136048896} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 4 a - 354\) , \( -1340\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(a-1\right){x}^2+\left(4a-354\right){x}-1340$ |
| 36.4-b1 |
36.4-b |
$2$ |
$2$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
36.4 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{7} \cdot 3^{30} \cdot 47^{12} \) |
$5.02481$ |
$(2,a), (2,a+1), (3,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$10.73996845$ |
$1.164582133$ |
10.89677081 |
\( \frac{877271516290057}{9037745167392} a + \frac{2950564876055141}{2259436291848} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 26304 a - 35724\) , \( 4557684 a + 2593676\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(-a-1\right){x}^2+\left(26304a-35724\right){x}+4557684a+2593676$ |
| 36.4-b2 |
36.4-b |
$2$ |
$2$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
36.4 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{18} \cdot 47^{12} \) |
$5.02481$ |
$(2,a), (2,a+1), (3,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$5.369984225$ |
$2.329164266$ |
10.89677081 |
\( -\frac{54702997655}{544195584} a + \frac{199235612291}{136048896} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -6356 a - 19944\) , \( 567072 a + 1079408\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(-a-1\right){x}^2+\left(-6356a-19944\right){x}+567072a+1079408$ |
| 36.6-a1 |
36.6-a |
$2$ |
$2$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
36.6 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{30} \) |
$5.02481$ |
$(2,a), (2,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$2.723367735$ |
$2.329164266$ |
5.526257210 |
\( \frac{54702997655}{544195584} a + \frac{247413150503}{181398528} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -4 a - 350\) , \( -1340\bigr] \) |
${y}^2+{x}{y}={x}^3-a{x}^2+\left(-4a-350\right){x}-1340$ |
| 36.6-a2 |
36.6-a |
$2$ |
$2$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
36.6 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{7} \cdot 3^{42} \) |
$5.02481$ |
$(2,a), (2,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$5.446735470$ |
$1.164582133$ |
5.526257210 |
\( -\frac{877271516290057}{9037745167392} a + \frac{4226510340170207}{3012581722464} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -24 a + 1170\) , \( -1092 a - 11660\bigr] \) |
${y}^2+{x}{y}={x}^3-a{x}^2+\left(-24a+1170\right){x}-1092a-11660$ |
| 36.6-b1 |
36.6-b |
$2$ |
$2$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
36.6 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{18} \cdot 47^{12} \) |
$5.02481$ |
$(2,a), (2,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$5.369984225$ |
$2.329164266$ |
10.89677081 |
\( \frac{54702997655}{544195584} a + \frac{247413150503}{181398528} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 6358 a - 26301\) , \( -560715 a + 1620179\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(a+1\right){x}^2+\left(6358a-26301\right){x}-560715a+1620179$ |
| 36.6-b2 |
36.6-b |
$2$ |
$2$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
36.6 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{7} \cdot 3^{30} \cdot 47^{12} \) |
$5.02481$ |
$(2,a), (2,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$10.73996845$ |
$1.164582133$ |
10.89677081 |
\( -\frac{877271516290057}{9037745167392} a + \frac{4226510340170207}{3012581722464} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -26302 a - 9421\) , \( -4583987 a + 7141939\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(a+1\right){x}^2+\left(-26302a-9421\right){x}-4583987a+7141939$ |
| 48.2-a1 |
48.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
48.2 |
\( 2^{4} \cdot 3 \) |
\( 2^{13} \cdot 3^{8} \cdot 23^{12} \) |
$5.39951$ |
$(2,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$4.282756389$ |
0.746239194 |
\( -\frac{337254817}{13122} a - \frac{1134094519}{4374} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -1276 a - 5651\) , \( 76900 a - 514\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+a{x}^2+\left(-1276a-5651\right){x}+76900a-514$ |
| 48.2-a2 |
48.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
48.2 |
\( 2^{4} \cdot 3 \) |
\( 2^{13} \cdot 3^{2} \cdot 17^{12} \) |
$5.39951$ |
$(2,a), (3,a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$8.565512779$ |
0.746239194 |
\( \frac{32729}{18} a - \frac{413137}{6} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 111 a + 577\) , \( -142 a + 10806\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+a{x}^2+\left(111a+577\right){x}-142a+10806$ |
| 48.2-a3 |
48.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
48.2 |
\( 2^{4} \cdot 3 \) |
\( 2^{14} \cdot 3^{4} \cdot 23^{12} \) |
$5.39951$ |
$(2,a), (3,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$8.565512779$ |
0.746239194 |
\( \frac{9499}{324} a + \frac{34327}{108} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -81 a - 271\) , \( 1730 a - 1722\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+a{x}^2+\left(-81a-271\right){x}+1730a-1722$ |
| 48.2-a4 |
48.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
48.2 |
\( 2^{4} \cdot 3 \) |
\( 2^{16} \cdot 3^{14} \) |
$5.39951$ |
$(2,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$8.565512779$ |
0.746239194 |
\( -\frac{35329}{144} a + \frac{228095}{48} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -25 a + 369\) , \( 114 a - 730\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+a{x}^2+\left(-25a+369\right){x}+114a-730$ |
| 48.2-b1 |
48.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
48.2 |
\( 2^{4} \cdot 3 \) |
\( 2^{25} \cdot 3^{8} \) |
$5.39951$ |
$(2,a), (3,a+2)$ |
$0 \le r \le 1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
|
\( 2^{4} \) |
$1$ |
$4.282756389$ |
4.801593410 |
\( -\frac{337254817}{13122} a - \frac{1134094519}{4374} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 256\) , \( -71 a + 140\bigr] \) |
${y}^2+a{x}{y}={x}^3+256{x}-71a+140$ |
| 48.2-b2 |
48.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
48.2 |
\( 2^{4} \cdot 3 \) |
\( 2^{13} \cdot 3^{2} \) |
$5.39951$ |
$(2,a), (3,a+2)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
|
\( 2^{3} \) |
$1$ |
$8.565512779$ |
4.801593410 |
\( \frac{32729}{18} a - \frac{413137}{6} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -5 a + 361\) , \( 25 a - 1310\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(-5a+361\right){x}+25a-1310$ |
| 48.2-b3 |
48.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
48.2 |
\( 2^{4} \cdot 3 \) |
\( 2^{26} \cdot 3^{4} \) |
$5.39951$ |
$(2,a), (3,a+2)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
|
\( 2^{4} \) |
$1$ |
$8.565512779$ |
4.801593410 |
\( \frac{9499}{324} a + \frac{34327}{108} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -5 a + 356\) , \( 24 a - 1248\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(-5a+356\right){x}+24a-1248$ |
| 48.2-b4 |
48.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
48.2 |
\( 2^{4} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \cdot 47^{12} \) |
$5.39951$ |
$(2,a), (3,a+2)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
|
\( 2^{3} \) |
$1$ |
$8.565512779$ |
4.801593410 |
\( -\frac{35329}{144} a + \frac{228095}{48} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 298 a - 6323\) , \( -17662 a + 216030\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(298a-6323\right){x}-17662a+216030$ |
| 48.3-a1 |
48.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
48.3 |
\( 2^{4} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \cdot 11^{12} \) |
$5.39951$ |
$(2,a), (2,a+1), (3,a)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
|
\( 2^{3} \) |
$1$ |
$8.088661327$ |
6.796198235 |
\( -\frac{341159}{36} a - \frac{2369209}{9} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -17 a + 1324\) , \( -746 a - 18720\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(-a-1\right){x}^2+\left(-17a+1324\right){x}-746a-18720$ |
| 48.3-a2 |
48.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
48.3 |
\( 2^{4} \cdot 3 \) |
\( 2^{15} \cdot 3^{4} \cdot 11^{12} \) |
$5.39951$ |
$(2,a), (2,a+1), (3,a)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
|
\( 2^{2} \) |
$1$ |
$8.088661327$ |
6.796198235 |
\( \frac{22793}{1296} a + \frac{160987}{324} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 30 a + 232\) , \( -254 a - 576\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(-a-1\right){x}^2+\left(30a+232\right){x}-254a-576$ |
| 48.3-b1 |
48.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
48.3 |
\( 2^{4} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \cdot 59^{12} \) |
$5.39951$ |
$(2,a), (2,a+1), (3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$8.088661327$ |
0.704695243 |
\( -\frac{341159}{36} a - \frac{2369209}{9} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -1537 a - 20004\) , \( -112176 a - 653364\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(-a+1\right){x}^2+\left(-1537a-20004\right){x}-112176a-653364$ |
| 48.3-b2 |
48.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
48.3 |
\( 2^{4} \cdot 3 \) |
\( 2^{15} \cdot 3^{4} \cdot 59^{12} \) |
$5.39951$ |
$(2,a), (2,a+1), (3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$8.088661327$ |
0.704695243 |
\( \frac{22793}{1296} a + \frac{160987}{324} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -576 a - 880\) , \( 1558 a - 336940\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(-a+1\right){x}^2+\left(-576a-880\right){x}+1558a-336940$ |
| 48.8-a1 |
48.8-a |
$2$ |
$2$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
48.8 |
\( 2^{4} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \cdot 59^{12} \) |
$5.39951$ |
$(2,a), (2,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$8.088661327$ |
0.704695243 |
\( \frac{341159}{36} a - \frac{3272665}{12} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 1535 a - 21541\) , \( 112175 a - 765540\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(1535a-21541\right){x}+112175a-765540$ |
| 48.8-a2 |
48.8-a |
$2$ |
$2$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
48.8 |
\( 2^{4} \cdot 3 \) |
\( 2^{15} \cdot 3^{4} \cdot 59^{12} \) |
$5.39951$ |
$(2,a), (2,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$8.088661327$ |
0.704695243 |
\( -\frac{22793}{1296} a + \frac{222247}{432} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 574 a - 1456\) , \( -1559 a - 335382\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(574a-1456\right){x}-1559a-335382$ |
| 48.8-b1 |
48.8-b |
$2$ |
$2$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
48.8 |
\( 2^{4} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \cdot 11^{12} \) |
$5.39951$ |
$(2,a), (2,a+1), (3,a+2)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
|
\( 2^{3} \) |
$1$ |
$8.088661327$ |
6.796198235 |
\( \frac{341159}{36} a - \frac{3272665}{12} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 18 a + 1175\) , \( 763 a - 18291\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+{x}^2+\left(18a+1175\right){x}+763a-18291$ |
| 48.8-b2 |
48.8-b |
$2$ |
$2$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
48.8 |
\( 2^{4} \cdot 3 \) |
\( 2^{15} \cdot 3^{4} \cdot 11^{12} \) |
$5.39951$ |
$(2,a), (2,a+1), (3,a+2)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
|
\( 2^{2} \) |
$1$ |
$8.088661327$ |
6.796198235 |
\( -\frac{22793}{1296} a + \frac{222247}{432} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -29 a + 130\) , \( 224 a - 700\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+{x}^2+\left(-29a+130\right){x}+224a-700$ |
| 48.9-a1 |
48.9-a |
$4$ |
$4$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
48.9 |
\( 2^{4} \cdot 3 \) |
\( 2^{13} \cdot 3^{8} \cdot 23^{12} \) |
$5.39951$ |
$(2,a+1), (3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$4.282756389$ |
0.746239194 |
\( \frac{337254817}{13122} a - \frac{1869769187}{6561} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 1211 a - 6993\) , \( -82617 a - 87756\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(1211a-6993\right){x}-82617a-87756$ |
| 48.9-a2 |
48.9-a |
$4$ |
$4$ |
\(\Q(\sqrt{-527}) \) |
$2$ |
$[0, 1]$ |
48.9 |
\( 2^{4} \cdot 3 \) |
\( 2^{13} \cdot 3^{2} \cdot 17^{12} \) |
$5.39951$ |
$(2,a+1), (3,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$8.565512779$ |
0.746239194 |
\( -\frac{32729}{18} a - \frac{603341}{9} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -176 a + 622\) , \( 653 a + 29606\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(-176a+622\right){x}+653a+29606$ |
*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.
