| 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 |
| 4.1-a1 |
4.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$1.99012$ |
$(a+8)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$0.488466730$ |
$17.46386550$ |
3.250130334 |
\( -256 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2 a\) , \( 24 a - 201\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+2a{x}+24a-201$ |
| 4.1-b1 |
4.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{8} \) |
$1.99012$ |
$(a+8)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$0.488466730$ |
$17.46386550$ |
3.250130334 |
\( -256 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2 a\) , \( -24 a - 201\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-2a{x}-24a-201$ |
| 8.1-a1 |
8.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$2.36667$ |
$(a+8)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$7.093349492$ |
$16.97825510$ |
3.823741961 |
\( -1372 \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -15 a + 64\) , \( -64 a - 31\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-15a+64\right){x}-64a-31$ |
| 8.1-a2 |
8.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{11} \) |
$2.36667$ |
$(a+8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$7.093349492$ |
$16.97825510$ |
3.823741961 |
\( -1065365700481 a + 8388697917160 \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -105 a - 646\) , \( -1158 a - 8655\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-105a-646\right){x}-1158a-8655$ |
| 8.1-a3 |
8.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{10} \) |
$2.36667$ |
$(a+8)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$14.18669898$ |
$16.97825510$ |
3.823741961 |
\( 4096766 \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -95 a - 566\) , \( -1434 a - 10819\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-95a-566\right){x}-1434a-10819$ |
| 8.1-a4 |
8.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{11} \) |
$2.36667$ |
$(a+8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$28.37339796$ |
$4.244563776$ |
3.823741961 |
\( 1065365700481 a + 8388697917160 \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -1365 a - 10566\) , \( -79630 a - 626535\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-1365a-10566\right){x}-79630a-626535$ |
| 8.1-b1 |
8.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$2.36667$ |
$(a+8)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$2.251153358$ |
$6.969635407$ |
3.985192396 |
\( -76995328 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -178 a - 1386\) , \( 3122 a + 24571\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-178a-1386\right){x}+3122a+24571$ |
| 8.1-c1 |
8.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$2.36667$ |
$(a+8)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$7.093349492$ |
$16.97825510$ |
3.823741961 |
\( -1372 \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 15 a + 64\) , \( 64 a - 31\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(15a+64\right){x}+64a-31$ |
| 8.1-c2 |
8.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{11} \) |
$2.36667$ |
$(a+8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$28.37339796$ |
$4.244563776$ |
3.823741961 |
\( -1065365700481 a + 8388697917160 \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 1365 a - 10566\) , \( 79630 a - 626535\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(1365a-10566\right){x}+79630a-626535$ |
| 8.1-c3 |
8.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{10} \) |
$2.36667$ |
$(a+8)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$14.18669898$ |
$16.97825510$ |
3.823741961 |
\( 4096766 \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 95 a - 566\) , \( 1434 a - 10819\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(95a-566\right){x}+1434a-10819$ |
| 8.1-c4 |
8.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{11} \) |
$2.36667$ |
$(a+8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$7.093349492$ |
$16.97825510$ |
3.823741961 |
\( 1065365700481 a + 8388697917160 \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 105 a - 646\) , \( 1158 a - 8655\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(105a-646\right){x}+1158a-8655$ |
| 8.1-d1 |
8.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \) |
$2.36667$ |
$(a+8)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$2.251153358$ |
$6.969635407$ |
3.985192396 |
\( -76995328 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 178 a - 1386\) , \( -3122 a + 24571\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(178a-1386\right){x}-3122a+24571$ |
| 16.1-a1 |
16.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$2.81446$ |
$(a+8)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$17.46386550$ |
2.217913137 |
\( -256 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 2 a\) , \( -24 a + 201\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+2a{x}-24a+201$ |
| 16.1-b1 |
16.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$2.81446$ |
$(a+8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$4.406113792$ |
$16.97825510$ |
4.750320624 |
\( -1372 \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 5 a + 54\) , \( 14 a + 121\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(5a+54\right){x}+14a+121$ |
| 16.1-b2 |
16.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{11} \) |
$2.81446$ |
$(a+8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$17.62445517$ |
$4.244563776$ |
4.750320624 |
\( -1065365700481 a + 8388697917160 \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -85 a - 656\) , \( 208 a + 1645\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-85a-656\right){x}+208a+1645$ |
| 16.1-b3 |
16.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{10} \) |
$2.81446$ |
$(a+8)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$8.812227585$ |
$16.97825510$ |
4.750320624 |
\( 4096766 \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -75 a - 576\) , \( 584 a + 4609\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-75a-576\right){x}+584a+4609$ |
| 16.1-b4 |
16.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{11} \) |
$2.81446$ |
$(a+8)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$17.62445517$ |
$16.97825510$ |
4.750320624 |
\( 1065365700481 a + 8388697917160 \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -1345 a - 10576\) , \( 66080 a + 520325\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-1345a-10576\right){x}+66080a+520325$ |
| 16.1-c1 |
16.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$2.81446$ |
$(a+8)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$5.130565640$ |
$6.969635407$ |
4.541292378 |
\( -76995328 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -178 a - 1386\) , \( -3122 a - 24571\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-178a-1386\right){x}-3122a-24571$ |
| 16.1-d1 |
16.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$2.81446$ |
$(a+8)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$17.46386550$ |
2.217913137 |
\( -256 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -2 a\) , \( 24 a + 201\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-2a{x}+24a+201$ |
| 16.1-e1 |
16.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$2.81446$ |
$(a+8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$4.406113792$ |
$16.97825510$ |
4.750320624 |
\( -1372 \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -5 a + 54\) , \( -14 a + 121\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-5a+54\right){x}-14a+121$ |
| 16.1-e2 |
16.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{11} \) |
$2.81446$ |
$(a+8)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$17.62445517$ |
$16.97825510$ |
4.750320624 |
\( -1065365700481 a + 8388697917160 \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 1345 a - 10576\) , \( -66080 a + 520325\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1345a-10576\right){x}-66080a+520325$ |
| 16.1-e3 |
16.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{10} \) |
$2.81446$ |
$(a+8)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$8.812227585$ |
$16.97825510$ |
4.750320624 |
\( 4096766 \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 75 a - 576\) , \( -584 a + 4609\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(75a-576\right){x}-584a+4609$ |
| 16.1-e4 |
16.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{11} \) |
$2.81446$ |
$(a+8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$17.62445517$ |
$4.244563776$ |
4.750320624 |
\( 1065365700481 a + 8388697917160 \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 85 a - 656\) , \( -208 a + 1645\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(85a-656\right){x}-208a+1645$ |
| 16.1-f1 |
16.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$2.81446$ |
$(a+8)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$5.130565640$ |
$6.969635407$ |
4.541292378 |
\( -76995328 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 178 a - 1386\) , \( 3122 a - 24571\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(178a-1386\right){x}+3122a-24571$ |
| 18.1-a1 |
18.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{3} \cdot 3^{6} \) |
$2.89856$ |
$(a+8), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3^{2} \) |
$1$ |
$6.162328540$ |
3.521774282 |
\( -\frac{197188201}{108} a - \frac{506242892}{27} \) |
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -12775 a - 100571\) , \( -2290615 a - 18036275\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-12775a-100571\right){x}-2290615a-18036275$ |
| 18.1-a2 |
18.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2 \cdot 3^{2} \) |
$2.89856$ |
$(a+8), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$9$ |
\( 1 \) |
$1$ |
$6.162328540$ |
3.521774282 |
\( \frac{31882878208804455881}{6} a - \frac{125523017031142935536}{3} \) |
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -3490 a - 27461\) , \( -5344906 a - 42085787\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-3490a-27461\right){x}-5344906a-42085787$ |
| 18.1-b1 |
18.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{6} \) |
$2.89856$ |
$(a+8), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$4.528981747$ |
0.575181257 |
\( -\frac{3442951}{55296} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 25 a - 178\) , \( 1100 a - 8678\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(25a-178\right){x}+1100a-8678$ |
| 18.1-c1 |
18.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{3} \cdot 3^{6} \) |
$2.89856$ |
$(a+8), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$9$ |
\( 3^{2} \) |
$1$ |
$6.978269328$ |
3.988084909 |
\( -\frac{197188201}{108} a - \frac{506242892}{27} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 15 a + 65\) , \( 44 a + 233\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(15a+65\right){x}+44a+233$ |
| 18.1-c2 |
18.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2 \cdot 3^{2} \) |
$2.89856$ |
$(a+8), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$81$ |
\( 1 \) |
$1$ |
$0.775363258$ |
3.988084909 |
\( \frac{31882878208804455881}{6} a - \frac{125523017031142935536}{3} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 180 a - 1225\) , \( 3488 a - 26779\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(180a-1225\right){x}+3488a-26779$ |
| 18.1-d1 |
18.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2 \cdot 3^{2} \) |
$2.89856$ |
$(a+8), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$9$ |
\( 1 \) |
$1$ |
$6.162328540$ |
3.521774282 |
\( -\frac{31882878208804455881}{6} a - \frac{125523017031142935536}{3} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( 3489 a - 27461\) , \( 5344906 a - 42085787\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(3489a-27461\right){x}+5344906a-42085787$ |
| 18.1-d2 |
18.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{3} \cdot 3^{6} \) |
$2.89856$ |
$(a+8), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3^{2} \) |
$1$ |
$6.162328540$ |
3.521774282 |
\( \frac{197188201}{108} a - \frac{506242892}{27} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( 12774 a - 100571\) , \( 2290615 a - 18036275\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(12774a-100571\right){x}+2290615a-18036275$ |
| 18.1-e1 |
18.1-e |
$2$ |
$3$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2 \cdot 3^{2} \) |
$2.89856$ |
$(a+8), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$81$ |
\( 1 \) |
$1$ |
$0.775363258$ |
3.988084909 |
\( -\frac{31882878208804455881}{6} a - \frac{125523017031142935536}{3} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -152 a - 1194\) , \( -4713 a - 37071\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-152a-1194\right){x}-4713a-37071$ |
| 18.1-e2 |
18.1-e |
$2$ |
$3$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{3} \cdot 3^{6} \) |
$2.89856$ |
$(a+8), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$9$ |
\( 3^{2} \) |
$1$ |
$6.978269328$ |
3.988084909 |
\( \frac{197188201}{108} a - \frac{506242892}{27} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 13 a + 96\) , \( 21 a + 171\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(13a+96\right){x}+21a+171$ |
| 18.1-f1 |
18.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{6} \) |
$2.89856$ |
$(a+8), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$4.528981747$ |
0.575181257 |
\( -\frac{3442951}{55296} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( -25 a - 178\) , \( -1100 a - 8678\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-25a-178\right){x}-1100a-8678$ |
| 23.1-a1 |
23.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
23.1 |
\( 23 \) |
\( - 23^{3} \) |
$3.08174$ |
$(2a-15)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Nn |
$1$ |
\( 3 \) |
$0.376074690$ |
$16.35587698$ |
2.343545300 |
\( \frac{21020020992}{12167} a + \frac{165513309120}{12167} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( -a + 90\) , \( -2 a + 160\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-a+90\right){x}-2a+160$ |
| 23.1-b1 |
23.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
23.1 |
\( 23 \) |
\( - 23^{3} \) |
$3.08174$ |
$(2a-15)$ |
$0 \le r \le 1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
|
\( 3 \) |
$1$ |
$9.206038960$ |
4.156419992 |
\( \frac{18076672}{12167} a - \frac{121299264}{12167} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -8 a - 10\) , \( -40 a - 189\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-8a-10\right){x}-40a-189$ |
| 23.1-b2 |
23.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
23.1 |
\( 23 \) |
\( -23 \) |
$3.08174$ |
$(2a-15)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
|
\( 1 \) |
$1$ |
$1.022893217$ |
4.156419992 |
\( \frac{16422706187264}{23} a - \frac{129308538785088}{23} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -423 a - 3280\) , \( -15455 a - 121580\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-423a-3280\right){x}-15455a-121580$ |
| 23.1-c1 |
23.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
23.1 |
\( 23 \) |
\( - 23^{3} \) |
$3.08174$ |
$(2a-15)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.767172497$ |
$29.53914912$ |
5.756057951 |
\( \frac{18076672}{12167} a - \frac{121299264}{12167} \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 39 a - 113\) , \( -127 a + 1536\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(39a-113\right){x}-127a+1536$ |
| 23.1-c2 |
23.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
23.1 |
\( 23 \) |
\( -23 \) |
$3.08174$ |
$(2a-15)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.767172497$ |
$29.53914912$ |
5.756057951 |
\( \frac{16422706187264}{23} a - \frac{129308538785088}{23} \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 2344 a - 18263\) , \( -165437 a + 1303185\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2344a-18263\right){x}-165437a+1303185$ |
| 23.1-d1 |
23.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
23.1 |
\( 23 \) |
\( - 23^{3} \) |
$3.08174$ |
$(2a-15)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Nn |
$1$ |
\( 1 \) |
$1.594284551$ |
$8.839083389$ |
3.579375160 |
\( \frac{21020020992}{12167} a + \frac{165513309120}{12167} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( -4725 a - 37110\) , \( -521984 a - 4109940\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-4725a-37110\right){x}-521984a-4109940$ |
| 23.2-a1 |
23.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
23.2 |
\( 23 \) |
\( - 23^{3} \) |
$3.08174$ |
$(-2a-15)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Nn |
$1$ |
\( 3 \) |
$0.376074690$ |
$16.35587698$ |
2.343545300 |
\( -\frac{21020020992}{12167} a + \frac{165513309120}{12167} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( 90\) , \( 2 a + 160\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+90{x}+2a+160$ |
| 23.2-b1 |
23.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
23.2 |
\( 23 \) |
\( -23 \) |
$3.08174$ |
$(-2a-15)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
|
\( 1 \) |
$1$ |
$1.022893217$ |
4.156419992 |
\( -\frac{16422706187264}{23} a - \frac{129308538785088}{23} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 422 a - 3280\) , \( 15454 a - 121580\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(422a-3280\right){x}+15454a-121580$ |
| 23.2-b2 |
23.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
23.2 |
\( 23 \) |
\( - 23^{3} \) |
$3.08174$ |
$(-2a-15)$ |
$0 \le r \le 1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
|
\( 3 \) |
$1$ |
$9.206038960$ |
4.156419992 |
\( -\frac{18076672}{12167} a - \frac{121299264}{12167} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 7 a - 10\) , \( 39 a - 189\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(7a-10\right){x}+39a-189$ |
| 23.2-c1 |
23.2-c |
$2$ |
$3$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
23.2 |
\( 23 \) |
\( -23 \) |
$3.08174$ |
$(-2a-15)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.767172497$ |
$29.53914912$ |
5.756057951 |
\( -\frac{16422706187264}{23} a - \frac{129308538785088}{23} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -2345 a - 18263\) , \( 165437 a + 1303185\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2345a-18263\right){x}+165437a+1303185$ |
| 23.2-c2 |
23.2-c |
$2$ |
$3$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
23.2 |
\( 23 \) |
\( - 23^{3} \) |
$3.08174$ |
$(-2a-15)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.767172497$ |
$29.53914912$ |
5.756057951 |
\( -\frac{18076672}{12167} a - \frac{121299264}{12167} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -40 a - 113\) , \( 127 a + 1536\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-40a-113\right){x}+127a+1536$ |
| 23.2-d1 |
23.2-d |
$1$ |
$1$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
23.2 |
\( 23 \) |
\( - 23^{3} \) |
$3.08174$ |
$(-2a-15)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Nn |
$1$ |
\( 1 \) |
$1.594284551$ |
$8.839083389$ |
3.579375160 |
\( -\frac{21020020992}{12167} a + \frac{165513309120}{12167} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( 4724 a - 37110\) , \( 521984 a - 4109940\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(4724a-37110\right){x}+521984a-4109940$ |
| 32.1-a1 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$3.34697$ |
$(a+8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$3.700238080$ |
$13.75037163$ |
3.230860926 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}$ |
| 32.1-a2 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$3.34697$ |
$(a+8)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$7.400476160$ |
$27.50074327$ |
3.230860926 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1008 a - 7937\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(1008a-7937\right){x}$ |
| 32.1-a3 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$3.34697$ |
$(a+8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$3.700238080$ |
$13.75037163$ |
3.230860926 |
\( 287496 \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 57\) , \( 134\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+57{x}+134$ |
| 32.1-a4 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{62}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$3.34697$ |
$(a+8)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$3.700238080$ |
$55.00148654$ |
3.230860926 |
\( 287496 \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 88\) , \( 153\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+88{x}+153$ |
*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.
