| 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 |
| 8.1-a1 |
8.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \cdot 3^{12} \) |
$1.75259$ |
$(-a-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.661042397$ |
$47.99530637$ |
2.720562010 |
\( 2000 \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 299 a - 1675\) , \( -2165 a + 12733\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(299a-1675\right){x}-2165a+12733$ |
| 8.1-a2 |
8.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \cdot 3^{12} \) |
$1.75259$ |
$(-a-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.330521198$ |
$47.99530637$ |
2.720562010 |
\( 1098500 \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 3819 a - 22200\) , \( -305876 a + 1783657\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(3819a-22200\right){x}-305876a+1783657$ |
| 8.1-b1 |
8.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{4} \cdot 3^{12} \) |
$1.75259$ |
$(-a-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.661042397$ |
$47.99530637$ |
2.720562010 |
\( 2000 \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -8 a + 31\) , \( -12 a + 60\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-8a+31\right){x}-12a+60$ |
| 8.1-b2 |
8.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{8} \cdot 3^{12} \) |
$1.75259$ |
$(-a-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.330521198$ |
$47.99530637$ |
2.720562010 |
\( 1098500 \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -28 a - 94\) , \( 104 a + 704\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-28a-94\right){x}+104a+704$ |
| 9.1-a1 |
9.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{22} \) |
$1.80496$ |
$(3,a+1), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B |
$1$ |
\( 5 \) |
$0.067234990$ |
$26.06321475$ |
1.502636295 |
\( -\frac{13549359104}{243} \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 34966 a - 203870\) , \( -8650334 a + 50439692\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(34966a-203870\right){x}-8650334a+50439692$ |
| 9.1-a2 |
9.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{14} \) |
$1.80496$ |
$(3,a+1), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B |
$1$ |
\( 1 \) |
$0.336174951$ |
$26.06321475$ |
1.502636295 |
\( \frac{4096}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( -234 a + 1380\) , \( -2056 a + 12000\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-234a+1380\right){x}-2056a+12000$ |
| 9.1-b1 |
9.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{20} \) |
$1.80496$ |
$(3,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.152294828$ |
$11.95476739$ |
1.561193855 |
\( -\frac{873722816}{59049} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 114 a - 684\) , \( -1292 a + 7522\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(114a-684\right){x}-1292a+7522$ |
| 9.1-b2 |
9.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$1.80496$ |
$(3,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$0.761474144$ |
$11.95476739$ |
1.561193855 |
\( \frac{64}{9} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -6 a + 16\) , \( -3 a + 6\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6a+16\right){x}-3a+6$ |
| 9.1-b3 |
9.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{2} \) |
$1.80496$ |
$(3,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 1 \) |
$1.522948288$ |
$23.90953478$ |
1.561193855 |
\( \frac{85184}{3} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 26939 a - 157082\) , \( 5753558 a - 33548720\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(26939a-157082\right){x}+5753558a-33548720$ |
| 9.1-b4 |
9.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{10} \) |
$1.80496$ |
$(3,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 5 \) |
$0.304589657$ |
$23.90953478$ |
1.561193855 |
\( \frac{58591911104}{243} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 2378459 a - 13868682\) , \( -4810865707 a + 28051926510\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2378459a-13868682\right){x}-4810865707a+28051926510$ |
| 9.1-c1 |
9.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{28} \) |
$1.80496$ |
$(3,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.978485520$ |
$5.121307518$ |
3.437603564 |
\( \frac{5359375}{6561} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 73995 a + 431478\) , \( -28055528 a - 163590421\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(73995a+431478\right){x}-28055528a-163590421$ |
| 9.1-c2 |
9.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{20} \) |
$1.80496$ |
$(3,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.489242760$ |
$20.48523007$ |
3.437603564 |
\( \frac{274625}{81} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -27485 a - 160247\) , \( -4151770 a - 24208758\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-27485a-160247\right){x}-4151770a-24208758$ |
| 9.1-d1 |
9.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{28} \) |
$1.80496$ |
$(3,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.978485520$ |
$5.121307518$ |
3.437603564 |
\( \frac{5359375}{6561} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 12 a + 114\) , \( -62 a - 301\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(12a+114\right){x}-62a-301$ |
| 9.1-d2 |
9.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{20} \) |
$1.80496$ |
$(3,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.489242760$ |
$20.48523007$ |
3.437603564 |
\( \frac{274625}{81} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -8 a - 11\) , \( -24 a - 104\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-8a-11\right){x}-24a-104$ |
| 9.1-e1 |
9.1-e |
$4$ |
$10$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{20} \) |
$1.80496$ |
$(3,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.152294828$ |
$11.95476739$ |
1.561193855 |
\( -\frac{873722816}{59049} \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( 585435 a - 3413604\) , \( -621874868 a + 3626122516\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(585435a-3413604\right){x}-621874868a+3626122516$ |
| 9.1-e2 |
9.1-e |
$4$ |
$10$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$1.80496$ |
$(3,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$0.761474144$ |
$11.95476739$ |
1.561193855 |
\( \frac{64}{9} \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -2445 a + 14296\) , \( 2477531 a - 14446288\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2445a+14296\right){x}+2477531a-14446288$ |
| 9.1-e3 |
9.1-e |
$4$ |
$10$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{2} \) |
$1.80496$ |
$(3,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 1 \) |
$1.522948288$ |
$23.90953478$ |
1.561193855 |
\( \frac{85184}{3} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 131974160 a - 769534922\) , \( 1931295231412 a - 11261289589020\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(131974160a-769534922\right){x}+1931295231412a-11261289589020$ |
| 9.1-e4 |
9.1-e |
$4$ |
$10$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{10} \) |
$1.80496$ |
$(3,a+1), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 5 \) |
$0.304589657$ |
$23.90953478$ |
1.561193855 |
\( \frac{58591911104}{243} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 11649718640 a - 67928948922\) , \( -1652733141687323 a + 9637007444195410\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(11649718640a-67928948922\right){x}-1652733141687323a+9637007444195410$ |
| 9.1-f1 |
9.1-f |
$2$ |
$5$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{22} \) |
$1.80496$ |
$(3,a+1), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B |
$1$ |
\( 5 \) |
$0.067234990$ |
$26.06321475$ |
1.502636295 |
\( -\frac{13549359104}{243} \) |
\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( -198 a - 1230\) , \( 4334 a + 25428\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-198a-1230\right){x}+4334a+25428$ |
| 9.1-f2 |
9.1-f |
$2$ |
$5$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{14} \) |
$1.80496$ |
$(3,a+1), (3,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B |
$1$ |
\( 1 \) |
$0.336174951$ |
$26.06321475$ |
1.502636295 |
\( \frac{4096}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( 2 a + 20\) , \( -4 a - 24\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a+20\right){x}-4a-24$ |
| 10.1-a1 |
10.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{14} \cdot 5^{4} \) |
$1.85314$ |
$(-a-6), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.088987910$ |
0.693624990 |
\( \frac{144789383}{40000} a + \frac{2243100323}{80000} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 9 a - 45\) , \( 94 a - 542\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(9a-45\right){x}+94a-542$ |
| 10.1-a2 |
10.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{7} \cdot 5^{8} \) |
$1.85314$ |
$(-a-6), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$4.044493955$ |
0.693624990 |
\( \frac{1255304262655889}{6250000} a + \frac{3659838385944071}{3125000} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 49 a - 285\) , \( -258 a + 1490\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(49a-285\right){x}-258a+1490$ |
| 10.1-b1 |
10.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{14} \cdot 5^{4} \) |
$1.85314$ |
$(-a-6), (5,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.060400957$ |
$8.088987910$ |
2.942082419 |
\( \frac{144789383}{40000} a + \frac{2243100323}{80000} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 61007 a - 355719\) , \( 17284800 a - 100786844\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(61007a-355719\right){x}+17284800a-100786844$ |
| 10.1-b2 |
10.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{7} \cdot 5^{8} \) |
$1.85314$ |
$(-a-6), (5,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.120801915$ |
$4.044493955$ |
2.942082419 |
\( \frac{1255304262655889}{6250000} a + \frac{3659838385944071}{3125000} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( 259767 a - 1514679\) , \( -156462288 a + 912324068\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(259767a-1514679\right){x}-156462288a+912324068$ |
| 10.2-a1 |
10.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{14} \cdot 5^{4} \) |
$1.85314$ |
$(-a-6), (5,a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.088987910$ |
0.693624990 |
\( -\frac{144789383}{40000} a + \frac{2243100323}{80000} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 932267 a - 5435982\) , \( 1163982351 a - 6787125048\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(932267a-5435982\right){x}+1163982351a-6787125048$ |
| 10.2-a2 |
10.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{7} \cdot 5^{8} \) |
$1.85314$ |
$(-a-6), (5,a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$4.044493955$ |
0.693624990 |
\( -\frac{1255304262655889}{6250000} a + \frac{3659838385944071}{3125000} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 14842627 a - 86546622\) , \( 75190940799 a - 438434758680\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(14842627a-86546622\right){x}+75190940799a-438434758680$ |
| 10.2-b1 |
10.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{14} \cdot 5^{4} \) |
$1.85314$ |
$(-a-6), (5,a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.060400957$ |
$8.088987910$ |
2.942082419 |
\( -\frac{144789383}{40000} a + \frac{2243100323}{80000} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 190 a - 1099\) , \( 3037 a - 17712\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(190a-1099\right){x}+3037a-17712$ |
| 10.2-b2 |
10.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{7} \cdot 5^{8} \) |
$1.85314$ |
$(-a-6), (5,a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.120801915$ |
$4.044493955$ |
2.942082419 |
\( -\frac{1255304262655889}{6250000} a + \frac{3659838385944071}{3125000} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 3030 a - 17659\) , \( 213629 a - 1245664\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(3030a-17659\right){x}+213629a-1245664$ |
| 16.1-a1 |
16.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \cdot 3^{12} \) |
$2.08419$ |
$(-a-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1.901185676$ |
$39.17784241$ |
3.193490281 |
\( 2000 \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 1436754 a - 8377575\) , \( 836060782 a - 4875030092\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(1436754a-8377575\right){x}+836060782a-4875030092$ |
| 16.1-a2 |
16.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \cdot 3^{12} \) |
$2.08419$ |
$(-a-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$3.802371352$ |
$9.794460603$ |
3.193490281 |
\( 1098500 \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 18677734 a - 108908900\) , \( 106033997628 a - 618279139278\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(18677734a-108908900\right){x}+106033997628a-618279139278$ |
| 16.1-b1 |
16.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \cdot 3^{12} \) |
$2.08419$ |
$(-a-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1.901185676$ |
$39.17784241$ |
3.193490281 |
\( 2000 \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -8463 a - 49269\) , \( -387319 a - 2258305\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-8463a-49269\right){x}-387319a-2258305$ |
| 16.1-b2 |
16.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \cdot 3^{12} \) |
$2.08419$ |
$(-a-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$3.802371352$ |
$9.794460603$ |
3.193490281 |
\( 1098500 \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -109943 a - 640994\) , \( -48009030 a - 279938211\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-109943a-640994\right){x}-48009030a-279938211$ |
| 17.1-a1 |
17.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
17.1 |
\( 17 \) |
\( 17^{8} \) |
$2.11602$ |
$(-3a+17)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$5.723560337$ |
$2.393455763$ |
1.174687146 |
\( -\frac{35937}{83521} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( -14\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-{x}-14$ |
| 17.1-a2 |
17.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$2.11602$ |
$(-3a+17)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.430890084$ |
$38.29529222$ |
1.174687146 |
\( \frac{35937}{17} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-{x}$ |
| 17.1-a3 |
17.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
17.1 |
\( 17 \) |
\( 17^{4} \) |
$2.11602$ |
$(-3a+17)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$2.861780168$ |
$9.573823055$ |
1.174687146 |
\( \frac{20346417}{289} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -6\) , \( -4\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-6{x}-4$ |
| 17.1-a4 |
17.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$2.11602$ |
$(-3a+17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1.430890084$ |
$2.393455763$ |
1.174687146 |
\( \frac{82483294977}{17} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -91\) , \( -310\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-91{x}-310$ |
| 17.1-b1 |
17.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
17.1 |
\( 17 \) |
\( 17^{8} \) |
$2.11602$ |
$(-3a+17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.035256177$ |
$2.393455763$ |
2.491789170 |
\( -\frac{35937}{83521} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -280 a - 1644\) , \( -410521 a - 2393734\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-280a-1644\right){x}-410521a-2393734$ |
| 17.1-b2 |
17.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$2.11602$ |
$(-3a+17)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$3.035256177$ |
$38.29529222$ |
2.491789170 |
\( \frac{35937}{17} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -280 a - 1644\) , \( 995 a + 5796\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-280a-1644\right){x}+995a+5796$ |
| 17.1-b3 |
17.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
17.1 |
\( 17 \) |
\( 17^{4} \) |
$2.11602$ |
$(-3a+17)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$6.070512355$ |
$9.573823055$ |
2.491789170 |
\( \frac{20346417}{289} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -2380 a - 13889\) , \( -166271 a - 969524\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2380a-13889\right){x}-166271a-969524$ |
| 17.1-b4 |
17.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$2.11602$ |
$(-3a+17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$3.035256177$ |
$2.393455763$ |
2.491789170 |
\( \frac{82483294977}{17} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -38080 a - 222054\) , \( -10005565 a - 58341974\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-38080a-222054\right){x}-10005565a-58341974$ |
| 18.1-a1 |
18.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2^{5} \cdot 3^{22} \) |
$2.14648$ |
$(-a-6), (3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$4$ |
\( 2^{4} \cdot 5 \) |
$1$ |
$0.435939855$ |
2.990522735 |
\( -\frac{203806678257976965611}{52488} a + \frac{148548367096218745832}{6561} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -3410637 a - 19887245\) , \( -8775001088 a - 51166609211\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3410637a-19887245\right){x}-8775001088a-51166609211$ |
| 18.1-a2 |
18.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2 \cdot 3^{62} \) |
$2.14648$ |
$(-a-6), (3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$4$ |
\( 2^{4} \cdot 5 \) |
$1$ |
$0.435939855$ |
2.990522735 |
\( -\frac{6211909509974716433819}{24315330918113857602} a + \frac{18172789822403039399912}{12157665459056928801} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 8103718 a + 47252405\) , \( 556798743074 a + 3246666685985\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(8103718a+47252405\right){x}+556798743074a+3246666685985$ |
| 18.1-a3 |
18.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2 \cdot 3^{62} \) |
$2.14648$ |
$(-a-6), (3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$16$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$0.435939855$ |
2.990522735 |
\( \frac{6211909509974716433819}{24315330918113857602} a + \frac{18172789822403039399912}{12157665459056928801} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -61719832 a - 359885355\) , \( -413435180474 a - 2410720648967\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-61719832a-359885355\right){x}-413435180474a-2410720648967$ |
| 18.1-a4 |
18.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{16} \) |
$2.14648$ |
$(-a-6), (3,a+1), (3,a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \cdot 5 \) |
$1$ |
$6.975037684$ |
2.990522735 |
\( \frac{141420761}{9216} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -220297 a - 1284525\) , \( -127690376 a - 744556427\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-220297a-1284525\right){x}-127690376a-744556427$ |
| 18.1-a5 |
18.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{52} \) |
$2.14648$ |
$(-a-6), (3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2Cs, 5B |
$4$ |
\( 2^{4} \cdot 5 \) |
$1$ |
$1.743759421$ |
2.990522735 |
\( \frac{211293405175481}{6973568802} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -25184377 a - 146848875\) , \( 161354769508 a + 940851899017\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-25184377a-146848875\right){x}+161354769508a+940851899017$ |
| 18.1-a6 |
18.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{20} \) |
$2.14648$ |
$(-a-6), (3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2Cs, 5B |
$4$ |
\( 2^{4} \cdot 5 \) |
$1$ |
$1.743759421$ |
2.990522735 |
\( \frac{551569744601}{2592} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -3467657 a - 20219725\) , \( -8482309192 a - 49459936843\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3467657a-20219725\right){x}-8482309192a-49459936843$ |
| 18.1-a7 |
18.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{32} \) |
$2.14648$ |
$(-a-6), (3,a+1), (3,a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \cdot 5 \) |
$1$ |
$6.975037684$ |
2.990522735 |
\( \frac{206226044828441}{236196} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -24981417 a - 145665425\) , \( 164156817952 a + 957190508701\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-24981417a-145665425\right){x}+164156817952a+957190508701$ |
| 18.1-a8 |
18.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2^{5} \cdot 3^{22} \) |
$2.14648$ |
$(-a-6), (3,a+1), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$16$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$0.435939855$ |
2.990522735 |
\( \frac{203806678257976965611}{52488} a + \frac{148548367096218745832}{6561} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -55482437 a - 323515405\) , \( -543123237520 a - 3166925470939\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-55482437a-323515405\right){x}-543123237520a-3166925470939$ |
| 18.1-b1 |
18.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{5} \cdot 3^{6} \) |
$2.14648$ |
$(-a-6), (3,a+1), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 5 \) |
$1$ |
$2.326446237$ |
0.997455595 |
\( -\frac{1164473711}{1944} a - \frac{3397746967}{972} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 573 a - 3311\) , \( 24049 a - 140165\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(573a-3311\right){x}+24049a-140165$ |
| 18.1-b2 |
18.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2 \cdot 3^{30} \) |
$2.14648$ |
$(-a-6), (3,a+1), (3,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 5 \) |
$1$ |
$2.326446237$ |
0.997455595 |
\( \frac{256048834252921}{1694577218886} a + \frac{717381555090197}{847288609443} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 3708 a - 21591\) , \( -2114775 a + 12331215\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(3708a-21591\right){x}-2114775a+12331215$ |
*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.
