| 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 |
| 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 |
\( \frac{256048834252921}{1694577218886} a + \frac{717381555090197}{847288609443} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 3708 a - 21591\) , \( -2114775 a + 12331215\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(3708a-21591\right){x}-2114775a+12331215$ |
| 18.1-c1 |
18.1-c |
$2$ |
$5$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
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 |
\( \frac{1164473711}{1944} a - \frac{3397746967}{972} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -575 a - 3311\) , \( -24050 a - 140165\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-575a-3311\right){x}-24050a-140165$ |
| 18.1-c2 |
18.1-c |
$2$ |
$5$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
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 |
\( -\frac{256048834252921}{1694577218886} a + \frac{717381555090197}{847288609443} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -3710 a - 21591\) , \( 2114774 a + 12331215\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3710a-21591\right){x}+2114774a+12331215$ |
| 18.1-d1 |
18.1-d |
$2$ |
$5$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
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 |
$1$ |
\( 5^{2} \) |
$1$ |
$2.326446237$ |
4.987277977 |
\( \frac{1164473711}{1944} a - \frac{3397746967}{972} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 2 a - 2\) , \( 6 a - 55\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a-2\right){x}+6a-55$ |
| 18.1-d2 |
18.1-d |
$2$ |
$5$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
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 |
$1$ |
\( 5^{2} \) |
$1$ |
$2.326446237$ |
4.987277977 |
\( -\frac{256048834252921}{1694577218886} a + \frac{717381555090197}{847288609443} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -13 a + 78\) , \( -14 a + 151\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-13a+78\right){x}-14a+151$ |
| 18.1-e1 |
18.1-e |
$2$ |
$5$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
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 |
$1$ |
\( 5^{2} \) |
$1$ |
$2.326446237$ |
4.987277977 |
\( -\frac{1164473711}{1944} a - \frac{3397746967}{972} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -3 a - 2\) , \( -7 a - 55\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a-2\right){x}-7a-55$ |
| 18.1-e2 |
18.1-e |
$2$ |
$5$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
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 |
$1$ |
\( 5^{2} \) |
$1$ |
$2.326446237$ |
4.987277977 |
\( \frac{256048834252921}{1694577218886} a + \frac{717381555090197}{847288609443} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 12 a + 78\) , \( 13 a + 151\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(12a+78\right){x}+13a+151$ |
| 18.1-f1 |
18.1-f |
$8$ |
$20$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
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 |
\( -\frac{203806678257976965611}{52488} a + \frac{148548367096218745832}{6561} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -307 a - 6346\) , \( -15106 a - 223719\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-307a-6346\right){x}-15106a-223719$ |
| 18.1-f2 |
18.1-f |
$8$ |
$20$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
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 |
\( -\frac{6211909509974716433819}{24315330918113857602} a + \frac{18172789822403039399912}{12157665459056928801} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 2088 a + 7104\) , \( 1636360 a + 9432569\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2088a+7104\right){x}+1636360a+9432569$ |
| 18.1-f3 |
18.1-f |
$8$ |
$20$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
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 |
\( \frac{6211909509974716433819}{24315330918113857602} a + \frac{18172789822403039399912}{12157665459056928801} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -12662 a - 73136\) , \( -1237372 a - 7090263\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-12662a-73136\right){x}-1237372a-7090263$ |
| 18.1-f4 |
18.1-f |
$8$ |
$20$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
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 |
\( \frac{141420761}{9216} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -47 a - 266\) , \( -442 a - 2631\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-47a-266\right){x}-442a-2631$ |
| 18.1-f5 |
18.1-f |
$8$ |
$20$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
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 |
\( \frac{211293405175481}{6973568802} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -4967 a - 31016\) , \( 459902 a + 2709765\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4967a-31016\right){x}+459902a+2709765$ |
| 18.1-f6 |
18.1-f |
$8$ |
$20$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
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 |
\( \frac{551569744601}{2592} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -687 a - 4266\) , \( -25658 a - 152455\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-687a-4266\right){x}-25658a-152455$ |
| 18.1-f7 |
18.1-f |
$8$ |
$20$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
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 |
\( \frac{206226044828441}{236196} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -4927 a - 30766\) , \( 468086 a + 2758161\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4927a-30766\right){x}+468086a+2758161$ |
| 18.1-f8 |
18.1-f |
$8$ |
$20$ |
\(\Q(\sqrt{34}) \) |
$2$ |
$[2, 0]$ |
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 |
\( \frac{203806678257976965611}{52488} a + \frac{148548367096218745832}{6561} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -11307 a - 66186\) , \( -1602674 a - 9348007\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-11307a-66186\right){x}-1602674a-9348007$ |
*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.
