| 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 |
| 5.1-a1 |
5.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{7} \) |
$1.63108$ |
$(a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$4$ |
\( 1 \) |
$1$ |
$5.815991412$ |
1.905858325 |
\( -\frac{46571978743}{78125} a - \frac{253225529329}{78125} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -3 a + 16\) , \( -10 a - 26\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-3a+16\right){x}-10a-26$ |
| 5.1-b1 |
5.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{5} \) |
$1.63108$ |
$(a+6)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.494901142$ |
$13.14214171$ |
2.131333739 |
\( -\frac{650642}{3125} a + \frac{4146049}{3125} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -a + 3\) , \( -21 a - 126\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-a+3\right){x}-21a-126$ |
| 5.2-a1 |
5.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
5.2 |
\( 5 \) |
\( - 5^{7} \) |
$1.63108$ |
$(-a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$4$ |
\( 1 \) |
$1$ |
$5.815991412$ |
1.905858325 |
\( \frac{46571978743}{78125} a - \frac{299797508072}{78125} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 3 a + 13\) , \( 10 a - 36\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(3a+13\right){x}+10a-36$ |
| 5.2-b1 |
5.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
5.2 |
\( 5 \) |
\( - 5^{5} \) |
$1.63108$ |
$(-a+7)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.494901142$ |
$13.14214171$ |
2.131333739 |
\( \frac{650642}{3125} a + \frac{3495407}{3125} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 2 a + 1\) , \( 18 a - 148\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a+1\right){x}+18a-148$ |
| 19.1-a1 |
19.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
19.1 |
\( 19 \) |
\( 19^{3} \) |
$2.27730$ |
$(a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$5.135504310$ |
$1.580377555$ |
3.989349332 |
\( \frac{74427084845}{6859} a - \frac{491903364112}{6859} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 293 a - 1917\) , \( 7474 a - 49316\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(293a-1917\right){x}+7474a-49316$ |
| 19.1-a2 |
19.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
19.1 |
\( 19 \) |
\( 19 \) |
$2.27730$ |
$(a+7)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$15.40651293$ |
$14.22339800$ |
3.989349332 |
\( \frac{1945}{19} a + \frac{9463}{19} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 3 a - 2\) , \( 25 a - 128\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(3a-2\right){x}+25a-128$ |
| 19.2-a1 |
19.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
19.2 |
\( 19 \) |
\( 19^{3} \) |
$2.27730$ |
$(a-8)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$5.135504310$ |
$1.580377555$ |
3.989349332 |
\( -\frac{74427084845}{6859} a - \frac{417476279267}{6859} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -295 a - 1624\) , \( -7475 a - 41842\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-295a-1624\right){x}-7475a-41842$ |
| 19.2-a2 |
19.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
19.2 |
\( 19 \) |
\( 19 \) |
$2.27730$ |
$(a-8)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$15.40651293$ |
$14.22339800$ |
3.989349332 |
\( -\frac{1945}{19} a + \frac{11408}{19} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -5 a + 1\) , \( -26 a - 103\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-5a+1\right){x}-26a-103$ |
| 20.1-a1 |
20.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{8} \cdot 5^{3} \) |
$2.30669$ |
$(a+6), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.280265921$ |
$13.10929472$ |
3.611916758 |
\( -\frac{2549849}{1000} a + \frac{35365181}{2000} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( 39 a + 223\) , \( 439 a + 2460\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(39a+223\right){x}+439a+2460$ |
| 20.1-b1 |
20.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{2} \cdot 5^{4} \) |
$2.30669$ |
$(a+6), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$10.73849265$ |
3.518926383 |
\( \frac{9737943}{1250} a - \frac{82146821}{1250} \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 112 a - 732\) , \( 1854 a - 12221\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(112a-732\right){x}+1854a-12221$ |
| 20.2-a1 |
20.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( - 2^{8} \cdot 5^{3} \) |
$2.30669$ |
$(-a+7), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.280265921$ |
$13.10929472$ |
3.611916758 |
\( \frac{2549849}{1000} a + \frac{30265483}{2000} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -18 a + 281\) , \( -215 a + 1817\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-18a+281\right){x}-215a+1817$ |
| 20.2-b1 |
20.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( 2^{2} \cdot 5^{4} \) |
$2.30669$ |
$(-a+7), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$10.73849265$ |
3.518926383 |
\( -\frac{9737943}{1250} a - \frac{36204439}{625} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( -114 a - 619\) , \( -1855 a - 10366\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-114a-619\right){x}-1855a-10366$ |
| 25.2-a1 |
25.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{11} \) |
$2.43903$ |
$(-a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$13.46108098$ |
4.411098889 |
\( \frac{650642}{3125} a + \frac{3495407}{3125} \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 259 a - 1726\) , \( -33971 a + 224311\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(259a-1726\right){x}-33971a+224311$ |
| 25.2-b1 |
25.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{13} \) |
$2.43903$ |
$(-a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$7.144251569$ |
2.341119573 |
\( \frac{46571978743}{78125} a - \frac{299797508072}{78125} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 330 a - 2018\) , \( -7479 a + 49775\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(330a-2018\right){x}-7479a+49775$ |
| 25.2-c1 |
25.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{8} \) |
$2.43903$ |
$(-a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$0.523501812$ |
$21.27018917$ |
5.473279902 |
\( -1322 a - 5601 \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 81 a - 416\) , \( 186 a - 897\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(81a-416\right){x}+186a-897$ |
| 25.2-d1 |
25.2-d |
$1$ |
$1$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{2} \) |
$2.43903$ |
$(-a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$16.42238347$ |
1.345374075 |
\( -1322 a - 5601 \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -5 a + 14\) , \( -6 a + 28\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-5a+14\right){x}-6a+28$ |
| 25.3-a1 |
25.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
25.3 |
\( 5^{2} \) |
\( - 5^{11} \) |
$2.43903$ |
$(a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$13.46108098$ |
4.411098889 |
\( -\frac{650642}{3125} a + \frac{4146049}{3125} \) |
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -261 a - 1466\) , \( 33970 a + 190341\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-261a-1466\right){x}+33970a+190341$ |
| 25.3-b1 |
25.3-b |
$1$ |
$1$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
25.3 |
\( 5^{2} \) |
\( - 5^{13} \) |
$2.43903$ |
$(a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$7.144251569$ |
2.341119573 |
\( -\frac{46571978743}{78125} a - \frac{253225529329}{78125} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( -309 a - 1728\) , \( 5752 a + 32229\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-309a-1728\right){x}+5752a+32229$ |
| 25.3-c1 |
25.3-c |
$1$ |
$1$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
25.3 |
\( 5^{2} \) |
\( - 5^{8} \) |
$2.43903$ |
$(a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$0.523501812$ |
$21.27018917$ |
5.473279902 |
\( 1322 a - 6923 \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -64 a - 371\) , \( -540 a - 3031\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-64a-371\right){x}-540a-3031$ |
| 25.3-d1 |
25.3-d |
$1$ |
$1$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
25.3 |
\( 5^{2} \) |
\( - 5^{2} \) |
$2.43903$ |
$(a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$16.42238347$ |
1.345374075 |
\( 1322 a - 6923 \) |
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( 3 a + 10\) , \( 5 a + 23\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(3a+10\right){x}+5a+23$ |
| 28.1-a1 |
28.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{2} \cdot 7 \) |
$2.50912$ |
$(-a+6), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$19.80355729$ |
1.622370627 |
\( -\frac{729}{14} a + \frac{10341}{14} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -3 a + 20\) , \( -5 a + 33\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-3a+20\right){x}-5a+33$ |
| 28.2-a1 |
28.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{2} \cdot 7 \) |
$2.50912$ |
$(-a-5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$19.80355729$ |
1.622370627 |
\( \frac{729}{14} a + \frac{4806}{7} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 3 a + 17\) , \( 5 a + 28\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(3a+17\right){x}+5a+28$ |
| 35.1-a1 |
35.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5^{5} \cdot 7 \) |
$2.65307$ |
$(a+6), (-a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$1$ |
$4.734585374$ |
1.939361734 |
\( -\frac{20760720058}{21875} a - \frac{116327829399}{21875} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -420 a + 2843\) , \( -144365 a + 953394\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-420a+2843\right){x}-144365a+953394$ |
| 35.1-b1 |
35.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( - 5 \cdot 7^{2} \) |
$2.65307$ |
$(a+6), (-a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$4$ |
\( 2 \) |
$0.132386000$ |
$25.34125738$ |
4.397411107 |
\( -\frac{560947}{245} a + \frac{3682739}{245} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( 192 a - 1169\) , \( 3412 a - 22332\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(192a-1169\right){x}+3412a-22332$ |
| 35.1-c1 |
35.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( - 5 \cdot 7^{2} \) |
$2.65307$ |
$(a+6), (-a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$4$ |
\( 2 \) |
$1$ |
$7.695100308$ |
5.043257443 |
\( -\frac{29384618}{245} a + \frac{193266361}{245} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( 45 a - 282\) , \( 321 a - 2108\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(45a-282\right){x}+321a-2108$ |
| 35.1-d1 |
35.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( - 5^{2} \cdot 7^{3} \) |
$2.65307$ |
$(a+6), (-a+6)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$26.18320699$ |
0.268126486 |
\( -\frac{51175483}{8575} a + \frac{339579426}{8575} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 115 a + 714\) , \( 5187 a + 29176\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(115a+714\right){x}+5187a+29176$ |
| 35.1-d2 |
35.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( - 5^{2} \cdot 7^{12} \) |
$2.65307$ |
$(a+6), (-a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.272900874$ |
0.268126486 |
\( \frac{164379193191481}{346032180025} a + \frac{1412465273436668}{346032180025} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -5380 a - 30076\) , \( -471673 a - 2642803\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-5380a-30076\right){x}-471673a-2642803$ |
| 35.1-d3 |
35.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5^{4} \cdot 7^{6} \) |
$2.65307$ |
$(a+6), (-a+6)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$13.09160349$ |
0.268126486 |
\( \frac{40952612073}{73530625} a + \frac{383222654069}{73530625} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -1410 a - 7831\) , \( 61080 a + 342360\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1410a-7831\right){x}+61080a+342360$ |
| 35.1-d4 |
35.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5^{8} \cdot 7^{3} \) |
$2.65307$ |
$(a+6), (-a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$6.545801749$ |
0.268126486 |
\( \frac{709081131937929}{133984375} a + \frac{4153850803311212}{133984375} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -21840 a - 122306\) , \( 4300245 a + 24095579\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-21840a-122306\right){x}+4300245a+24095579$ |
| 35.1-e1 |
35.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( - 5^{5} \cdot 7^{4} \) |
$2.65307$ |
$(a+6), (-a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 5 \) |
$0.577041228$ |
$4.314327744$ |
4.079029430 |
\( -\frac{1884863872467}{7503125} a - \frac{7139149778176}{7503125} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( a - 19\) , \( -2 a + 8\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(a-19\right){x}-2a+8$ |
| 35.4-a1 |
35.4-a |
$1$ |
$1$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
35.4 |
\( 5 \cdot 7 \) |
\( 5^{5} \cdot 7 \) |
$2.65307$ |
$(-a+7), (-a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$1$ |
$4.734585374$ |
1.939361734 |
\( \frac{20760720058}{21875} a - \frac{137088549457}{21875} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 420 a + 2423\) , \( 144365 a + 809029\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(420a+2423\right){x}+144365a+809029$ |
| 35.4-b1 |
35.4-b |
$1$ |
$1$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
35.4 |
\( 5 \cdot 7 \) |
\( - 5 \cdot 7^{2} \) |
$2.65307$ |
$(-a+7), (-a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$4$ |
\( 2 \) |
$0.132386000$ |
$25.34125738$ |
4.397411107 |
\( \frac{560947}{245} a + \frac{3121792}{245} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -171 a - 958\) , \( -4580 a - 25663\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-171a-958\right){x}-4580a-25663$ |
| 35.4-c1 |
35.4-c |
$1$ |
$1$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
35.4 |
\( 5 \cdot 7 \) |
\( - 5 \cdot 7^{2} \) |
$2.65307$ |
$(-a+7), (-a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$4$ |
\( 2 \) |
$1$ |
$7.695100308$ |
5.043257443 |
\( \frac{29384618}{245} a + \frac{163881743}{245} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -45 a - 237\) , \( -321 a - 1787\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-45a-237\right){x}-321a-1787$ |
| 35.4-d1 |
35.4-d |
$4$ |
$4$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
35.4 |
\( 5 \cdot 7 \) |
\( - 5^{2} \cdot 7^{12} \) |
$2.65307$ |
$(-a+7), (-a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.272900874$ |
0.268126486 |
\( -\frac{164379193191481}{346032180025} a + \frac{1576844466628149}{346032180025} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 5380 a - 35456\) , \( 471673 a - 3114476\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(5380a-35456\right){x}+471673a-3114476$ |
| 35.4-d2 |
35.4-d |
$4$ |
$4$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
35.4 |
\( 5 \cdot 7 \) |
\( 5^{4} \cdot 7^{6} \) |
$2.65307$ |
$(-a+7), (-a-5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$13.09160349$ |
0.268126486 |
\( -\frac{40952612073}{73530625} a + \frac{424175266142}{73530625} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 1410 a - 9241\) , \( -61080 a + 403440\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(1410a-9241\right){x}-61080a+403440$ |
| 35.4-d3 |
35.4-d |
$4$ |
$4$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
35.4 |
\( 5 \cdot 7 \) |
\( - 5^{2} \cdot 7^{3} \) |
$2.65307$ |
$(-a+7), (-a-5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$26.18320699$ |
0.268126486 |
\( \frac{51175483}{8575} a + \frac{288403943}{8575} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -115 a + 829\) , \( -5187 a + 34363\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-115a+829\right){x}-5187a+34363$ |
| 35.4-d4 |
35.4-d |
$4$ |
$4$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
35.4 |
\( 5 \cdot 7 \) |
\( 5^{8} \cdot 7^{3} \) |
$2.65307$ |
$(-a+7), (-a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$6.545801749$ |
0.268126486 |
\( -\frac{709081131937929}{133984375} a + \frac{4862931935249141}{133984375} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 21840 a - 144146\) , \( -4300245 a + 28395824\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(21840a-144146\right){x}-4300245a+28395824$ |
| 35.4-e1 |
35.4-e |
$1$ |
$1$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
35.4 |
\( 5 \cdot 7 \) |
\( - 5^{5} \cdot 7^{4} \) |
$2.65307$ |
$(-a+7), (-a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 5 \) |
$0.577041228$ |
$4.314327744$ |
4.079029430 |
\( \frac{1884863872467}{7503125} a - \frac{9024013650643}{7503125} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -a - 18\) , \( 2 a + 6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a-18\right){x}+2a+6$ |
| 36.1-a1 |
36.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{2} \) |
$2.67182$ |
$(2), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$5.179486261$ |
0.848640095 |
\( \frac{22114693}{96} a - \frac{291601691}{192} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( 86 a - 524\) , \( 1303 a - 8542\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(86a-524\right){x}+1303a-8542$ |
| 36.1-b1 |
36.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{6} \) |
$2.67182$ |
$(2), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1.747494296$ |
$15.62848146$ |
4.474756529 |
\( \frac{7422461}{54} a + \frac{41726609}{54} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -183 a - 1015\) , \( -4089 a - 22894\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-183a-1015\right){x}-4089a-22894$ |
| 36.1-c1 |
36.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{30} \cdot 3^{26} \) |
$2.67182$ |
$(2), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
|
|
$25$ |
\( 1 \) |
$1$ |
$1.167068544$ |
2.390249513 |
\( \frac{382356821298941}{52242776064} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -461179 a - 2584112\) , \( 364725235 a + 2043656815\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-461179a-2584112\right){x}+364725235a+2043656815$ |
| 36.1-d1 |
36.1-d |
$2$ |
$5$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{4} \) |
$2.67182$ |
$(2), (3)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B.1.1 |
$4$ |
\( 2 \) |
$1$ |
$26.23185940$ |
0.687679249 |
\( -\frac{89254693709}{72} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( 28398 a - 187476\) , \( -6351233 a + 41939018\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(28398a-187476\right){x}-6351233a+41939018$ |
| 36.1-d2 |
36.1-d |
$2$ |
$5$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{30} \cdot 3^{20} \) |
$2.67182$ |
$(2), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B.1.2 |
$4$ |
\( 2 \) |
$1$ |
$1.049274376$ |
0.687679249 |
\( \frac{910134926371}{1934917632} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( -61577 a + 406654\) , \( -33781663 a + 223069768\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-61577a+406654\right){x}-33781663a+223069768$ |
| 36.1-e1 |
36.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{6} \) |
$2.67182$ |
$(2), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1.747494296$ |
$15.62848146$ |
4.474756529 |
\( -\frac{7422461}{54} a + \frac{24574535}{27} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 181 a - 1198\) , \( 4088 a - 26983\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(181a-1198\right){x}+4088a-26983$ |
| 36.1-f1 |
36.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{149}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{2} \) |
$2.67182$ |
$(2), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$5.179486261$ |
0.848640095 |
\( -\frac{22114693}{96} a - \frac{82457435}{64} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( -87 a - 438\) , \( -1303 a - 7239\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-87a-438\right){x}-1303a-7239$ |
*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.
