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 |
$2$ |
$5$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( 5 \) |
$1.34289$ |
$(-a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 1 \) |
$0.641608148$ |
$15.50812655$ |
1.980151940 |
\( -\frac{3848179}{5} a - \frac{19994526}{5} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( a + 2\) , \( 2 a - 14\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(a+2\right){x}+2a-14$ |
5.1-a2 |
5.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( 5^{5} \) |
$1.34289$ |
$(-a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 5 \) |
$0.128321629$ |
$15.50812655$ |
1.980151940 |
\( \frac{198551}{3125} a + \frac{4288299}{3125} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( 10 a + 60\) , \( 30 a + 144\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(10a+60\right){x}+30a+144$ |
5.2-a1 |
5.2-a |
$2$ |
$5$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
5.2 |
\( 5 \) |
\( 5 \) |
$1.34289$ |
$(-a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 1 \) |
$0.641608148$ |
$15.50812655$ |
1.980151940 |
\( \frac{3848179}{5} a - 4768541 \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -a + 3\) , \( -2 a - 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a+3\right){x}-2a-12$ |
5.2-a2 |
5.2-a |
$2$ |
$5$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
5.2 |
\( 5 \) |
\( 5^{5} \) |
$1.34289$ |
$(-a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 5 \) |
$0.128321629$ |
$15.50812655$ |
1.980151940 |
\( -\frac{198551}{3125} a + \frac{179474}{125} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( -11 a + 70\) , \( -30 a + 174\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-11a+70\right){x}-30a+174$ |
9.1-a1 |
9.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$1.55546$ |
$(3)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2Cn, 5B.1.1 |
$4$ |
\( 2 \) |
$1$ |
$53.44923674$ |
1.701887307 |
\( \frac{5451776}{9} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( 147 a - 802\) , \( -1944 a + 10734\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(147a-802\right){x}-1944a+10734$ |
9.1-a2 |
9.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{20} \) |
$1.55546$ |
$(3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2Cn, 5B.1.2 |
$4$ |
\( 2 \) |
$1$ |
$2.137969469$ |
1.701887307 |
\( \frac{162413858816}{59049} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -4547 a - 20565\) , \( -380826 a - 1723220\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-4547a-20565\right){x}-380826a-1723220$ |
16.1-a1 |
16.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$1.79609$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2Cn |
$1$ |
\( 1 \) |
$1$ |
$28.53203897$ |
2.839043989 |
\( 8192 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -107 a - 474\) , \( 1354 a + 6133\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-107a-474\right){x}+1354a+6133$ |
20.1-a1 |
20.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{6} \cdot 5^{2} \) |
$1.89914$ |
$(-a+5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$3.698133822$ |
2.207868412 |
\( \frac{15552051}{200} a - \frac{86150501}{200} \) |
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 12 a - 62\) , \( 33 a - 189\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(12a-62\right){x}+33a-189$ |
20.1-b1 |
20.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{10} \cdot 5 \) |
$1.89914$ |
$(-a+5), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 5 \) |
$0.826677722$ |
$35.06575035$ |
3.204912481 |
\( \frac{399186649}{160} a - \frac{550561031}{40} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}-{x}$ |
20.1-b2 |
20.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{30} \cdot 5^{3} \) |
$1.89914$ |
$(-a+5), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \cdot 5 \) |
$2.480033166$ |
$3.896194484$ |
3.204912481 |
\( \frac{33018991747}{2048000} a + \frac{298808284781}{4096000} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -5 a + 9\) , \( -32 a + 126\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-5a+9\right){x}-32a+126$ |
20.1-b3 |
20.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{10} \cdot 5^{9} \) |
$1.89914$ |
$(-a+5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 5 \) |
$7.440099499$ |
$0.432910498$ |
3.204912481 |
\( \frac{13045120502973079218167}{31250000} a + \frac{118056718014440500348441}{62500000} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -165 a - 631\) , \( -1824 a - 14850\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-165a-631\right){x}-1824a-14850$ |
20.1-c1 |
20.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{2} \cdot 5^{3} \) |
$1.89914$ |
$(-a+5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.314258750$ |
$15.26503460$ |
2.864017950 |
\( \frac{32104703}{125} a + \frac{290543569}{250} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -a + 18\) , \( -1605 a + 8876\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a+18\right){x}-1605a+8876$ |
20.1-d1 |
20.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{2} \cdot 5 \) |
$1.89914$ |
$(-a+5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.698555442$ |
$17.36166181$ |
2.413578794 |
\( \frac{5849}{10} a - \frac{7022}{5} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 6 a + 22\) , \( 12 a + 51\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(6a+22\right){x}+12a+51$ |
20.1-e1 |
20.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{10} \cdot 5^{3} \) |
$1.89914$ |
$(-a+5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$9.354152722$ |
0.930772984 |
\( -\frac{1460239}{1000} a - \frac{74748269}{4000} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 29 a - 151\) , \( 247 a - 1370\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(29a-151\right){x}+247a-1370$ |
20.2-a1 |
20.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( 2^{6} \cdot 5^{2} \) |
$1.89914$ |
$(-a-4), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$3.698133822$ |
2.207868412 |
\( -\frac{15552051}{200} a - \frac{1411969}{4} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( -13 a - 49\) , \( -34 a - 155\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-13a-49\right){x}-34a-155$ |
20.2-b1 |
20.2-b |
$3$ |
$9$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( - 2^{10} \cdot 5 \) |
$1.89914$ |
$(-a-4), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 5 \) |
$0.826677722$ |
$35.06575035$ |
3.204912481 |
\( -\frac{399186649}{160} a - \frac{360611495}{32} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -a - 1\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}$ |
20.2-b2 |
20.2-b |
$3$ |
$9$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( - 2^{30} \cdot 5^{3} \) |
$1.89914$ |
$(-a-4), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \cdot 5 \) |
$2.480033166$ |
$3.896194484$ |
3.204912481 |
\( -\frac{33018991747}{2048000} a + \frac{14593850731}{163840} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 4 a + 4\) , \( 32 a + 94\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(4a+4\right){x}+32a+94$ |
20.2-b3 |
20.2-b |
$3$ |
$9$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( - 2^{10} \cdot 5^{9} \) |
$1.89914$ |
$(-a-4), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 5 \) |
$7.440099499$ |
$0.432910498$ |
3.204912481 |
\( -\frac{13045120502973079218167}{31250000} a + \frac{5765878360815466351391}{2500000} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 164 a - 796\) , \( 1824 a - 16674\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(164a-796\right){x}+1824a-16674$ |
20.2-c1 |
20.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( - 2^{2} \cdot 5^{3} \) |
$1.89914$ |
$(-a-4), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.314258750$ |
$15.26503460$ |
2.864017950 |
\( -\frac{32104703}{125} a + \frac{14190119}{10} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( a + 17\) , \( 1605 a + 7271\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(a+17\right){x}+1605a+7271$ |
20.2-d1 |
20.2-d |
$1$ |
$1$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( - 2^{2} \cdot 5 \) |
$1.89914$ |
$(-a-4), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.698555442$ |
$17.36166181$ |
2.413578794 |
\( -\frac{5849}{10} a - \frac{1639}{2} \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 6 a + 30\) , \( 10 a + 45\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6a+30\right){x}+10a+45$ |
20.2-e1 |
20.2-e |
$1$ |
$1$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( 2^{10} \cdot 5^{3} \) |
$1.89914$ |
$(-a-4), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$9.354152722$ |
0.930772984 |
\( \frac{1460239}{1000} a - \frac{3223569}{160} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -29 a - 122\) , \( -247 a - 1123\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-29a-122\right){x}-247a-1123$ |
23.1-a1 |
23.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
23.1 |
\( 23 \) |
\( 23 \) |
$1.96667$ |
$(a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.258708686$ |
$38.37034411$ |
1.975495359 |
\( \frac{5167}{23} a + \frac{72696}{23} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 8 a + 38\) , \( 10 a + 45\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(8a+38\right){x}+10a+45$ |
23.1-b1 |
23.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
23.1 |
\( 23 \) |
\( 23^{5} \) |
$1.96667$ |
$(a+1)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 1 \) |
$0.479508602$ |
$16.13990941$ |
3.080326841 |
\( \frac{374006021987}{6436343} a + \frac{1708281385917}{6436343} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -a - 2\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a-2\right){x}+2$ |
23.1-b2 |
23.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
23.1 |
\( 23 \) |
\( 23 \) |
$1.96667$ |
$(a+1)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 1 \) |
$0.479508602$ |
$16.13990941$ |
3.080326841 |
\( -\frac{955576606153}{23} a + \frac{5279566914072}{23} \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -596 a - 2705\) , \( -20349 a - 92081\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-596a-2705\right){x}-20349a-92081$ |
23.2-a1 |
23.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
23.2 |
\( 23 \) |
\( 23 \) |
$1.96667$ |
$(a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.258708686$ |
$38.37034411$ |
1.975495359 |
\( -\frac{5167}{23} a + \frac{77863}{23} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 7 a + 19\) , \( 10 a + 29\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(7a+19\right){x}+10a+29$ |
23.2-b1 |
23.2-b |
$2$ |
$5$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
23.2 |
\( 23 \) |
\( 23^{5} \) |
$1.96667$ |
$(a-2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 1 \) |
$0.479508602$ |
$16.13990941$ |
3.080326841 |
\( -\frac{374006021987}{6436343} a + \frac{2082287407904}{6436343} \) |
\( \bigl[1\) , \( -a\) , \( 1\) , \( a - 3\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(a-3\right){x}+2$ |
23.2-b2 |
23.2-b |
$2$ |
$5$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
23.2 |
\( 23 \) |
\( 23 \) |
$1.96667$ |
$(a-2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B |
$1$ |
\( 1 \) |
$0.479508602$ |
$16.13990941$ |
3.080326841 |
\( \frac{955576606153}{23} a + \frac{4323990307919}{23} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 607 a - 3288\) , \( 17655 a - 97398\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(607a-3288\right){x}+17655a-97398$ |
25.1-a1 |
25.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{21} \) |
$2.00809$ |
$(-a+5), (-a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$4$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$1.171301932$ |
2.330977968 |
\( -\frac{119964801985712901}{95367431640625} a - \frac{299119538708793324}{95367431640625} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -205 a - 925\) , \( -4792 a - 21690\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-205a-925\right){x}-4792a-21690$ |
25.1-a2 |
25.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{9} \) |
$2.00809$ |
$(-a+5), (-a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$4$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$1.171301932$ |
2.330977968 |
\( -\frac{4249908337092597081}{3125} a + \frac{4696095852603791361}{625} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 3415 a - 18885\) , \( 253720 a - 1401794\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(3415a-18885\right){x}+253720a-1401794$ |
25.1-a3 |
25.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{21} \) |
$2.00809$ |
$(-a+5), (-a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$4$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$1.171301932$ |
2.330977968 |
\( \frac{119964801985712901}{95367431640625} a - \frac{16763373627780249}{3814697265625} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 205 a - 1155\) , \( 4586 a - 25352\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(205a-1155\right){x}+4586a-25352$ |
25.1-a4 |
25.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$2.00809$ |
$(-a+5), (-a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 5 \) |
$1$ |
$18.74083092$ |
2.330977968 |
\( -\frac{527266286001}{3125} a + \frac{2913149611026}{3125} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -10 a - 40\) , \( -104 a - 470\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-10a-40\right){x}-104a-470$ |
25.1-a5 |
25.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{12} \) |
$2.00809$ |
$(-a+5), (-a-4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2Cs, 5B |
$4$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$4.685207731$ |
2.330977968 |
\( -\frac{113561587315449}{9765625} a + \frac{25113206197026}{390625} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 210 a - 1180\) , \( 4423 a - 24447\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(210a-1180\right){x}+4423a-24447$ |
25.1-a6 |
25.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{12} \) |
$2.00809$ |
$(-a+5), (-a-4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2Cs, 5B |
$4$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$4.685207731$ |
2.330977968 |
\( \frac{113561587315449}{9765625} a + \frac{514268567610201}{9765625} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -210 a - 945\) , \( -4634 a - 20968\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-210a-945\right){x}-4634a-20968$ |
25.1-a7 |
25.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$2.00809$ |
$(-a+5), (-a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 5 \) |
$1$ |
$18.74083092$ |
2.330977968 |
\( \frac{527266286001}{3125} a + \frac{95435333001}{125} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 10 a - 75\) , \( 93 a - 524\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(10a-75\right){x}+93a-524$ |
25.1-a8 |
25.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{9} \) |
$2.00809$ |
$(-a+5), (-a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B |
$4$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$1.171301932$ |
2.330977968 |
\( \frac{4249908337092597081}{3125} a + \frac{19230570925926359724}{3125} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -3415 a - 15445\) , \( -257136 a - 1163518\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-3415a-15445\right){x}-257136a-1163518$ |
25.2-a1 |
25.2-a |
$2$ |
$5$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{7} \) |
$2.00809$ |
$(-a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.935445035$ |
2.760410296 |
\( -\frac{3848179}{5} a - \frac{19994526}{5} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( -13 a - 50\) , \( 29 a + 131\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-13a-50\right){x}+29a+131$ |
25.2-a2 |
25.2-a |
$2$ |
$5$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{11} \) |
$2.00809$ |
$(-a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.935445035$ |
2.760410296 |
\( \frac{198551}{3125} a + \frac{4288299}{3125} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -27 a + 187\) , \( -185 a + 1067\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-27a+187\right){x}-185a+1067$ |
25.3-a1 |
25.3-a |
$2$ |
$5$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{7} \) |
$2.00809$ |
$(-a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.935445035$ |
2.760410296 |
\( \frac{3848179}{5} a - 4768541 \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 12 a - 63\) , \( -29 a + 160\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(12a-63\right){x}-29a+160$ |
25.3-a2 |
25.3-a |
$2$ |
$5$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
25.3 |
\( 5^{2} \) |
\( 5^{11} \) |
$2.00809$ |
$(-a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.935445035$ |
2.760410296 |
\( -\frac{198551}{3125} a + \frac{179474}{125} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 27 a + 160\) , \( 185 a + 882\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(27a+160\right){x}+185a+882$ |
31.1-a1 |
31.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
31.1 |
\( 31 \) |
\( -31 \) |
$2.11904$ |
$(a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$39.05829395$ |
3.886445507 |
\( \frac{35123200}{31} a - \frac{193880064}{31} \) |
\( \bigl[0\) , \( 1\) , \( a + 1\) , \( -2\) , \( -a - 7\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+{x}^{2}-2{x}-a-7$ |
31.2-a1 |
31.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
31.2 |
\( 31 \) |
\( -31 \) |
$2.11904$ |
$(a-8)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$39.05829395$ |
3.886445507 |
\( -\frac{35123200}{31} a - \frac{158756864}{31} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( -2\) , \( -7\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}-2{x}-7$ |
36.1-a1 |
36.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{6} \) |
$2.19976$ |
$(2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$23.05611434$ |
1.147084561 |
\( -\frac{125}{108} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -3 a - 10\) , \( 393 a + 1777\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-3a-10\right){x}+393a+1777$ |
36.1-a2 |
36.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{12} \) |
$2.19976$ |
$(2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$23.05611434$ |
1.147084561 |
\( \frac{114084125}{1458} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 405 a - 2225\) , \( -9297 a + 51356\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(405a-2225\right){x}-9297a+51356$ |
36.1-b1 |
36.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{46} \cdot 3^{16} \) |
$2.19976$ |
$(2), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
|
|
$49$ |
\( 2 \) |
$1$ |
$0.185842275$ |
1.812215760 |
\( -\frac{58253143347125}{55037657088} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -32304 a - 146168\) , \( -11438336 a - 51757760\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-32304a-146168\right){x}-11438336a-51757760$ |
37.1-a1 |
37.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
37.1 |
\( 37 \) |
\( 37^{2} \) |
$2.21488$ |
$(-2a+9)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cn |
$1$ |
\( 2 \) |
$1$ |
$15.56525947$ |
3.097602410 |
\( -\frac{17375232}{1369} a + \frac{105893888}{1369} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( a + 4\) , \( a - 11\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(a+4\right){x}+a-11$ |
37.1-b1 |
37.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
37.1 |
\( 37 \) |
\( 37 \) |
$2.21488$ |
$(-2a+9)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$26.36878876$ |
2.623792548 |
\( \frac{456700}{37} a - \frac{2523239}{37} \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 11 a - 12\) , \( -3 a + 111\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(11a-12\right){x}-3a+111$ |
37.1-c1 |
37.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
37.1 |
\( 37 \) |
\( 37^{4} \) |
$2.21488$ |
$(-2a+9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cn |
$1$ |
\( 2^{2} \) |
$0.239583287$ |
$21.25081451$ |
4.052858127 |
\( -\frac{10136517844992}{1874161} a + \frac{56085506084864}{1874161} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( -76 a - 338\) , \( 659 a + 2980\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-76a-338\right){x}+659a+2980$ |
37.2-a1 |
37.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
37.2 |
\( 37 \) |
\( 37^{2} \) |
$2.21488$ |
$(2a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cn |
$1$ |
\( 2 \) |
$1$ |
$15.56525947$ |
3.097602410 |
\( \frac{17375232}{1369} a + \frac{88518656}{1369} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -a + 5\) , \( -a - 10\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a+5\right){x}-a-10$ |
37.2-b1 |
37.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
37.2 |
\( 37 \) |
\( 37 \) |
$2.21488$ |
$(2a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$26.36878876$ |
2.623792548 |
\( -\frac{456700}{37} a - \frac{2066539}{37} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 2 a + 11\) , \( a + 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2a+11\right){x}+a+4$ |
37.2-c1 |
37.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{101}) \) |
$2$ |
$[2, 0]$ |
37.2 |
\( 37 \) |
\( 37^{4} \) |
$2.21488$ |
$(2a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cn |
$1$ |
\( 2^{2} \) |
$0.239583287$ |
$21.25081451$ |
4.052858127 |
\( \frac{10136517844992}{1874161} a + \frac{45948988239872}{1874161} \) |
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( 76 a - 414\) , \( -659 a + 3639\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(76a-414\right){x}-659a+3639$ |
*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.