| 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 |
| 36.1-a1 |
36.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{4} \) |
$19.57963$ |
$(3/23a^3+7/23a^2-53/23a-128/23), (3/23a^3+7/23a^2-30/23a-59/23)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.285216073$ |
$204.1774933$ |
4.991545974 |
\( -\frac{65221}{36} a^{3} + \frac{65221}{24} a^{2} + \frac{2804503}{72} a - \frac{2698279}{36} \) |
\( \bigl[-\frac{4}{23} a^{3} + \frac{6}{23} a^{2} + \frac{63}{23} a - \frac{21}{23}\) , \( -\frac{1}{23} a^{3} - \frac{10}{23} a^{2} + \frac{33}{23} a + \frac{104}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} + \frac{10}{23} a - \frac{80}{23}\) , \( -\frac{20}{23} a^{3} - \frac{16}{23} a^{2} + \frac{315}{23} a + \frac{378}{23}\) , \( -\frac{30}{23} a^{3} + \frac{22}{23} a^{2} + \frac{346}{23} a + \frac{291}{23}\bigr] \) |
${y}^2+\left(-\frac{4}{23}a^{3}+\frac{6}{23}a^{2}+\frac{63}{23}a-\frac{21}{23}\right){x}{y}+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}+\frac{10}{23}a-\frac{80}{23}\right){y}={x}^{3}+\left(-\frac{1}{23}a^{3}-\frac{10}{23}a^{2}+\frac{33}{23}a+\frac{104}{23}\right){x}^{2}+\left(-\frac{20}{23}a^{3}-\frac{16}{23}a^{2}+\frac{315}{23}a+\frac{378}{23}\right){x}-\frac{30}{23}a^{3}+\frac{22}{23}a^{2}+\frac{346}{23}a+\frac{291}{23}$ |
| 36.1-a2 |
36.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{12} \) |
$19.57963$ |
$(3/23a^3+7/23a^2-53/23a-128/23), (3/23a^3+7/23a^2-30/23a-59/23)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.855648221$ |
$204.1774933$ |
4.991545974 |
\( \frac{275587}{16767} a^{3} - \frac{275587}{11178} a^{2} - \frac{11850241}{33534} a + \frac{9679561}{16767} \) |
\( \bigl[\frac{1}{23} a^{3} + \frac{10}{23} a^{2} - \frac{33}{23} a - \frac{58}{23}\) , \( \frac{1}{23} a^{3} + \frac{10}{23} a^{2} - \frac{33}{23} a - \frac{58}{23}\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{20}{23} a + \frac{1}{23}\) , \( -\frac{41}{23} a^{3} + \frac{257}{23} a^{2} - \frac{303}{23} a - \frac{37}{23}\) , \( -\frac{461}{23} a^{3} + \frac{2359}{23} a^{2} - \frac{542}{23} a - \frac{4772}{23}\bigr] \) |
${y}^2+\left(\frac{1}{23}a^{3}+\frac{10}{23}a^{2}-\frac{33}{23}a-\frac{58}{23}\right){x}{y}+\left(-\frac{2}{23}a^{3}+\frac{3}{23}a^{2}+\frac{20}{23}a+\frac{1}{23}\right){y}={x}^{3}+\left(\frac{1}{23}a^{3}+\frac{10}{23}a^{2}-\frac{33}{23}a-\frac{58}{23}\right){x}^{2}+\left(-\frac{41}{23}a^{3}+\frac{257}{23}a^{2}-\frac{303}{23}a-\frac{37}{23}\right){x}-\frac{461}{23}a^{3}+\frac{2359}{23}a^{2}-\frac{542}{23}a-\frac{4772}{23}$ |
| 36.1-a3 |
36.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{24} \) |
$19.57963$ |
$(3/23a^3+7/23a^2-53/23a-128/23), (3/23a^3+7/23a^2-30/23a-59/23)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1.711296443$ |
$204.1774933$ |
4.991545974 |
\( -\frac{62446099201}{12223143} a^{3} + \frac{62446099201}{8148762} a^{2} + \frac{2685182265643}{24446286} a + \frac{2502971947885}{24446286} \) |
\( \bigl[-\frac{4}{23} a^{3} + \frac{6}{23} a^{2} + \frac{63}{23} a - \frac{44}{23}\) , \( \frac{3}{23} a^{3} - \frac{16}{23} a^{2} - \frac{30}{23} a + \frac{148}{23}\) , \( \frac{1}{23} a^{3} + \frac{10}{23} a^{2} - \frac{33}{23} a - \frac{58}{23}\) , \( -\frac{582}{23} a^{3} + \frac{1655}{23} a^{2} + \frac{7453}{23} a - \frac{16775}{23}\) , \( -\frac{7718}{23} a^{3} + \frac{23629}{23} a^{2} + \frac{90083}{23} a - \frac{215446}{23}\bigr] \) |
${y}^2+\left(-\frac{4}{23}a^{3}+\frac{6}{23}a^{2}+\frac{63}{23}a-\frac{44}{23}\right){x}{y}+\left(\frac{1}{23}a^{3}+\frac{10}{23}a^{2}-\frac{33}{23}a-\frac{58}{23}\right){y}={x}^{3}+\left(\frac{3}{23}a^{3}-\frac{16}{23}a^{2}-\frac{30}{23}a+\frac{148}{23}\right){x}^{2}+\left(-\frac{582}{23}a^{3}+\frac{1655}{23}a^{2}+\frac{7453}{23}a-\frac{16775}{23}\right){x}-\frac{7718}{23}a^{3}+\frac{23629}{23}a^{2}+\frac{90083}{23}a-\frac{215446}{23}$ |
| 36.1-a4 |
36.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{8} \) |
$19.57963$ |
$(3/23a^3+7/23a^2-53/23a-128/23), (3/23a^3+7/23a^2-30/23a-59/23)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$0.570432147$ |
$204.1774933$ |
4.991545974 |
\( \frac{32734969937}{162} a^{3} - \frac{32734969937}{108} a^{2} - \frac{1407603707291}{324} a + \frac{2712170905513}{324} \) |
\( \bigl[-\frac{4}{23} a^{3} + \frac{6}{23} a^{2} + \frac{63}{23} a - \frac{21}{23}\) , \( -\frac{1}{23} a^{3} - \frac{10}{23} a^{2} + \frac{33}{23} a + \frac{104}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} + \frac{10}{23} a - \frac{80}{23}\) , \( \frac{10}{23} a^{3} - \frac{176}{23} a^{2} + \frac{475}{23} a + \frac{248}{23}\) , \( -\frac{288}{23} a^{3} + \frac{1398}{23} a^{2} + \frac{74}{23} a - \frac{3559}{23}\bigr] \) |
${y}^2+\left(-\frac{4}{23}a^{3}+\frac{6}{23}a^{2}+\frac{63}{23}a-\frac{21}{23}\right){x}{y}+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}+\frac{10}{23}a-\frac{80}{23}\right){y}={x}^{3}+\left(-\frac{1}{23}a^{3}-\frac{10}{23}a^{2}+\frac{33}{23}a+\frac{104}{23}\right){x}^{2}+\left(\frac{10}{23}a^{3}-\frac{176}{23}a^{2}+\frac{475}{23}a+\frac{248}{23}\right){x}-\frac{288}{23}a^{3}+\frac{1398}{23}a^{2}+\frac{74}{23}a-\frac{3559}{23}$ |
| 36.1-b1 |
36.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{4} \) |
$19.57963$ |
$(3/23a^3+7/23a^2-53/23a-128/23), (3/23a^3+7/23a^2-30/23a-59/23)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$175.5346369$ |
2.507637671 |
\( -\frac{10252380854909575}{18} a^{3} + \frac{8994388425170596}{3} a^{2} - \frac{11174401771805525}{9} a - \frac{91096381047574225}{18} \) |
\( \bigl[-\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( \frac{3}{23} a^{3} + \frac{7}{23} a^{2} - \frac{53}{23} a - \frac{82}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{80}{23}\) , \( -\frac{3359}{23} a^{3} + \frac{10202}{23} a^{2} + \frac{39892}{23} a - \frac{95162}{23}\) , \( \frac{79308}{23} a^{3} - \frac{240172}{23} a^{2} - \frac{942764}{23} a + \frac{2238473}{23}\bigr] \) |
${y}^2+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}-\frac{13}{23}a-\frac{103}{23}\right){x}{y}+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}-\frac{13}{23}a-\frac{80}{23}\right){y}={x}^{3}+\left(\frac{3}{23}a^{3}+\frac{7}{23}a^{2}-\frac{53}{23}a-\frac{82}{23}\right){x}^{2}+\left(-\frac{3359}{23}a^{3}+\frac{10202}{23}a^{2}+\frac{39892}{23}a-\frac{95162}{23}\right){x}+\frac{79308}{23}a^{3}-\frac{240172}{23}a^{2}-\frac{942764}{23}a+\frac{2238473}{23}$ |
| 36.1-b2 |
36.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{8} \) |
$19.57963$ |
$(3/23a^3+7/23a^2-53/23a-128/23), (3/23a^3+7/23a^2-30/23a-59/23)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$175.5346369$ |
2.507637671 |
\( \frac{9424370227}{3726} a^{3} - \frac{8266189870}{621} a^{2} + \frac{20508942091}{3726} a + \frac{83693153569}{3726} \) |
\( \bigl[-\frac{1}{23} a^{3} + \frac{13}{23} a^{2} + \frac{10}{23} a - \frac{80}{23}\) , \( -\frac{1}{23} a^{3} - \frac{10}{23} a^{2} + \frac{56}{23} a + \frac{104}{23}\) , \( \frac{1}{23} a^{3} + \frac{10}{23} a^{2} - \frac{33}{23} a - \frac{58}{23}\) , \( \frac{56}{23} a^{3} - \frac{153}{23} a^{2} - \frac{583}{23} a + \frac{1628}{23}\) , \( \frac{473}{23} a^{3} - \frac{1388}{23} a^{2} - \frac{5512}{23} a + \frac{13046}{23}\bigr] \) |
${y}^2+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}+\frac{10}{23}a-\frac{80}{23}\right){x}{y}+\left(\frac{1}{23}a^{3}+\frac{10}{23}a^{2}-\frac{33}{23}a-\frac{58}{23}\right){y}={x}^{3}+\left(-\frac{1}{23}a^{3}-\frac{10}{23}a^{2}+\frac{56}{23}a+\frac{104}{23}\right){x}^{2}+\left(\frac{56}{23}a^{3}-\frac{153}{23}a^{2}-\frac{583}{23}a+\frac{1628}{23}\right){x}+\frac{473}{23}a^{3}-\frac{1388}{23}a^{2}-\frac{5512}{23}a+\frac{13046}{23}$ |
| 36.1-c1 |
36.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{8} \) |
$19.57963$ |
$(3/23a^3+7/23a^2-53/23a-128/23), (3/23a^3+7/23a^2-30/23a-59/23)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$151.6101902$ |
2.165859860 |
\( -\frac{23214293789}{3726} a^{3} + \frac{23427341521}{1242} a^{2} + \frac{137987207246}{1863} a - \frac{655029174587}{3726} \) |
\( \bigl[-\frac{4}{23} a^{3} + \frac{6}{23} a^{2} + \frac{63}{23} a - \frac{21}{23}\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a + \frac{1}{23}\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a + \frac{1}{23}\) , \( -\frac{34}{23} a^{3} + \frac{120}{23} a^{2} + \frac{133}{23} a - \frac{144}{23}\) , \( \frac{153}{23} a^{3} - \frac{885}{23} a^{2} + \frac{540}{23} a + \frac{1660}{23}\bigr] \) |
${y}^2+\left(-\frac{4}{23}a^{3}+\frac{6}{23}a^{2}+\frac{63}{23}a-\frac{21}{23}\right){x}{y}+\left(-\frac{2}{23}a^{3}+\frac{3}{23}a^{2}+\frac{43}{23}a+\frac{1}{23}\right){y}={x}^{3}+\left(-\frac{2}{23}a^{3}+\frac{3}{23}a^{2}+\frac{43}{23}a+\frac{1}{23}\right){x}^{2}+\left(-\frac{34}{23}a^{3}+\frac{120}{23}a^{2}+\frac{133}{23}a-\frac{144}{23}\right){x}+\frac{153}{23}a^{3}-\frac{885}{23}a^{2}+\frac{540}{23}a+\frac{1660}{23}$ |
| 36.1-c2 |
36.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{4} \) |
$19.57963$ |
$(3/23a^3+7/23a^2-53/23a-128/23), (3/23a^3+7/23a^2-30/23a-59/23)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$151.6101902$ |
2.165859860 |
\( \frac{580944170959110571}{414} a^{3} - \frac{586311573205942589}{138} a^{2} - \frac{6906474861365038289}{414} a + \frac{8196505266269022536}{207} \) |
\( \bigl[-\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( \frac{5}{23} a^{3} + \frac{4}{23} a^{2} - \frac{96}{23} a - \frac{37}{23}\) , \( 1\) , \( \frac{1349}{23} a^{3} - \frac{7141}{23} a^{2} + \frac{3001}{23} a + \frac{12194}{23}\) , \( \frac{38522}{23} a^{3} - \frac{202798}{23} a^{2} + \frac{83980}{23} a + \frac{342322}{23}\bigr] \) |
${y}^2+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}-\frac{13}{23}a-\frac{103}{23}\right){x}{y}+{y}={x}^{3}+\left(\frac{5}{23}a^{3}+\frac{4}{23}a^{2}-\frac{96}{23}a-\frac{37}{23}\right){x}^{2}+\left(\frac{1349}{23}a^{3}-\frac{7141}{23}a^{2}+\frac{3001}{23}a+\frac{12194}{23}\right){x}+\frac{38522}{23}a^{3}-\frac{202798}{23}a^{2}+\frac{83980}{23}a+\frac{342322}{23}$ |
| 36.1-d1 |
36.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{8} \) |
$19.57963$ |
$(3/23a^3+7/23a^2-53/23a-128/23), (3/23a^3+7/23a^2-30/23a-59/23)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$175.5346369$ |
2.507637671 |
\( -\frac{23214293789}{3726} a^{3} + \frac{23427341521}{1242} a^{2} + \frac{137987207246}{1863} a - \frac{655029174587}{3726} \) |
\( \bigl[\frac{1}{23} a^{3} + \frac{10}{23} a^{2} - \frac{33}{23} a - \frac{58}{23}\) , \( -a - 1\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{20}{23} a + \frac{1}{23}\) , \( -\frac{31}{23} a^{3} + \frac{150}{23} a^{2} - \frac{12}{23} a - \frac{272}{23}\) , \( -\frac{228}{23} a^{3} + \frac{1216}{23} a^{2} - \frac{503}{23} a - \frac{2094}{23}\bigr] \) |
${y}^2+\left(\frac{1}{23}a^{3}+\frac{10}{23}a^{2}-\frac{33}{23}a-\frac{58}{23}\right){x}{y}+\left(-\frac{2}{23}a^{3}+\frac{3}{23}a^{2}+\frac{20}{23}a+\frac{1}{23}\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-\frac{31}{23}a^{3}+\frac{150}{23}a^{2}-\frac{12}{23}a-\frac{272}{23}\right){x}-\frac{228}{23}a^{3}+\frac{1216}{23}a^{2}-\frac{503}{23}a-\frac{2094}{23}$ |
| 36.1-d2 |
36.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{4} \) |
$19.57963$ |
$(3/23a^3+7/23a^2-53/23a-128/23), (3/23a^3+7/23a^2-30/23a-59/23)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$175.5346369$ |
2.507637671 |
\( \frac{580944170959110571}{414} a^{3} - \frac{586311573205942589}{138} a^{2} - \frac{6906474861365038289}{414} a + \frac{8196505266269022536}{207} \) |
\( \bigl[-\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -\frac{1}{23} a^{3} - \frac{10}{23} a^{2} + \frac{10}{23} a + \frac{81}{23}\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{125}{23}\) , \( \frac{1365}{23} a^{3} - \frac{7211}{23} a^{2} + \frac{2979}{23} a + \frac{12255}{23}\) , \( -\frac{32196}{23} a^{3} + \frac{169504}{23} a^{2} - \frac{70144}{23} a - \frac{286283}{23}\bigr] \) |
${y}^2+\left(-\frac{3}{23}a^{3}+\frac{16}{23}a^{2}+\frac{30}{23}a-\frac{102}{23}\right){x}{y}+\left(-\frac{3}{23}a^{3}+\frac{16}{23}a^{2}+\frac{30}{23}a-\frac{125}{23}\right){y}={x}^{3}+\left(-\frac{1}{23}a^{3}-\frac{10}{23}a^{2}+\frac{10}{23}a+\frac{81}{23}\right){x}^{2}+\left(\frac{1365}{23}a^{3}-\frac{7211}{23}a^{2}+\frac{2979}{23}a+\frac{12255}{23}\right){x}-\frac{32196}{23}a^{3}+\frac{169504}{23}a^{2}-\frac{70144}{23}a-\frac{286283}{23}$ |
| 36.1-e1 |
36.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{4} \) |
$19.57963$ |
$(3/23a^3+7/23a^2-53/23a-128/23), (3/23a^3+7/23a^2-30/23a-59/23)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$151.6101902$ |
2.165859860 |
\( -\frac{10252380854909575}{18} a^{3} + \frac{8994388425170596}{3} a^{2} - \frac{11174401771805525}{9} a - \frac{91096381047574225}{18} \) |
\( \bigl[-\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -\frac{5}{23} a^{3} - \frac{4}{23} a^{2} + \frac{96}{23} a + \frac{60}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{80}{23}\) , \( -\frac{3369}{23} a^{3} + \frac{10171}{23} a^{2} + \frac{40130}{23} a - \frac{94812}{23}\) , \( -\frac{86034}{23} a^{3} + \frac{260542}{23} a^{2} + \frac{1022743}{23} a - \frac{2428425}{23}\bigr] \) |
${y}^2+\left(-\frac{3}{23}a^{3}+\frac{16}{23}a^{2}+\frac{30}{23}a-\frac{102}{23}\right){x}{y}+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}-\frac{13}{23}a-\frac{80}{23}\right){y}={x}^{3}+\left(-\frac{5}{23}a^{3}-\frac{4}{23}a^{2}+\frac{96}{23}a+\frac{60}{23}\right){x}^{2}+\left(-\frac{3369}{23}a^{3}+\frac{10171}{23}a^{2}+\frac{40130}{23}a-\frac{94812}{23}\right){x}-\frac{86034}{23}a^{3}+\frac{260542}{23}a^{2}+\frac{1022743}{23}a-\frac{2428425}{23}$ |
| 36.1-e2 |
36.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{8} \) |
$19.57963$ |
$(3/23a^3+7/23a^2-53/23a-128/23), (3/23a^3+7/23a^2-30/23a-59/23)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$151.6101902$ |
2.165859860 |
\( \frac{9424370227}{3726} a^{3} - \frac{8266189870}{621} a^{2} + \frac{20508942091}{3726} a + \frac{83693153569}{3726} \) |
\( \bigl[-\frac{4}{23} a^{3} + \frac{6}{23} a^{2} + \frac{63}{23} a - \frac{44}{23}\) , \( \frac{3}{23} a^{3} + \frac{7}{23} a^{2} - \frac{76}{23} a - \frac{36}{23}\) , \( \frac{1}{23} a^{3} + \frac{10}{23} a^{2} - \frac{33}{23} a - \frac{81}{23}\) , \( \frac{48}{23} a^{3} - \frac{141}{23} a^{2} - \frac{664}{23} a + \frac{1655}{23}\) , \( -\frac{267}{23} a^{3} + \frac{826}{23} a^{2} + \frac{3107}{23} a - \frac{7583}{23}\bigr] \) |
${y}^2+\left(-\frac{4}{23}a^{3}+\frac{6}{23}a^{2}+\frac{63}{23}a-\frac{44}{23}\right){x}{y}+\left(\frac{1}{23}a^{3}+\frac{10}{23}a^{2}-\frac{33}{23}a-\frac{81}{23}\right){y}={x}^{3}+\left(\frac{3}{23}a^{3}+\frac{7}{23}a^{2}-\frac{76}{23}a-\frac{36}{23}\right){x}^{2}+\left(\frac{48}{23}a^{3}-\frac{141}{23}a^{2}-\frac{664}{23}a+\frac{1655}{23}\right){x}-\frac{267}{23}a^{3}+\frac{826}{23}a^{2}+\frac{3107}{23}a-\frac{7583}{23}$ |
| 36.1-f1 |
36.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{4} \) |
$19.57963$ |
$(3/23a^3+7/23a^2-53/23a-128/23), (3/23a^3+7/23a^2-30/23a-59/23)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.285216073$ |
$204.1774933$ |
4.991545974 |
\( -\frac{65221}{36} a^{3} + \frac{65221}{24} a^{2} + \frac{2804503}{72} a - \frac{2698279}{36} \) |
\( \bigl[\frac{1}{23} a^{3} + \frac{10}{23} a^{2} - \frac{33}{23} a - \frac{58}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{126}{23}\) , \( 0\) , \( -\frac{6}{23} a^{3} + \frac{32}{23} a^{2} - \frac{32}{23} a + \frac{26}{23}\) , \( 0\bigr] \) |
${y}^2+\left(\frac{1}{23}a^{3}+\frac{10}{23}a^{2}-\frac{33}{23}a-\frac{58}{23}\right){x}{y}={x}^{3}+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}-\frac{13}{23}a-\frac{126}{23}\right){x}^{2}+\left(-\frac{6}{23}a^{3}+\frac{32}{23}a^{2}-\frac{32}{23}a+\frac{26}{23}\right){x}$ |
| 36.1-f2 |
36.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{12} \) |
$19.57963$ |
$(3/23a^3+7/23a^2-53/23a-128/23), (3/23a^3+7/23a^2-30/23a-59/23)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.855648221$ |
$204.1774933$ |
4.991545974 |
\( \frac{275587}{16767} a^{3} - \frac{275587}{11178} a^{2} - \frac{11850241}{33534} a + \frac{9679561}{16767} \) |
\( \bigl[-\frac{4}{23} a^{3} + \frac{6}{23} a^{2} + \frac{63}{23} a - \frac{21}{23}\) , \( -\frac{3}{23} a^{3} - \frac{7}{23} a^{2} + \frac{53}{23} a + \frac{36}{23}\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a + \frac{1}{23}\) , \( -\frac{42}{23} a^{3} + \frac{201}{23} a^{2} - \frac{132}{23} a + \frac{159}{23}\) , \( \frac{319}{23} a^{3} - \frac{1663}{23} a^{2} + \frac{352}{23} a + \frac{3900}{23}\bigr] \) |
${y}^2+\left(-\frac{4}{23}a^{3}+\frac{6}{23}a^{2}+\frac{63}{23}a-\frac{21}{23}\right){x}{y}+\left(-\frac{2}{23}a^{3}+\frac{3}{23}a^{2}+\frac{43}{23}a+\frac{1}{23}\right){y}={x}^{3}+\left(-\frac{3}{23}a^{3}-\frac{7}{23}a^{2}+\frac{53}{23}a+\frac{36}{23}\right){x}^{2}+\left(-\frac{42}{23}a^{3}+\frac{201}{23}a^{2}-\frac{132}{23}a+\frac{159}{23}\right){x}+\frac{319}{23}a^{3}-\frac{1663}{23}a^{2}+\frac{352}{23}a+\frac{3900}{23}$ |
| 36.1-f3 |
36.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{24} \) |
$19.57963$ |
$(3/23a^3+7/23a^2-53/23a-128/23), (3/23a^3+7/23a^2-30/23a-59/23)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1.711296443$ |
$204.1774933$ |
4.991545974 |
\( -\frac{62446099201}{12223143} a^{3} + \frac{62446099201}{8148762} a^{2} + \frac{2685182265643}{24446286} a + \frac{2502971947885}{24446286} \) |
\( \bigl[-\frac{1}{23} a^{3} + \frac{13}{23} a^{2} + \frac{10}{23} a - \frac{80}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} + \frac{10}{23} a - \frac{80}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} + \frac{10}{23} a - \frac{80}{23}\) , \( -\frac{594}{23} a^{3} + \frac{1765}{23} a^{2} + \frac{7642}{23} a - \frac{17804}{23}\) , \( \frac{5515}{23} a^{3} - \frac{17001}{23} a^{2} - \frac{63039}{23} a + \frac{151745}{23}\bigr] \) |
${y}^2+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}+\frac{10}{23}a-\frac{80}{23}\right){x}{y}+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}+\frac{10}{23}a-\frac{80}{23}\right){y}={x}^{3}+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}+\frac{10}{23}a-\frac{80}{23}\right){x}^{2}+\left(-\frac{594}{23}a^{3}+\frac{1765}{23}a^{2}+\frac{7642}{23}a-\frac{17804}{23}\right){x}+\frac{5515}{23}a^{3}-\frac{17001}{23}a^{2}-\frac{63039}{23}a+\frac{151745}{23}$ |
| 36.1-f4 |
36.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{5}, \sqrt{7})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{8} \) |
$19.57963$ |
$(3/23a^3+7/23a^2-53/23a-128/23), (3/23a^3+7/23a^2-30/23a-59/23)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$0.570432147$ |
$204.1774933$ |
4.991545974 |
\( \frac{32734969937}{162} a^{3} - \frac{32734969937}{108} a^{2} - \frac{1407603707291}{324} a + \frac{2712170905513}{324} \) |
\( \bigl[\frac{1}{23} a^{3} + \frac{10}{23} a^{2} - \frac{33}{23} a - \frac{58}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{126}{23}\) , \( 0\) , \( \frac{24}{23} a^{3} - \frac{128}{23} a^{2} + \frac{128}{23} a - \frac{104}{23}\) , \( 16 a^{3} - 82 a^{2} + 14 a + 190\bigr] \) |
${y}^2+\left(\frac{1}{23}a^{3}+\frac{10}{23}a^{2}-\frac{33}{23}a-\frac{58}{23}\right){x}{y}={x}^{3}+\left(-\frac{1}{23}a^{3}+\frac{13}{23}a^{2}-\frac{13}{23}a-\frac{126}{23}\right){x}^{2}+\left(\frac{24}{23}a^{3}-\frac{128}{23}a^{2}+\frac{128}{23}a-\frac{104}{23}\right){x}+16a^{3}-82a^{2}+14a+190$ |
*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.
