| 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 |
| 3.1-a1 |
3.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
3.1 |
\( 3 \) |
\( 3^{6} \) |
$1.82569$ |
$(4a-33)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.098151491$ |
$12.39339744$ |
0.940286078 |
\( -\frac{69080}{729} a + \frac{561383}{729} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -4341374076373 a + 35868811829901\) , \( -5900369621288497233 a + 48749369197338362502\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-4341374076373a+35868811829901\right){x}-5900369621288497233a+48749369197338362502$ |
| 3.2-a1 |
3.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
3.2 |
\( 3 \) |
\( 3^{6} \) |
$1.82569$ |
$(-4a-29)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.098151491$ |
$12.39339744$ |
0.940286078 |
\( \frac{69080}{729} a + \frac{164101}{243} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 4341374076373 a + 31527437753528\) , \( 5900369621288497233 a + 42848999576049865269\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(4341374076373a+31527437753528\right){x}+5900369621288497233a+42848999576049865269$ |
| 5.1-a1 |
5.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{3} \) |
$2.07439$ |
$(42a+305)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.865552435$ |
$16.37214716$ |
5.476987520 |
\( -\frac{23547}{125} a + \frac{171167}{125} \) |
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( 46 a - 265\) , \( 375 a - 2750\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(46a-265\right){x}+375a-2750$ |
| 5.1-b1 |
5.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{11} \) |
$2.07439$ |
$(42a+305)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$16.46473870$ |
1.060587054 |
\( -\frac{214445085523}{48828125} a + \frac{1675549070103}{48828125} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 19204313 a - 158667475\) , \( -125942795752 a + 1040550380230\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(19204313a-158667475\right){x}-125942795752a+1040550380230$ |
| 5.1-c1 |
5.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( -5 \) |
$2.07439$ |
$(42a+305)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.920190073$ |
$5.818769000$ |
0.689811030 |
\( -\frac{9300750563}{5} a + \frac{76843613543}{5} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -4206 a - 30470\) , \( -11265179 a - 81808543\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-4206a-30470\right){x}-11265179a-81808543$ |
| 5.2-a1 |
5.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
5.2 |
\( 5 \) |
\( - 5^{3} \) |
$2.07439$ |
$(-42a+347)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.865552435$ |
$16.37214716$ |
5.476987520 |
\( \frac{23547}{125} a + \frac{29524}{25} \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -48 a - 218\) , \( -376 a - 2375\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-48a-218\right){x}-376a-2375$ |
| 5.2-b1 |
5.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
5.2 |
\( 5 \) |
\( - 5^{11} \) |
$2.07439$ |
$(-42a+347)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$16.46473870$ |
1.060587054 |
\( \frac{214445085523}{48828125} a + \frac{292220796916}{9765625} \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( -19204283 a - 139463161\) , \( 125784128277 a + 913455326568\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-19204283a-139463161\right){x}+125784128277a+913455326568$ |
| 5.2-c1 |
5.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
5.2 |
\( 5 \) |
\( -5 \) |
$2.07439$ |
$(-42a+347)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.920190073$ |
$5.818769000$ |
0.689811030 |
\( \frac{9300750563}{5} a + 13508572596 \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 4204 a - 34675\) , \( 11265178 a - 93073722\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(4204a-34675\right){x}+11265178a-93073722$ |
| 6.1-a1 |
6.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$2.17113$ |
$(-393a-2854), (4a-33)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$5.682388063$ |
1.464139170 |
\( \frac{41905}{144} a - \frac{1308589}{144} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 214554023999 a - 1772664087172\) , \( 161924419707872386 a - 1337833699421706392\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(214554023999a-1772664087172\right){x}+161924419707872386a-1337833699421706392$ |
| 6.2-a1 |
6.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{8} \cdot 3^{10} \) |
$2.17113$ |
$(-393a-2854), (-4a-29)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{4} \) |
$0.232102627$ |
$2.491583090$ |
1.192056634 |
\( -\frac{93971271127}{15116544} a - \frac{227470174439}{5038848} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( -9764 a - 70887\) , \( -1503911 a - 10921559\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-9764a-70887\right){x}-1503911a-10921559$ |
| 6.3-a1 |
6.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
6.3 |
\( 2 \cdot 3 \) |
\( 2^{8} \cdot 3^{10} \) |
$2.17113$ |
$(393a-3247), (4a-33)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{4} \) |
$0.232102627$ |
$2.491583090$ |
1.192056634 |
\( \frac{93971271127}{15116544} a - \frac{194095448611}{3779136} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 9763 a - 80651\) , \( 1503910 a - 12425470\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(9763a-80651\right){x}+1503910a-12425470$ |
| 6.4-a1 |
6.4-a |
$1$ |
$1$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
6.4 |
\( 2 \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$2.17113$ |
$(393a-3247), (-4a-29)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$5.682388063$ |
1.464139170 |
\( -\frac{41905}{144} a - \frac{105557}{12} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -214554023999 a - 1558110063173\) , \( -161924419707872386 a - 1175909279713834006\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-214554023999a-1558110063173\right){x}-161924419707872386a-1175909279713834006$ |
| 8.1-a1 |
8.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{10} \) |
$2.33303$ |
$(-393a-2854), (393a-3247)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$17.50871291$ |
6.767012065 |
\( \frac{205095}{4} a - 424003 \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -155623712751 a - 1130152995312\) , \( -220529441662692987 a - 1601504068188817996\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-155623712751a-1130152995312\right){x}-220529441662692987a-1601504068188817996$ |
| 8.1-a2 |
8.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{14} \) |
$2.33303$ |
$(-393a-2854), (393a-3247)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$17.50871291$ |
6.767012065 |
\( \frac{615}{64} a + \frac{3917}{16} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -2879460343066 a + 23790352869908\) , \( -22072265823414034036 a + 182362988204191549224\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2879460343066a+23790352869908\right){x}-22072265823414034036a+182362988204191549224$ |
| 8.2-a1 |
8.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{10} \) |
$2.33303$ |
$(-393a-2854), (393a-3247)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$17.50871291$ |
6.767012065 |
\( -\frac{205095}{4} a - \frac{1490917}{4} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 155623712751 a - 1285776708064\) , \( 220529597286405738 a - 1822034795628219047\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(155623712751a-1285776708064\right){x}+220529597286405738a-1822034795628219047$ |
| 8.2-a2 |
8.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{14} \) |
$2.33303$ |
$(-393a-2854), (393a-3247)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$17.50871291$ |
6.767012065 |
\( -\frac{615}{64} a + \frac{16283}{64} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 2879460343066 a + 20910892526841\) , \( 22072268702874377102 a + 160290743291670042029\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(2879460343066a+20910892526841\right){x}+22072268702874377102a+160290743291670042029$ |
| 9.1-a1 |
9.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{14} \) |
$2.40275$ |
$(4a-33), (-4a-29)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 13 \) |
$0.104467467$ |
$10.69929866$ |
1.871979992 |
\( \frac{320811008}{1594323} a - \frac{479805440}{531441} \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 2 a + 27\) , \( -7 a - 43\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a+27\right){x}-7a-43$ |
| 9.1-b1 |
9.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{14} \) |
$2.40275$ |
$(4a-33), (-4a-29)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 13 \) |
$0.104467467$ |
$10.69929866$ |
1.871979992 |
\( -\frac{320811008}{1594323} a - \frac{1118605312}{1594323} \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 28\) , \( 6 a - 22\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+28{x}+6a-22$ |
| 9.2-a1 |
9.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{12} \) |
$2.40275$ |
$(-4a-29)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.621988785$ |
$13.36635588$ |
2.142136022 |
\( \frac{69080}{729} a + \frac{164101}{243} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 94292549638867 a - 779053281394174\) , \( -16166936807774180458175 a + 133572644057528458001109\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(94292549638867a-779053281394174\right){x}-16166936807774180458175a+133572644057528458001109$ |
| 9.3-a1 |
9.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{12} \) |
$2.40275$ |
$(4a-33)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.621988785$ |
$13.36635588$ |
2.142136022 |
\( -\frac{69080}{729} a + \frac{561383}{729} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -94292549638865 a - 684760731755309\) , \( 16166936902066730097041 a + 117405707934515009298242\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-94292549638865a-684760731755309\right){x}+16166936902066730097041a+117405707934515009298242$ |
| 10.1-a1 |
10.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5^{4} \) |
$2.46687$ |
$(-393a-2854), (42a+305)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$9$ |
\( 2^{2} \) |
$1$ |
$6.395669047$ |
3.707831337 |
\( -\frac{42065073657}{1250} a + \frac{347546978127}{1250} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 1525 a + 11078\) , \( -49633 a - 360449\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(1525a+11078\right){x}-49633a-360449$ |
| 10.1-a2 |
10.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{2} \cdot 5^{2} \) |
$2.46687$ |
$(-393a-2854), (42a+305)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$9$ |
\( 2^{2} \) |
$1$ |
$25.58267618$ |
3.707831337 |
\( -\frac{137781}{100} a + \frac{1360341}{100} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -440 a - 3192\) , \( -6468 a - 46981\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-440a-3192\right){x}-6468a-46981$ |
| 10.1-a3 |
10.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{4} \cdot 5 \) |
$2.46687$ |
$(-393a-2854), (42a+305)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$9$ |
\( 2^{2} \) |
$1$ |
$25.58267618$ |
3.707831337 |
\( \frac{311283}{80} a + \frac{2261817}{80} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -301847945 a + 2493894083\) , \( 83168335943804 a - 687144056166351\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-301847945a+2493894083\right){x}+83168335943804a-687144056166351$ |
| 10.1-a4 |
10.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5 \) |
$2.46687$ |
$(-393a-2854), (42a+305)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$9$ |
\( 1 \) |
$1$ |
$25.58267618$ |
3.707831337 |
\( \frac{1108809}{10} a + \frac{8086581}{10} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 5551343499175 a - 45865684889662\) , \( -13975489044229409233 a + 115466711216257393799\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(5551343499175a-45865684889662\right){x}-13975489044229409233a+115466711216257393799$ |
| 10.1-b1 |
10.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{4} \cdot 5 \) |
$2.46687$ |
$(-393a-2854), (42a+305)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$45.82091107$ |
0.655907633 |
\( -\frac{158427}{80} a - \frac{1009153}{80} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 1458645850 a - 12051459274\) , \( -12542104233495 a + 103623960706852\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(1458645850a-12051459274\right){x}-12542104233495a+103623960706852$ |
| 10.1-b2 |
10.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{12} \cdot 5^{3} \) |
$2.46687$ |
$(-393a-2854), (42a+305)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$5.091212341$ |
0.655907633 |
\( -\frac{2443224002163}{512000} a + \frac{20186919561143}{512000} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 74600274745 a - 616353985989\) , \( 30900206069901702 a - 255300201624744684\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(74600274745a-616353985989\right){x}+30900206069901702a-255300201624744684$ |
| 10.1-c1 |
10.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{20} \cdot 5^{5} \) |
$2.46687$ |
$(-393a-2854), (42a+305)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \cdot 5^{2} \) |
$0.004732542$ |
$12.01851031$ |
1.465536488 |
\( -\frac{42315024127923}{3276800000} a - \frac{282970654783497}{3276800000} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -3246049045286 a - 23573091703152\) , \( 8908795207432475757 a + 64696448962976666859\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(-3246049045286a-23573091703152\right){x}+8908795207432475757a+64696448962976666859$ |
| 10.4-a1 |
10.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
10.4 |
\( 2 \cdot 5 \) |
\( - 2^{4} \cdot 5 \) |
$2.46687$ |
$(393a-3247), (-42a+347)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$9$ |
\( 2^{2} \) |
$1$ |
$25.58267618$ |
3.707831337 |
\( -\frac{311283}{80} a + \frac{128655}{4} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 301847944 a + 2192046139\) , \( -83168335943805 a - 603975720222546\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(301847944a+2192046139\right){x}-83168335943805a-603975720222546$ |
| 10.4-a2 |
10.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
10.4 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5 \) |
$2.46687$ |
$(393a-3247), (-42a+347)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$9$ |
\( 1 \) |
$1$ |
$25.58267618$ |
3.707831337 |
\( -\frac{1108809}{10} a + 919539 \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -5551343499176 a - 40314341390486\) , \( 13975489044229409232 a + 101491222172027984567\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-5551343499176a-40314341390486\right){x}+13975489044229409232a+101491222172027984567$ |
| 10.4-a3 |
10.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
10.4 |
\( 2 \cdot 5 \) |
\( 2^{2} \cdot 5^{2} \) |
$2.46687$ |
$(393a-3247), (-42a+347)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$9$ |
\( 2^{2} \) |
$1$ |
$25.58267618$ |
3.707831337 |
\( \frac{137781}{100} a + \frac{61128}{5} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 439 a - 3631\) , \( 6467 a - 53448\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(439a-3631\right){x}+6467a-53448$ |
| 10.4-a4 |
10.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
10.4 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5^{4} \) |
$2.46687$ |
$(393a-3247), (-42a+347)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$9$ |
\( 2^{2} \) |
$1$ |
$6.395669047$ |
3.707831337 |
\( \frac{42065073657}{1250} a + \frac{30548190447}{125} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -1526 a + 12604\) , \( 49632 a - 410081\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-1526a+12604\right){x}+49632a-410081$ |
| 10.4-b1 |
10.4-b |
$2$ |
$3$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
10.4 |
\( 2 \cdot 5 \) |
\( - 2^{4} \cdot 5 \) |
$2.46687$ |
$(393a-3247), (-42a+347)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$45.82091107$ |
0.655907633 |
\( \frac{158427}{80} a - \frac{58379}{4} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -1458645851 a - 10592813423\) , \( 12542104233495 a + 91081856473357\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1458645851a-10592813423\right){x}+12542104233495a+91081856473357$ |
| 10.4-b2 |
10.4-b |
$2$ |
$3$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
10.4 |
\( 2 \cdot 5 \) |
\( - 2^{12} \cdot 5^{3} \) |
$2.46687$ |
$(393a-3247), (-42a+347)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$5.091212341$ |
0.655907633 |
\( \frac{2443224002163}{512000} a + \frac{887184777949}{25600} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -74600274746 a - 541753711243\) , \( -30900206069901702 a - 224399995554842982\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-74600274746a-541753711243\right){x}-30900206069901702a-224399995554842982$ |
| 10.4-c1 |
10.4-c |
$1$ |
$1$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
10.4 |
\( 2 \cdot 5 \) |
\( - 2^{20} \cdot 5^{5} \) |
$2.46687$ |
$(393a-3247), (-42a+347)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \cdot 5^{2} \) |
$0.004732542$ |
$12.01851031$ |
1.465536488 |
\( \frac{42315024127923}{3276800000} a - \frac{16264283945571}{163840000} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( 3246049045285 a - 26819140748437\) , \( -8908795207432475757 a + 73605244170409142616\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(3246049045285a-26819140748437\right){x}-8908795207432475757a+73605244170409142616$ |
| 12.1-a1 |
12.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{12} \cdot 3^{6} \) |
$2.58192$ |
$(-393a-2854), (393a-3247), (4a-33)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.608677432$ |
$8.332565382$ |
1.742433196 |
\( -\frac{1155105490175}{186624} a - \frac{8388519071677}{186624} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -109875012 a - 797921935\) , \( 1746635994940 a + 12684223160642\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-109875012a-797921935\right){x}+1746635994940a+12684223160642$ |
| 12.1-a2 |
12.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{36} \cdot 3^{2} \) |
$2.58192$ |
$(-393a-2854), (393a-3247), (4a-33)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{3} \) |
$1.826032296$ |
$0.925840598$ |
1.742433196 |
\( \frac{3957464102312545}{150994944} a - \frac{32696921636360077}{150994944} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -53425492 a - 387980590\) , \( 3532329867892 a + 25652088043040\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-53425492a-387980590\right){x}+3532329867892a+25652088043040$ |
| 12.1-b1 |
12.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{7} \cdot 3^{2} \) |
$2.58192$ |
$(-393a-2854), (393a-3247), (4a-33)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$24.29184226$ |
4.694325348 |
\( \frac{41975}{576} a + \frac{224053}{576} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 2377802 a + 17267821\) , \( 4802429220 a + 34875660461\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2377802a+17267821\right){x}+4802429220a+34875660461$ |
| 12.1-b2 |
12.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{5} \cdot 3 \) |
$2.58192$ |
$(-393a-2854), (393a-3247), (4a-33)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$48.58368452$ |
4.694325348 |
\( -\frac{588307}{24} a + \frac{4929949}{24} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 3130349612 a - 25863221899\) , \( -265015387133466 a + 2189580277095197\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3130349612a-25863221899\right){x}-265015387133466a+2189580277095197$ |
| 12.1-c1 |
12.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{12} \cdot 3^{4} \) |
$2.58192$ |
$(-393a-2854), (393a-3247), (4a-33)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$0.075357670$ |
$15.86169634$ |
2.463874348 |
\( \frac{727753}{82944} a + \frac{4983083}{82944} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 8295391 a - 68537219\) , \( -790296498553 a + 6529498701981\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(8295391a-68537219\right){x}-790296498553a+6529498701981$ |
| 12.1-d1 |
12.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{7} \cdot 3^{10} \) |
$2.58192$ |
$(-393a-2854), (393a-3247), (4a-33)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$4.963368593$ |
1.598593384 |
\( -\frac{257391599}{1889568} a + \frac{348234941}{472392} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -282618 a + 2335036\) , \( 6240488 a - 51559476\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-282618a+2335036\right){x}+6240488a-51559476$ |
| 12.1-d2 |
12.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{11} \cdot 3^{5} \) |
$2.58192$ |
$(-393a-2854), (393a-3247), (4a-33)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$9.926737187$ |
1.598593384 |
\( \frac{14371175323}{248832} a + \frac{26198777993}{62208} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -202484638 a - 1470461109\) , \( -4364842603830 a - 31697868249837\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-202484638a-1470461109\right){x}-4364842603830a-31697868249837$ |
| 12.1-e1 |
12.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{24} \cdot 3^{2} \) |
$2.58192$ |
$(-393a-2854), (393a-3247), (4a-33)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{8} \) |
$0.025558483$ |
$9.025776102$ |
7.608185288 |
\( -\frac{68410025}{589824} a + \frac{81099869}{147456} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -23534319539 a - 170908284171\) , \( 12524406515554099 a + 90953334099442509\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-23534319539a-170908284171\right){x}+12524406515554099a+90953334099442509$ |
| 12.1-f1 |
12.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{11} \cdot 3^{7} \) |
$2.58192$ |
$(-393a-2854), (393a-3247), (4a-33)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$1$ |
$5.098398894$ |
9.852502296 |
\( \frac{2362709155}{139968} a - \frac{19856982493}{139968} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -241 a - 1735\) , \( 6707 a + 48689\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-241a-1735\right){x}+6707a+48689$ |
| 12.1-g1 |
12.1-g |
$1$ |
$1$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{15} \cdot 3^{11} \) |
$2.58192$ |
$(-393a-2854), (393a-3247), (4a-33)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$2.463358741$ |
$3.899443040$ |
2.475037105 |
\( -\frac{11309842751}{2902376448} a - \frac{31387382893}{2902376448} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( -8265 a - 60017\) , \( -7314912 a - 53121543\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-8265a-60017\right){x}-7314912a-53121543$ |
| 12.1-h1 |
12.1-h |
$1$ |
$1$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{24} \cdot 3^{4} \) |
$2.58192$ |
$(-393a-2854), (393a-3247), (4a-33)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \cdot 11 \) |
$1$ |
$0.816570576$ |
4.628794258 |
\( \frac{77681117635303}{339738624} a - \frac{163235940746803}{84934656} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 18606575967166652 a - 153729155890347509\) , \( 3849964978395963953436488 a - 31808746938748928238787861\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(18606575967166652a-153729155890347509\right){x}+3849964978395963953436488a-31808746938748928238787861$ |
| 12.1-i1 |
12.1-i |
$2$ |
$3$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{27} \cdot 3 \) |
$2.58192$ |
$(-393a-2854), (393a-3247), (4a-33)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$7.442553841$ |
$1.573925366$ |
3.018266545 |
\( -\frac{440836505995}{6291456} a - \frac{800335350617}{1572864} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -18 a + 148\) , \( 1670 a - 13798\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-18a+148\right){x}+1670a-13798$ |
| 12.1-i2 |
12.1-i |
$2$ |
$3$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{9} \cdot 3^{3} \) |
$2.58192$ |
$(-393a-2854), (393a-3247), (4a-33)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$2.480851280$ |
$14.16532829$ |
3.018266545 |
\( \frac{28445}{3456} a + \frac{44503}{864} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 2 a - 17\) , \( -62 a + 512\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(2a-17\right){x}-62a+512$ |
| 12.2-a1 |
12.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{36} \cdot 3^{2} \) |
$2.58192$ |
$(-393a-2854), (393a-3247), (-4a-29)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{3} \) |
$1.826032296$ |
$0.925840598$ |
1.742433196 |
\( -\frac{3957464102312545}{150994944} a - \frac{2394954794503961}{12582912} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 53425492 a - 441406082\) , \( -3532329867892 a + 29184417910932\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(53425492a-441406082\right){x}-3532329867892a+29184417910932$ |
| 12.2-a2 |
12.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{12} \cdot 3^{6} \) |
$2.58192$ |
$(-393a-2854), (393a-3247), (-4a-29)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.608677432$ |
$8.332565382$ |
1.742433196 |
\( \frac{1155105490175}{186624} a - \frac{795302046821}{15552} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 109875012 a - 907796947\) , \( -1746635994940 a + 14430859155582\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(109875012a-907796947\right){x}-1746635994940a+14430859155582$ |
| 12.2-b1 |
12.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{241}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{7} \cdot 3^{2} \) |
$2.58192$ |
$(-393a-2854), (393a-3247), (-4a-29)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$24.29184226$ |
4.694325348 |
\( -\frac{41975}{576} a + \frac{22169}{48} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -2377801 a + 19645622\) , \( -4800051420 a + 39658444059\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2377801a+19645622\right){x}-4800051420a+39658444059$ |
*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.
