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 |
4.1-a1 |
4.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{6} \) |
$2.23576$ |
$(-3a+28), (-3a-25)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3, 5$ |
3Ns, 5B.1.2 |
$25$ |
\( 3^{2} \) |
$1$ |
$0.088720921$ |
1.128330672 |
\( -\frac{7762509612594001}{8} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 15009962115660926840 a - 140281650063862322521\) , \( 94146372725548684750220817720 a - 879882867904615924996270935249\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(15009962115660926840a-140281650063862322521\right){x}+94146372725548684750220817720a-879882867904615924996270935249$ |
4.1-a2 |
4.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{30} \) |
$2.23576$ |
$(-3a+28), (-3a-25)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$3, 5$ |
3Ns, 5B.1.1 |
$1$ |
\( 3^{2} \cdot 5^{2} \) |
$1$ |
$2.218023042$ |
1.128330672 |
\( -\frac{13997521}{32768} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -18269609092248440 a - 152476385450157001\) , \( -8979833730671276656374200 a - 74944821330473578057889289\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-18269609092248440a-152476385450157001\right){x}-8979833730671276656374200a-74944821330473578057889289$ |
6.1-a1 |
6.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{7} \cdot 3^{8} \) |
$2.47428$ |
$(-3a+28), (26a-243)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \cdot 7 \) |
$1$ |
$2.942073802$ |
9.312567232 |
\( -\frac{17885764951}{839808} a - \frac{149237511971}{839808} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -983519970721626 a - 8208362280575830\) , \( -50049833920803194060535 a - 417711059393309230996834\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-983519970721626a-8208362280575830\right){x}-50049833920803194060535a-417711059393309230996834$ |
6.1-b1 |
6.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{2} \cdot 3^{2} \) |
$2.47428$ |
$(-3a+28), (26a-243)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$53.18837060$ |
3.006384456 |
\( -\frac{61860289}{36} a + \frac{576972199}{36} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( -37407 a - 312191\) , \( 12017370 a + 100295787\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-37407a-312191\right){x}+12017370a+100295787$ |
6.1-b2 |
6.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2 \cdot 3 \) |
$2.47428$ |
$(-3a+28), (26a-243)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$53.18837060$ |
3.006384456 |
\( \frac{373461059}{6} a + \frac{3116840965}{6} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( -6\) , \( -a - 12\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-6{x}-a-12$ |
6.2-a1 |
6.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{3} \cdot 3^{11} \) |
$2.47428$ |
$(-3a+28), (26a+217)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$8.475854132$ |
0.479083600 |
\( -\frac{231358159735}{1417176} a + \frac{719533421119}{472392} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 13826 a - 129175\) , \( -2536295 a + 23704109\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(13826a-129175\right){x}-2536295a+23704109$ |
6.2-b1 |
6.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{3} \cdot 3^{13} \) |
$2.47428$ |
$(-3a+28), (26a+217)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 13 \) |
$0.090717984$ |
$18.77386760$ |
2.502927816 |
\( -\frac{155033667913}{12754584} a - \frac{445409678207}{4251528} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( 5143583738317716 a - 48071434724010025\) , \( -736452672543977709228199 a + 6882815246456831671895385\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(5143583738317716a-48071434724010025\right){x}-736452672543977709228199a+6882815246456831671895385$ |
6.2-c1 |
6.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{3} \cdot 3 \) |
$2.47428$ |
$(-3a+28), (26a+217)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.902412291$ |
$7.363990971$ |
2.253706363 |
\( \frac{3966815}{24} a - \frac{12344039}{8} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 169647785224059 a - 1585511745967624\) , \( 3578367908069622245487 a - 33443079390308932843957\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(169647785224059a-1585511745967624\right){x}+3578367908069622245487a-33443079390308932843957$ |
6.2-d1 |
6.2-d |
$2$ |
$5$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{15} \cdot 3^{5} \) |
$2.47428$ |
$(-3a+28), (26a+217)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 3 \cdot 5^{2} \) |
$1$ |
$10.21126003$ |
1.731523625 |
\( -\frac{21389534721775}{7962624} a - \frac{59180172859913}{2654208} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( -57339913824558 a - 478553359179337\) , \( 702954879944245916135 a + 5866793245944407169255\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-57339913824558a-478553359179337\right){x}+702954879944245916135a+5866793245944407169255$ |
6.2-d2 |
6.2-d |
$2$ |
$5$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{3} \cdot 3 \) |
$2.47428$ |
$(-3a+28), (26a+217)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 3 \) |
$1$ |
$0.408450401$ |
1.731523625 |
\( -\frac{36117318693345370853625055}{24} a + \frac{112516319120675616097055847}{8} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( 247523046194992 a + 2065803335411323\) , \( 2986500215715667636925 a + 24925041129185797501155\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(247523046194992a+2065803335411323\right){x}+2986500215715667636925a+24925041129185797501155$ |
6.2-e1 |
6.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{12} \cdot 3^{2} \) |
$2.47428$ |
$(-3a+28), (26a+217)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$23.50060612$ |
1.328332794 |
\( -\frac{3941125}{36864} a + \frac{11756125}{12288} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 2527377 a - 23620591\) , \( -1657479982 a + 15490647087\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2527377a-23620591\right){x}-1657479982a+15490647087$ |
6.2-e2 |
6.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{6} \cdot 3^{4} \) |
$2.47428$ |
$(-3a+28), (26a+217)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$23.50060612$ |
1.328332794 |
\( \frac{56708125}{5184} a + \frac{160548875}{1728} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -4814374006498 a + 44994672501664\) , \( -4548671843351188043 a + 42511445856253447310\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4814374006498a+44994672501664\right){x}-4548671843351188043a+42511445856253447310$ |
6.2-f1 |
6.2-f |
$1$ |
$1$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{3} \cdot 3^{3} \) |
$2.47428$ |
$(-3a+28), (26a+217)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$0.213608567$ |
$39.15311215$ |
2.836377535 |
\( -\frac{63007}{216} a + \frac{193447}{72} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 10 a + 157\) , \( 38 a + 429\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(10a+157\right){x}+38a+429$ |
6.3-a1 |
6.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
6.3 |
\( 2 \cdot 3 \) |
\( - 2^{3} \cdot 3^{11} \) |
$2.47428$ |
$(-3a-25), (26a-243)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$8.475854132$ |
0.479083600 |
\( \frac{231358159735}{1417176} a + \frac{963621051811}{708588} \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -13828 a - 115348\) , \( 2536294 a + 21167814\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-13828a-115348\right){x}+2536294a+21167814$ |
6.3-b1 |
6.3-b |
$1$ |
$1$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
6.3 |
\( 2 \cdot 3 \) |
\( 2^{3} \cdot 3^{13} \) |
$2.47428$ |
$(-3a-25), (26a-243)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 13 \) |
$0.090717984$ |
$18.77386760$ |
2.502927816 |
\( \frac{155033667913}{12754584} a - \frac{745631351267}{6377292} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( -5143583738317718 a - 42927850985692308\) , \( 736452672543977709228198 a + 6146362573912853962667186\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-5143583738317718a-42927850985692308\right){x}+736452672543977709228198a+6146362573912853962667186$ |
6.3-c1 |
6.3-c |
$1$ |
$1$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
6.3 |
\( 2 \cdot 3 \) |
\( 2^{3} \cdot 3 \) |
$2.47428$ |
$(-3a-25), (26a-243)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.902412291$ |
$7.363990971$ |
2.253706363 |
\( -\frac{3966815}{24} a - \frac{16532651}{12} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( -169647785224060 a - 1415863960743564\) , \( -3578367908069622245487 a - 29864711482239310598470\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-169647785224060a-1415863960743564\right){x}-3578367908069622245487a-29864711482239310598470$ |
6.3-d1 |
6.3-d |
$2$ |
$5$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
6.3 |
\( 2 \cdot 3 \) |
\( - 2^{15} \cdot 3^{5} \) |
$2.47428$ |
$(-3a-25), (26a-243)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 3 \cdot 5^{2} \) |
$1$ |
$10.21126003$ |
1.731523625 |
\( \frac{21389534721775}{7962624} a - \frac{99465026650757}{3981312} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( 57339913824557 a - 535893273003894\) , \( -702954879944245916135 a + 6569748125888653085390\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(57339913824557a-535893273003894\right){x}-702954879944245916135a+6569748125888653085390$ |
6.3-d2 |
6.3-d |
$2$ |
$5$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
6.3 |
\( 2 \cdot 3 \) |
\( - 2^{3} \cdot 3 \) |
$2.47428$ |
$(-3a-25), (26a-243)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 3 \) |
$1$ |
$0.408450401$ |
1.731523625 |
\( \frac{36117318693345370853625055}{24} a + \frac{150715819334340738718771243}{12} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( -247523046194993 a + 2313326381606316\) , \( -2986500215715667636925 a + 27911541344901465138080\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-247523046194993a+2313326381606316\right){x}-2986500215715667636925a+27911541344901465138080$ |
6.3-e1 |
6.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
6.3 |
\( 2 \cdot 3 \) |
\( - 2^{6} \cdot 3^{4} \) |
$2.47428$ |
$(-3a-25), (26a-243)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$23.50060612$ |
1.328332794 |
\( -\frac{56708125}{5184} a + \frac{269177375}{2592} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 4814374006499 a + 40180298495166\) , \( 4548676657725194541 a + 37962814193200754433\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4814374006499a+40180298495166\right){x}+4548676657725194541a+37962814193200754433$ |
6.3-e2 |
6.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
6.3 |
\( 2 \cdot 3 \) |
\( - 2^{12} \cdot 3^{2} \) |
$2.47428$ |
$(-3a-25), (26a-243)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$23.50060612$ |
1.328332794 |
\( \frac{3941125}{36864} a + \frac{15663625}{18432} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -2527376 a - 21093214\) , \( 1654952605 a + 13812073891\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2527376a-21093214\right){x}+1654952605a+13812073891$ |
6.3-f1 |
6.3-f |
$1$ |
$1$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
6.3 |
\( 2 \cdot 3 \) |
\( - 2^{3} \cdot 3^{3} \) |
$2.47428$ |
$(-3a-25), (26a-243)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$0.213608567$ |
$39.15311215$ |
2.836377535 |
\( \frac{63007}{216} a + \frac{258667}{108} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -10 a + 89\) , \( -29 a + 300\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-10a+89\right){x}-29a+300$ |
6.4-a1 |
6.4-a |
$1$ |
$1$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
6.4 |
\( 2 \cdot 3 \) |
\( 2^{7} \cdot 3^{8} \) |
$2.47428$ |
$(-3a-25), (26a+217)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \cdot 7 \) |
$1$ |
$2.942073802$ |
9.312567232 |
\( \frac{17885764951}{839808} a - \frac{27853879487}{139968} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 983519970721626 a - 9191882251297456\) , \( 50049833920803194060535 a - 467760893314112425057369\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(983519970721626a-9191882251297456\right){x}+50049833920803194060535a-467760893314112425057369$ |
6.4-b1 |
6.4-b |
$2$ |
$2$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
6.4 |
\( 2 \cdot 3 \) |
\( - 2 \cdot 3 \) |
$2.47428$ |
$(-3a-25), (26a+217)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$53.18837060$ |
3.006384456 |
\( -\frac{373461059}{6} a + 581717004 \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -a - 6\) , \( -13\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-6\right){x}-13$ |
6.4-b2 |
6.4-b |
$2$ |
$2$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
6.4 |
\( 2 \cdot 3 \) |
\( - 2^{2} \cdot 3^{2} \) |
$2.47428$ |
$(-3a-25), (26a+217)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$53.18837060$ |
3.006384456 |
\( \frac{61860289}{36} a + \frac{85851985}{6} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( 37406 a - 349598\) , \( -12017371 a + 112313157\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(37406a-349598\right){x}-12017371a+112313157$ |
8.1-a1 |
8.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{15} \) |
$2.65878$ |
$(-3a+28), (-3a-25)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 1 \) |
$4.787043784$ |
$4.496135641$ |
2.433126178 |
\( -\frac{2188125793}{128} a - \frac{9252435989}{64} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 280745939363330 a - 2623824318751957\) , \( -7619068073651398925377 a + 71207071216092039025495\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(280745939363330a-2623824318751957\right){x}-7619068073651398925377a+71207071216092039025495$ |
8.1-a2 |
8.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{29} \) |
$2.65878$ |
$(-3a+28), (-3a-25)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 3 \) |
$1.595681261$ |
$4.496135641$ |
2.433126178 |
\( -\frac{27153241}{2097152} a - \frac{58274669}{1048576} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -789534123 a - 6589375007\) , \( -117958540081757 a - 984470534307289\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-789534123a-6589375007\right){x}-117958540081757a-984470534307289$ |
8.2-a1 |
8.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{15} \) |
$2.65878$ |
$(-3a+28), (-3a-25)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 1 \) |
$4.787043784$ |
$4.496135641$ |
2.433126178 |
\( \frac{2188125793}{128} a - \frac{20692997771}{128} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -280745939363332 a - 2343078379388627\) , \( 7619068073651398925376 a + 63588003142440640100118\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-280745939363332a-2343078379388627\right){x}+7619068073651398925376a+63588003142440640100118$ |
8.2-a2 |
8.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{29} \) |
$2.65878$ |
$(-3a+28), (-3a-25)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 3 \) |
$1.595681261$ |
$4.496135641$ |
2.433126178 |
\( \frac{27153241}{2097152} a - \frac{143702579}{2097152} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 789534121 a - 7378909130\) , \( 117958540081756 a - 1102429074389046\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(789534121a-7378909130\right){x}+117958540081756a-1102429074389046$ |
9.1-a1 |
9.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$2.73824$ |
$(26a-243), (26a+217)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1.240334716$ |
$12.47806199$ |
1.749620528 |
\( -\frac{4096}{27} a + \frac{4096}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 18\) , \( -3 a - 40\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+18{x}-3a-40$ |
9.1-b1 |
9.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{18} \) |
$2.73824$ |
$(26a-243), (26a+217)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.011005096$ |
0.283238754 |
\( -\frac{5071288251250}{43046721} a + \frac{47395768139125}{43046721} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 3290 a - 30748\) , \( 306756 a - 2866912\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(3290a-30748\right){x}+306756a-2866912$ |
9.1-b2 |
9.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{6} \) |
$2.73824$ |
$(26a-243), (26a+217)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$20.04402038$ |
0.283238754 |
\( -\frac{12244521250}{81} a + \frac{38145403375}{27} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 400128170 a + 3339430897\) , \( -7882451771672 a - 65786177939608\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(400128170a+3339430897\right){x}-7882451771672a-65786177939608$ |
9.1-b3 |
9.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{12} \) |
$2.73824$ |
$(26a-243), (26a+217)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$20.04402038$ |
0.283238754 |
\( -\frac{18590000}{6561} a + \frac{63018875}{2187} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -240 a - 2003\) , \( -3168 a - 26440\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-240a-2003\right){x}-3168a-26440$ |
9.1-b4 |
9.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{12} \) |
$2.73824$ |
$(26a-243), (26a+217)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$20.04402038$ |
0.283238754 |
\( \frac{18590000}{6561} a + \frac{170466625}{6561} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 240 a - 2243\) , \( 3168 a - 29608\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(240a-2243\right){x}+3168a-29608$ |
9.1-b5 |
9.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{18} \) |
$2.73824$ |
$(26a-243), (26a+217)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.011005096$ |
0.283238754 |
\( \frac{5071288251250}{43046721} a + \frac{14108159962625}{14348907} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -3290 a - 27458\) , \( -306756 a - 2560156\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-3290a-27458\right){x}-306756a-2560156$ |
9.1-b6 |
9.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{6} \) |
$2.73824$ |
$(26a-243), (26a+217)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$20.04402038$ |
0.283238754 |
\( \frac{12244521250}{81} a + \frac{102191688875}{81} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -400128170 a + 3739559067\) , \( 7882451771672 a - 73668629711280\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-400128170a+3739559067\right){x}+7882451771672a-73668629711280$ |
9.1-c1 |
9.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$2.73824$ |
$(26a-243), (26a+217)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1.240334716$ |
$12.47806199$ |
1.749620528 |
\( \frac{4096}{27} a + \frac{8192}{27} \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 2 a + 17\) , \( 2 a - 60\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a+17\right){x}+2a-60$ |
12.1-a1 |
12.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{17} \cdot 3^{2} \) |
$2.94243$ |
$(-3a+28), (-3a-25), (26a-243)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{2} \cdot 3 \cdot 5 \) |
$0.172320280$ |
$11.18429546$ |
13.07236307 |
\( -\frac{43728727}{294912} a - \frac{330648227}{294912} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -24495034424 a - 204433181443\) , \( 8066815305981780 a + 67324858114888553\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-24495034424a-204433181443\right){x}+8066815305981780a+67324858114888553$ |
12.1-a2 |
12.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{11} \cdot 3^{6} \) |
$2.94243$ |
$(-3a+28), (-3a-25), (26a-243)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
$0.057440093$ |
$11.18429546$ |
13.07236307 |
\( \frac{3517297}{46656} a + \frac{369554}{729} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 334039188424 a - 3121897855373\) , \( -1215978224562060848 a + 11364414544745209713\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(334039188424a-3121897855373\right){x}-1215978224562060848a+11364414544745209713$ |
12.1-b1 |
12.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{18} \cdot 3^{2} \) |
$2.94243$ |
$(-3a+28), (-3a-25), (26a-243)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$7.840987243$ |
4.431988027 |
\( -\frac{12725569}{9216} a + \frac{131569639}{9216} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( a + 25\) , \( 3 a + 15\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(a+25\right){x}+3a+15$ |
12.1-b2 |
12.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{21} \cdot 3 \) |
$2.94243$ |
$(-3a+28), (-3a-25), (26a-243)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \cdot 5 \) |
$1$ |
$7.840987243$ |
4.431988027 |
\( \frac{23892007}{196608} a + \frac{100778515}{98304} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -62105 a + 580458\) , \( 313660985 a - 2931445110\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-62105a+580458\right){x}+313660985a-2931445110$ |
12.1-c1 |
12.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{24} \cdot 3^{6} \) |
$2.94243$ |
$(-3a+28), (-3a-25), (26a-243)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{3} \cdot 3 \) |
$2.537823388$ |
$3.581631886$ |
6.165260345 |
\( -\frac{62850287725}{191102976} a - \frac{84359222897}{191102976} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( 410 a - 3836\) , \( -6559 a + 61278\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(410a-3836\right){x}-6559a+61278$ |
12.1-c2 |
12.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{21} \cdot 3^{3} \) |
$2.94243$ |
$(-3a+28), (-3a-25), (26a-243)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{2} \cdot 3 \) |
$5.075646776$ |
$3.581631886$ |
6.165260345 |
\( \frac{110648248535}{110592} a + \frac{464737746791}{55296} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( 1570952240 a - 14681967267\) , \( 99190866050446 a - 927028213235949\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(1570952240a-14681967267\right){x}+99190866050446a-927028213235949$ |
12.1-d1 |
12.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{18} \cdot 3^{5} \) |
$2.94243$ |
$(-3a+28), (-3a-25), (26a-243)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$7.704140248$ |
0.435463753 |
\( \frac{57406005709}{497664} a - \frac{268255589879}{248832} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -32863692 a - 274277151\) , \( -19140935357199 a - 159748389944415\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-32863692a-274277151\right){x}-19140935357199a-159748389944415$ |
12.1-e1 |
12.1-e |
$4$ |
$6$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{8} \cdot 3^{2} \) |
$2.94243$ |
$(-3a+28), (-3a-25), (26a-243)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.752914472$ |
$11.94453905$ |
2.033306563 |
\( -\frac{537107989}{576} a + \frac{2509875887}{288} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -3096086662677 a - 25839638986350\) , \( 102699774300421667218 a + 857122355098405338106\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-3096086662677a-25839638986350\right){x}+102699774300421667218a+857122355098405338106$ |
12.1-e2 |
12.1-e |
$4$ |
$6$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{8} \cdot 3^{6} \) |
$2.94243$ |
$(-3a+28), (-3a-25), (26a-243)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.250971490$ |
$11.94453905$ |
2.033306563 |
\( -\frac{5665741}{46656} a + \frac{53547295}{46656} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 645122677 a - 6029253967\) , \( -11876625521538 a + 110997790168544\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(645122677a-6029253967\right){x}-11876625521538a+110997790168544$ |
12.1-e3 |
12.1-e |
$4$ |
$6$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{7} \cdot 3^{3} \) |
$2.94243$ |
$(-3a+28), (-3a-25), (26a-243)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$0.501942981$ |
$23.88907810$ |
2.033306563 |
\( -\frac{37240843}{432} a + \frac{89698237}{108} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4275289848755191 a - 39956444251042022\) , \( -452314306357488759071486 a + 4227285635659043004554630\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(4275289848755191a-39956444251042022\right){x}-452314306357488759071486a+4227285635659043004554630$ |
12.1-e4 |
12.1-e |
$4$ |
$6$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{13} \cdot 3 \) |
$2.94243$ |
$(-3a+28), (-3a-25), (26a-243)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1.505828944$ |
$23.88907810$ |
2.033306563 |
\( \frac{84053687}{12288} a + \frac{380583395}{6144} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -18522321 a - 154585495\) , \( 128165281666 a + 1069655009582\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-18522321a-154585495\right){x}+128165281666a+1069655009582$ |
12.1-f1 |
12.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{12} \cdot 3^{9} \) |
$2.94243$ |
$(-3a+28), (-3a-25), (26a-243)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3^{3} \) |
$1$ |
$2.522505830$ |
3.849672405 |
\( -\frac{7790262311}{10077696} a - \frac{65014847347}{10077696} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -1430190 a - 11936227\) , \( -2939342474 a - 24531467191\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-1430190a-11936227\right){x}-2939342474a-24531467191$ |
12.2-a1 |
12.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{11} \cdot 3^{6} \) |
$2.94243$ |
$(-3a+28), (-3a-25), (26a+217)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
$0.057440093$ |
$11.18429546$ |
13.07236307 |
\( -\frac{3517297}{46656} a + \frac{9056251}{15552} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -334039188424 a - 2787858666949\) , \( 1215978224562060848 a + 10148436320183148865\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-334039188424a-2787858666949\right){x}+1215978224562060848a+10148436320183148865$ |
12.2-a2 |
12.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{313}) \) |
$2$ |
$[2, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( 2^{17} \cdot 3^{2} \) |
$2.94243$ |
$(-3a+28), (-3a-25), (26a+217)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{2} \cdot 3 \cdot 5 \) |
$0.172320280$ |
$11.18429546$ |
13.07236307 |
\( \frac{43728727}{294912} a - \frac{62396159}{49152} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 24495034424 a - 228928215867\) , \( -8066815305981780 a + 75391673420870333\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(24495034424a-228928215867\right){x}-8066815305981780a+75391673420870333$ |
*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.