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 |
432.1-a1 |
432.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{8} \cdot 3^{10} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.255688621$ |
$9.422156876$ |
3.642274763 |
\( \frac{23200}{81} a + \frac{44668}{81} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 29 a - 73\) , \( -402 a + 1065\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(29a-73\right){x}-402a+1065$ |
432.1-a2 |
432.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{10} \cdot 3^{14} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$0.127844310$ |
$9.422156876$ |
3.642274763 |
\( -\frac{631341130}{6561} a + \frac{1685171936}{6561} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 679 a - 1793\) , \( -15464 a + 40915\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(679a-1793\right){x}-15464a+40915$ |
432.1-a3 |
432.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{11} \cdot 3^{22} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$0.063922155$ |
$4.711078438$ |
3.642274763 |
\( \frac{454644971201}{43046721} a + \frac{1279443386915}{43046721} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 909 a - 2403\) , \( -3888 a + 10287\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(909a-2403\right){x}-3888a+10287$ |
432.1-a4 |
432.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{11} \cdot 3^{10} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.255688621$ |
$4.711078438$ |
3.642274763 |
\( -\frac{3992303075281}{81} a + \frac{10562789733245}{81} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 10849 a - 28703\) , \( -998048 a + 2640583\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(10849a-28703\right){x}-998048a+2640583$ |
432.1-b1 |
432.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{13} \cdot 3^{40} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$3.885572036$ |
$0.505267232$ |
2.968158376 |
\( -\frac{22026189082216125793}{3706040377703682} a - \frac{54626740869226485845}{3706040377703682} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -24792 a - 65544\) , \( 3553592 a + 9401848\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-24792a-65544\right){x}+3553592a+9401848$ |
432.1-b2 |
432.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{20} \cdot 3^{14} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.485696504$ |
$4.042137858$ |
2.968158376 |
\( \frac{4913}{1296} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 28 a + 76\) , \( 2848 a + 7536\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(28a+76\right){x}+2848a+7536$ |
432.1-b3 |
432.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{13} \cdot 3^{40} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$3.885572036$ |
$0.505267232$ |
2.968158376 |
\( \frac{22026189082216125793}{3706040377703682} a - \frac{54626740869226485845}{3706040377703682} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 11248 a + 29656\) , \( -916616 a - 2424792\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(11248a+29656\right){x}-916616a-2424792$ |
432.1-b4 |
432.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{26} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.942786018$ |
$2.021068929$ |
2.968158376 |
\( -\frac{15840177853915205}{86093442} a + \frac{20954710660855016}{43046721} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -3772 a - 10084\) , \( -131200 a - 346784\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3772a-10084\right){x}-131200a-346784$ |
432.1-b5 |
432.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{22} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.971393009$ |
$4.042137858$ |
2.968158376 |
\( \frac{838561807}{26244} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -1572 a - 4164\) , \( 53888 a + 142576\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1572a-4164\right){x}+53888a+142576$ |
432.1-b6 |
432.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{13} \cdot 3^{16} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.971393009$ |
$1.010534464$ |
2.968158376 |
\( -\frac{2350503708439404473473}{13122} a + \frac{6218848268321376696725}{13122} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -53992 a - 144544\) , \( -11203576 a - 29616296\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-53992a-144544\right){x}-11203576a-29616296$ |
432.1-b7 |
432.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{26} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.942786018$ |
$2.021068929$ |
2.968158376 |
\( \frac{15840177853915205}{86093442} a + \frac{20954710660855016}{43046721} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -24972 a - 66084\) , \( 3497216 a + 9252736\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-24972a-66084\right){x}+3497216a+9252736$ |
432.1-b8 |
432.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{13} \cdot 3^{16} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.885572036$ |
$1.010534464$ |
2.968158376 |
\( \frac{2350503708439404473473}{13122} a + \frac{6218848268321376696725}{13122} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -399552 a - 1057344\) , \( 223692872 a + 591834184\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-399552a-1057344\right){x}+223692872a+591834184$ |
432.1-c1 |
432.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{10} \cdot 3^{22} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.098868579$ |
1.586595513 |
\( \frac{207646}{6561} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -17 a + 40\) , \( -428 a + 1123\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-17a+40\right){x}-428a+1123$ |
432.1-c2 |
432.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{8} \cdot 3^{8} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.395474317$ |
1.586595513 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 14 a + 38\) , \( 70 a + 185\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(14a+38\right){x}+70a+185$ |
432.1-c3 |
432.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{4} \cdot 3^{10} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$16.79094863$ |
1.586595513 |
\( \frac{35152}{9} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 3 a - 15\) , \( 9 a - 27\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(3a-15\right){x}+9a-27$ |
432.1-c4 |
432.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{8} \cdot 3^{14} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$8.395474317$ |
1.586595513 |
\( \frac{1556068}{81} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 23 a - 70\) , \( -86 a + 223\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(23a-70\right){x}-86a+223$ |
432.1-c5 |
432.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{8} \cdot 3^{8} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.395474317$ |
1.586595513 |
\( \frac{28756228}{3} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 63 a - 180\) , \( 522 a - 1377\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(63a-180\right){x}+522a-1377$ |
432.1-c6 |
432.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{10} \cdot 3^{10} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.197737158$ |
1.586595513 |
\( \frac{3065617154}{9} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 383 a - 1060\) , \( -6584 a + 17323\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(383a-1060\right){x}-6584a+17323$ |
432.1-d1 |
432.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{8} \cdot 3^{4} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.784927655$ |
$18.58215309$ |
2.756427975 |
\( -\frac{10240}{3} a + \frac{32768}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 44 a - 112\) , \( 218 a - 575\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(44a-112\right){x}+218a-575$ |
432.1-d2 |
432.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( - 2^{4} \cdot 3^{5} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.392463827$ |
$18.58215309$ |
2.756427975 |
\( \frac{1384736}{9} a + \frac{3663920}{9} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -3 a - 6\) , \( 4 a + 11\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3a-6\right){x}+4a+11$ |
432.1-e1 |
432.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( - 2^{8} \cdot 3^{11} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$11.68590278$ |
2.208428044 |
\( -\frac{2000701444}{81} a + \frac{5293366760}{81} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 33 a + 84\) , \( 703 a + 1860\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(33a+84\right){x}+703a+1860$ |
432.1-e2 |
432.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{8} \cdot 3^{8} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$11.68590278$ |
2.208428044 |
\( \frac{16384}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 6 a - 12\) , \( 12 a - 33\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(6a-12\right){x}+12a-33$ |
432.1-e3 |
432.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{4} \cdot 3^{10} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$23.37180557$ |
2.208428044 |
\( \frac{109744}{9} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -32 a - 86\) , \( 111 a + 293\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-32a-86\right){x}+111a+293$ |
432.1-e4 |
432.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( - 2^{8} \cdot 3^{11} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$11.68590278$ |
2.208428044 |
\( \frac{2000701444}{81} a + \frac{5293366760}{81} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -497 a - 1316\) , \( 9249 a + 24470\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-497a-1316\right){x}+9249a+24470$ |
432.1-f1 |
432.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{8} \cdot 3^{4} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$26.93343130$ |
2.544970041 |
\( -\frac{10240}{3} a + \frac{32768}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 44 a - 112\) , \( -218 a + 575\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(44a-112\right){x}-218a+575$ |
432.1-f2 |
432.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( - 2^{4} \cdot 3^{5} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$13.46671565$ |
2.544970041 |
\( \frac{1384736}{9} a + \frac{3663920}{9} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -3 a - 9\) , \( -7 a - 19\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-3a-9\right){x}-7a-19$ |
432.1-g1 |
432.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{10} \cdot 3^{22} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.321540817$ |
$2.098868579$ |
4.081241752 |
\( \frac{207646}{6561} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -15 a + 45\) , \( 412 a - 1081\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-15a+45\right){x}+412a-1081$ |
432.1-g2 |
432.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{8} \cdot 3^{8} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.572326543$ |
$8.395474317$ |
4.081241752 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 14 a + 38\) , \( -70 a - 185\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(14a+38\right){x}-70a-185$ |
432.1-g3 |
432.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{4} \cdot 3^{10} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.286163271$ |
$16.79094863$ |
4.081241752 |
\( \frac{35152}{9} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 5 a - 10\) , \( -5 a + 14\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(5a-10\right){x}-5a+14$ |
432.1-g4 |
432.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{8} \cdot 3^{14} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.643081635$ |
$8.395474317$ |
4.081241752 |
\( \frac{1556068}{81} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 25 a - 65\) , \( 110 a - 291\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(25a-65\right){x}+110a-291$ |
432.1-g5 |
432.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{8} \cdot 3^{8} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.643081635$ |
$8.395474317$ |
4.081241752 |
\( \frac{28756228}{3} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 65 a - 175\) , \( -458 a + 1199\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(65a-175\right){x}-458a+1199$ |
432.1-g6 |
432.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{10} \cdot 3^{10} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.286163271$ |
$4.197737158$ |
4.081241752 |
\( \frac{3065617154}{9} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 385 a - 1055\) , \( 6968 a - 18381\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(385a-1055\right){x}+6968a-18381$ |
432.1-h1 |
432.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( - 2^{4} \cdot 3^{23} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$2.111610151$ |
2.793397663 |
\( \frac{4372537184}{4782969} a + \frac{435694064}{4782969} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -473 a - 1253\) , \( -5603 a - 14825\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-473a-1253\right){x}-5603a-14825$ |
432.1-h2 |
432.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{8} \cdot 3^{16} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$4.223220303$ |
2.793397663 |
\( -\frac{3723139072}{2187} a + \frac{9946148864}{2187} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 72 a - 204\) , \( 622 a - 1597\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(72a-204\right){x}+622a-1597$ |
432.1-i1 |
432.1-i |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{13} \cdot 3^{40} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2^{4} \) |
$1$ |
$0.186272011$ |
2.252934490 |
\( -\frac{22026189082216125793}{3706040377703682} a - \frac{54626740869226485845}{3706040377703682} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -24792 a - 65547\) , \( -3578384 a - 9467394\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-24792a-65547\right){x}-3578384a-9467394$ |
432.1-i2 |
432.1-i |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{20} \cdot 3^{14} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.490176095$ |
2.252934490 |
\( \frac{4913}{1296} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 28 a + 73\) , \( -2820 a - 7462\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(28a+73\right){x}-2820a-7462$ |
432.1-i3 |
432.1-i |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{13} \cdot 3^{40} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$1$ |
$0.186272011$ |
2.252934490 |
\( \frac{22026189082216125793}{3706040377703682} a - \frac{54626740869226485845}{3706040377703682} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 11248 a + 29653\) , \( 927864 a + 2454446\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(11248a+29653\right){x}+927864a+2454446$ |
432.1-i4 |
432.1-i |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{26} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$1$ |
$0.745088047$ |
2.252934490 |
\( -\frac{15840177853915205}{86093442} a + \frac{20954710660855016}{43046721} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -3772 a - 10087\) , \( 127428 a + 336698\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-3772a-10087\right){x}+127428a+336698$ |
432.1-i5 |
432.1-i |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{22} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$1.490176095$ |
2.252934490 |
\( \frac{838561807}{26244} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -1572 a - 4167\) , \( -55460 a - 146742\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-1572a-4167\right){x}-55460a-146742$ |
432.1-i6 |
432.1-i |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{13} \cdot 3^{16} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1$ |
$0.372544023$ |
2.252934490 |
\( -\frac{2350503708439404473473}{13122} a + \frac{6218848268321376696725}{13122} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -53992 a - 144547\) , \( 11149584 a + 29471750\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-53992a-144547\right){x}+11149584a+29471750$ |
432.1-i7 |
432.1-i |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{26} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{6} \) |
$1$ |
$0.745088047$ |
2.252934490 |
\( \frac{15840177853915205}{86093442} a + \frac{20954710660855016}{43046721} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -24972 a - 66087\) , \( -3522188 a - 9318822\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-24972a-66087\right){x}-3522188a-9318822$ |
432.1-i8 |
432.1-i |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{13} \cdot 3^{16} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2^{3} \) |
$1$ |
$0.372544023$ |
2.252934490 |
\( \frac{2350503708439404473473}{13122} a + \frac{6218848268321376696725}{13122} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -399552 a - 1057347\) , \( -224092424 a - 592891530\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-399552a-1057347\right){x}-224092424a-592891530$ |
432.1-j1 |
432.1-j |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( - 2^{4} \cdot 3^{15} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.223415482$ |
1.554079449 |
\( \frac{424736}{729} a + \frac{2140304}{729} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -3 a\) , \( a + 5\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}-3a{x}+a+5$ |
432.1-j2 |
432.1-j |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{8} \cdot 3^{12} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.223415482$ |
1.554079449 |
\( \frac{69632}{27} a + \frac{241664}{27} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 332 a - 874\) , \( 2132 a - 5639\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(332a-874\right){x}+2132a-5639$ |
432.1-j3 |
432.1-j |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{8} \cdot 3^{4} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.223415482$ |
1.554079449 |
\( -\frac{990466048}{3} a + \frac{2621198336}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 48 a - 126\) , \( 268 a - 709\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(48a-126\right){x}+268a-709$ |
432.1-j4 |
432.1-j |
$4$ |
$6$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( - 2^{4} \cdot 3^{5} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.223415482$ |
1.554079449 |
\( \frac{84645967328}{9} a + \frac{223951809488}{9} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -660 a - 1746\) , \( 15039 a + 39789\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-660a-1746\right){x}+15039a+39789$ |
432.1-k1 |
432.1-k |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{8} \cdot 3^{10} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$5.169386648$ |
1.953844500 |
\( \frac{23200}{81} a + \frac{44668}{81} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 27 a - 78\) , \( 430 a - 1141\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(27a-78\right){x}+430a-1141$ |
432.1-k2 |
432.1-k |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{10} \cdot 3^{14} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$5.169386648$ |
1.953844500 |
\( -\frac{631341130}{6561} a + \frac{1685171936}{6561} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 677 a - 1798\) , \( 16142 a - 42711\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(677a-1798\right){x}+16142a-42711$ |
432.1-k3 |
432.1-k |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{11} \cdot 3^{22} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.584693324$ |
1.953844500 |
\( \frac{454644971201}{43046721} a + \frac{1279443386915}{43046721} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 907 a - 2408\) , \( 4796 a - 12693\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(907a-2408\right){x}+4796a-12693$ |
432.1-k4 |
432.1-k |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{11} \cdot 3^{10} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.584693324$ |
1.953844500 |
\( -\frac{3992303075281}{81} a + \frac{10562789733245}{81} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 10847 a - 28708\) , \( 1008896 a - 2669289\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(10847a-28708\right){x}+1008896a-2669289$ |
*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.