| 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 |
| 256.1-a1 |
256.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{25} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.260186307$ |
$12.49771757$ |
2.264217622 |
\( -\frac{1241}{4} a + \frac{4185}{4} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 123 a - 411\) , \( -122 a + 410\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(123a-411\right){x}-122a+410$ |
| 256.1-a2 |
256.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{23} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.130093153$ |
$12.49771757$ |
2.264217622 |
\( \frac{18649}{2} a + \frac{47591}{2} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -3 a\) , \( 2 a\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}-3a{x}+2a$ |
| 256.1-b1 |
256.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{16} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.198924495$ |
$26.25608944$ |
3.636815999 |
\( 93184 a - 314368 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 7 a - 20\) , \( -11 a + 36\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(7a-20\right){x}-11a+36$ |
| 256.1-c1 |
256.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{23} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.130093153$ |
$12.49771757$ |
2.264217622 |
\( -\frac{18649}{2} a + 33120 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 3 a - 3\) , \( -2 a + 2\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(3a-3\right){x}-2a+2$ |
| 256.1-c2 |
256.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{25} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.260186307$ |
$12.49771757$ |
2.264217622 |
\( \frac{1241}{4} a + 736 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -123 a - 288\) , \( 122 a + 288\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-123a-288\right){x}+122a+288$ |
| 256.1-d1 |
256.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{16} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1.798029492$ |
$3.074480649$ |
3.849209920 |
\( -93184 a - 221184 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 68 a - 229\) , \( 2012 a - 6785\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(68a-229\right){x}+2012a-6785$ |
| 256.1-e1 |
256.1-e |
$6$ |
$18$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{27} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$8.704730694$ |
3.030598229 |
\( -\frac{10838595115443}{4} a + \frac{36550776099881}{4} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 4699 a - 15875\) , \( -301374 a + 1016354\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(4699a-15875\right){x}-301374a+1016354$ |
| 256.1-e2 |
256.1-e |
$6$ |
$18$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{51} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{3} \) |
$1$ |
$0.967192299$ |
3.030598229 |
\( -\frac{5519537297}{262144} a + \frac{18610505433}{262144} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 699 a - 2355\) , \( 16370 a - 55214\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(699a-2355\right){x}+16370a-55214$ |
| 256.1-e3 |
256.1-e |
$6$ |
$18$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{33} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$8.704730694$ |
3.030598229 |
\( -\frac{286425}{64} a + \frac{966617}{64} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 59 a - 195\) , \( -446 a + 1506\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(59a-195\right){x}-446a+1506$ |
| 256.1-e4 |
256.1-e |
$6$ |
$18$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{33} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$8.704730694$ |
3.030598229 |
\( \frac{286425}{64} a + 10628 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -59 a - 136\) , \( 446 a + 1060\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-59a-136\right){x}+446a+1060$ |
| 256.1-e5 |
256.1-e |
$6$ |
$18$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{51} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{3} \) |
$1$ |
$0.967192299$ |
3.030598229 |
\( \frac{5519537297}{262144} a + \frac{1636371017}{32768} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -699 a - 1656\) , \( -16370 a - 38844\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-699a-1656\right){x}-16370a-38844$ |
| 256.1-e6 |
256.1-e |
$6$ |
$18$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{27} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$8.704730694$ |
3.030598229 |
\( \frac{10838595115443}{4} a + \frac{12856090492219}{2} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -4699 a - 11176\) , \( 301374 a + 714980\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4699a-11176\right){x}+301374a+714980$ |
| 256.1-f1 |
256.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{16} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$10.96713457$ |
1.909133079 |
\( 1024 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 11 a + 28\) , \( -39 a - 92\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(11a+28\right){x}-39a-92$ |
| 256.1-g1 |
256.1-g |
$6$ |
$99$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{24} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-99$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$5.765812638$ |
1.003699148 |
\( -6548115718144 a - 15533972619264 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -6965 a - 16520\) , \( 528427 a + 1253576\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-6965a-16520\right){x}+528427a+1253576$ |
| 256.1-g2 |
256.1-g |
$6$ |
$99$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{24} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-99$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$9$ |
\( 1 \) |
$1$ |
$0.640645848$ |
1.003699148 |
\( -6548115718144 a - 15533972619264 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -395 a + 1315\) , \( -3275 a + 11027\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-395a+1315\right){x}-3275a+11027$ |
| 256.1-g3 |
256.1-g |
$6$ |
$99$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{24} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 1 \) |
$1$ |
$5.765812638$ |
1.003699148 |
\( -32768 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -85 a - 200\) , \( 651 a + 1544\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-85a-200\right){x}+651a+1544$ |
| 256.1-g4 |
256.1-g |
$6$ |
$99$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{24} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 1 \) |
$1$ |
$5.765812638$ |
1.003699148 |
\( -32768 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 85 a - 285\) , \( -651 a + 2195\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(85a-285\right){x}-651a+2195$ |
| 256.1-g5 |
256.1-g |
$6$ |
$99$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{24} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-99$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$9$ |
\( 1 \) |
$1$ |
$0.640645848$ |
1.003699148 |
\( 6548115718144 a - 22082088337408 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 395 a + 920\) , \( 3275 a + 7752\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(395a+920\right){x}+3275a+7752$ |
| 256.1-g6 |
256.1-g |
$6$ |
$99$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{24} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-99$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$5.765812638$ |
1.003699148 |
\( 6548115718144 a - 22082088337408 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 6965 a - 23485\) , \( -528427 a + 1782003\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(6965a-23485\right){x}-528427a+1782003$ |
| 256.1-h1 |
256.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{23} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.472709641$ |
$6.873550969$ |
2.262448170 |
\( -\frac{18649}{2} a + 33120 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 1224 a + 2904\) , \( -6608 a - 15676\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(1224a+2904\right){x}-6608a-15676$ |
| 256.1-h2 |
256.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{25} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.236354820$ |
$6.873550969$ |
2.262448170 |
\( \frac{1241}{4} a + 736 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 0\) , \( 32 a - 108\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+32a-108$ |
| 256.1-i1 |
256.1-i |
$1$ |
$1$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{16} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$10.96713457$ |
1.909133079 |
\( 1024 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -11 a + 39\) , \( 39 a - 131\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-11a+39\right){x}+39a-131$ |
| 256.1-j1 |
256.1-j |
$6$ |
$18$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{27} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{4} \) |
$1$ |
$0.372435636$ |
2.333978012 |
\( -\frac{10838595115443}{4} a + \frac{36550776099881}{4} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -11936 a - 28328\) , \( -1199616 a - 2845840\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-11936a-28328\right){x}-1199616a-2845840$ |
| 256.1-j2 |
256.1-j |
$6$ |
$18$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{51} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$3.351920727$ |
2.333978012 |
\( -\frac{5519537297}{262144} a + \frac{18610505433}{262144} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -576 a - 1368\) , \( 159488 a + 378352\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-576a-1368\right){x}+159488a+378352$ |
| 256.1-j3 |
256.1-j |
$6$ |
$18$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{33} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$3.351920727$ |
2.333978012 |
\( -\frac{286425}{64} a + \frac{966617}{64} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 64 a + 152\) , \( -5888 a - 13968\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(64a+152\right){x}-5888a-13968$ |
| 256.1-j4 |
256.1-j |
$6$ |
$18$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{33} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$3.351920727$ |
2.333978012 |
\( \frac{286425}{64} a + 10628 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -64 a + 216\) , \( 5888 a - 19856\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-64a+216\right){x}+5888a-19856$ |
| 256.1-j5 |
256.1-j |
$6$ |
$18$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{51} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$3.351920727$ |
2.333978012 |
\( \frac{5519537297}{262144} a + \frac{1636371017}{32768} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 576 a - 1944\) , \( -159488 a + 537840\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(576a-1944\right){x}-159488a+537840$ |
| 256.1-j6 |
256.1-j |
$6$ |
$18$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{27} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{4} \) |
$1$ |
$0.372435636$ |
2.333978012 |
\( \frac{10838595115443}{4} a + \frac{12856090492219}{2} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 11936 a - 40264\) , \( 1199616 a - 4045456\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(11936a-40264\right){x}+1199616a-4045456$ |
| 256.1-k1 |
256.1-k |
$1$ |
$1$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{16} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.198924495$ |
$26.25608944$ |
3.636815999 |
\( -93184 a - 221184 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -7 a - 13\) , \( 11 a + 25\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-7a-13\right){x}+11a+25$ |
| 256.1-l1 |
256.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{25} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.236354820$ |
$6.873550969$ |
2.262448170 |
\( -\frac{1241}{4} a + \frac{4185}{4} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 0\) , \( -32 a - 76\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-32a-76$ |
| 256.1-l2 |
256.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( - 2^{23} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.472709641$ |
$6.873550969$ |
2.262448170 |
\( \frac{18649}{2} a + \frac{47591}{2} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1224 a + 4128\) , \( 6608 a - 22284\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-1224a+4128\right){x}+6608a-22284$ |
| 256.1-m1 |
256.1-m |
$1$ |
$1$ |
\(\Q(\sqrt{33}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{16} \) |
$2.05331$ |
$(-a-2), (-a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1.798029492$ |
$3.074480649$ |
3.849209920 |
\( 93184 a - 314368 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -68 a - 161\) , \( -2012 a - 4773\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-68a-161\right){x}-2012a-4773$ |
*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.
