| 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 |
| 2904.1-a1 |
2904.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 11^{2} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$9.463890993$ |
2.731990006 |
\( \frac{2048}{891} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 6\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+{x}+6$ |
| 2904.1-a2 |
2904.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( - 2^{10} \cdot 3 \cdot 11^{10} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$1.182986374$ |
2.731990006 |
\( -\frac{699565826107226}{643076643} a + \frac{404115429694440}{214358881} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 1494 a - 2582\) , \( 42232 a - 73152\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(1494a-2582\right){x}+42232a-73152$ |
| 2904.1-a3 |
2904.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 11^{8} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$4.731945496$ |
2.731990006 |
\( \frac{122657188}{43923} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 104 a - 182\) , \( 540 a - 936\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(104a-182\right){x}+540a-936$ |
| 2904.1-a4 |
2904.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 11^{4} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$18.92778198$ |
2.731990006 |
\( \frac{37642192}{1089} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 44 a - 77\) , \( -180 a + 312\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(44a-77\right){x}-180a+312$ |
| 2904.1-a5 |
2904.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( - 2^{10} \cdot 3 \cdot 11^{10} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$1.182986374$ |
2.731990006 |
\( \frac{699565826107226}{643076643} a + \frac{404115429694440}{214358881} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -326 a + 538\) , \( 3128 a - 5472\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-326a+538\right){x}+3128a-5472$ |
| 2904.1-a6 |
2904.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 11^{2} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$18.92778198$ |
2.731990006 |
\( \frac{37736227588}{33} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 704 a - 1232\) , \( -13050 a + 22620\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(704a-1232\right){x}-13050a+22620$ |
| 2904.1-b1 |
2904.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{10} \cdot 3^{28} \cdot 11^{4} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.498945544$ |
1.730833227 |
\( -\frac{27403349188178}{578739249} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -7978 a - 13959\) , \( 520413 a + 901917\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-7978a-13959\right){x}+520413a+901917$ |
| 2904.1-b2 |
2904.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{14} \cdot 11^{2} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.995782177$ |
1.730833227 |
\( \frac{55635379958596}{24057} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -8018 a - 14029\) , \( 514973 a + 892487\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-8018a-14029\right){x}+514973a+892487$ |
| 2904.1-c1 |
2904.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 11^{2} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.435342364$ |
1.983395838 |
\( \frac{2048}{891} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( -6\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+{x}-6$ |
| 2904.1-c2 |
2904.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( - 2^{10} \cdot 3 \cdot 11^{10} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$3.435342364$ |
1.983395838 |
\( -\frac{699565826107226}{643076643} a + \frac{404115429694440}{214358881} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 1494 a - 2583\) , \( -40738 a + 70569\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(1494a-2583\right){x}-40738a+70569$ |
| 2904.1-c3 |
2904.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 11^{8} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$6.870684728$ |
1.983395838 |
\( \frac{122657188}{43923} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 104 a - 183\) , \( -436 a + 753\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(104a-183\right){x}-436a+753$ |
| 2904.1-c4 |
2904.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 11^{4} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$6.870684728$ |
1.983395838 |
\( \frac{37642192}{1089} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 44 a - 78\) , \( 224 a - 390\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(44a-78\right){x}+224a-390$ |
| 2904.1-c5 |
2904.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( - 2^{10} \cdot 3 \cdot 11^{10} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$3.435342364$ |
1.983395838 |
\( \frac{699565826107226}{643076643} a + \frac{404115429694440}{214358881} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -326 a + 537\) , \( -3454 a + 6009\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-326a+537\right){x}-3454a+6009$ |
| 2904.1-c6 |
2904.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 11^{2} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.717671182$ |
1.983395838 |
\( \frac{37736227588}{33} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 704 a - 1233\) , \( 13754 a - 23853\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(704a-1233\right){x}+13754a-23853$ |
| 2904.1-d1 |
2904.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{10} \cdot 3^{4} \cdot 11^{4} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.288730858$ |
$4.445245240$ |
2.964068881 |
\( \frac{1714750}{1089} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 30 a + 55\) , \( -29 a - 49\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(30a+55\right){x}-29a-49$ |
| 2904.1-d2 |
2904.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 11^{2} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.144365429$ |
$17.78098096$ |
2.964068881 |
\( \frac{62500}{33} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -10 a - 15\) , \( -9 a - 15\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-10a-15\right){x}-9a-15$ |
| 2904.1-e1 |
2904.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{10} \cdot 3^{2} \cdot 11^{8} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.895603434$ |
$2.097553121$ |
4.338384928 |
\( \frac{36382894}{43923} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 87 a + 152\) , \( -563 a - 976\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(87a+152\right){x}-563a-976$ |
| 2904.1-e2 |
2904.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 11^{4} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.447801717$ |
$8.390212485$ |
4.338384928 |
\( \frac{3650692}{1089} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -33 a - 58\) , \( -113 a - 196\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-33a-58\right){x}-113a-196$ |
| 2904.1-e3 |
2904.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 11^{2} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.895603434$ |
$33.56084994$ |
4.338384928 |
\( \frac{810448}{33} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -13 a - 23\) , \( 22 a + 38\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-13a-23\right){x}+22a+38$ |
| 2904.1-e4 |
2904.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{10} \cdot 3^{8} \cdot 11^{2} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.895603434$ |
$2.097553121$ |
4.338384928 |
\( \frac{5690357426}{891} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -473 a - 828\) , \( -7703 a - 13352\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-473a-828\right){x}-7703a-13352$ |
| 2904.1-f1 |
2904.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( - 2^{10} \cdot 3^{8} \cdot 11^{3} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.554508779$ |
$0.713094972$ |
2.926822156 |
\( -\frac{13295300649324500}{9801} a + \frac{23028136227748078}{9801} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 2110 a - 3641\) , \( 68809 a - 119209\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2110a-3641\right){x}+68809a-119209$ |
| 2904.1-f2 |
2904.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{8} \cdot 3 \cdot 11^{9} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.777254389$ |
$2.852379889$ |
2.926822156 |
\( -\frac{160107487024}{643076643} a + \frac{174681737980}{214358881} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -30 a + 59\) , \( 91 a - 145\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-30a+59\right){x}+91a-145$ |
| 2904.1-f3 |
2904.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 11^{6} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.888627194$ |
$11.40951955$ |
2.926822156 |
\( \frac{44705920}{43923} a + \frac{181101808}{43923} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 10 a - 16\) , \( 9 a - 16\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(10a-16\right){x}+9a-16$ |
| 2904.1-f4 |
2904.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 11^{6} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.777254389$ |
$2.852379889$ |
2.926822156 |
\( -\frac{82062022000}{131769} a + \frac{143604708532}{131769} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 130 a - 231\) , \( 1049 a - 1839\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(130a-231\right){x}+1049a-1839$ |
| 2904.1-f5 |
2904.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{8} \cdot 3 \cdot 11^{3} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.444313597$ |
$22.81903911$ |
2.926822156 |
\( \frac{2723160064}{363} a + \frac{1578383360}{121} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -30 a - 54\) , \( 112 a + 201\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-30a-54\right){x}+112a+201$ |
| 2904.1-f6 |
2904.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( - 2^{10} \cdot 3^{2} \cdot 11^{9} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.554508779$ |
$0.713094972$ |
2.926822156 |
\( \frac{20025234470666780}{643076643} a + \frac{34684175376660278}{643076643} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 70 a - 261\) , \( 1169 a - 2901\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(70a-261\right){x}+1169a-2901$ |
| 2904.1-g1 |
2904.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{10} \cdot 3^{2} \cdot 11^{8} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.441181952$ |
$3.261428330$ |
3.322958686 |
\( \frac{36382894}{43923} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 87 a + 155\) , \( 650 a + 1129\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(87a+155\right){x}+650a+1129$ |
| 2904.1-g2 |
2904.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 11^{4} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.220590976$ |
$13.04571332$ |
3.322958686 |
\( \frac{3650692}{1089} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -33 a - 55\) , \( 80 a + 139\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-33a-55\right){x}+80a+139$ |
| 2904.1-g3 |
2904.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 11^{2} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.441181952$ |
$13.04571332$ |
3.322958686 |
\( \frac{810448}{33} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -13 a - 20\) , \( -35 a - 60\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-13a-20\right){x}-35a-60$ |
| 2904.1-g4 |
2904.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{10} \cdot 3^{8} \cdot 11^{2} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.441181952$ |
$13.04571332$ |
3.322958686 |
\( \frac{5690357426}{891} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -473 a - 825\) , \( 7230 a + 12525\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-473a-825\right){x}+7230a+12525$ |
| 2904.1-h1 |
2904.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( - 2^{10} \cdot 3^{2} \cdot 11^{9} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.554508779$ |
$0.713094972$ |
2.926822156 |
\( -\frac{20025234470666780}{643076643} a + \frac{34684175376660278}{643076643} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 8010 a - 13879\) , \( 521425 a - 903139\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(8010a-13879\right){x}+521425a-903139$ |
| 2904.1-h2 |
2904.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{8} \cdot 3 \cdot 11^{9} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.777254389$ |
$2.852379889$ |
2.926822156 |
\( \frac{160107487024}{643076643} a + \frac{174681737980}{214358881} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -210 a + 361\) , \( -4237 a + 7337\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-210a+361\right){x}-4237a+7337$ |
| 2904.1-h3 |
2904.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 11^{6} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.888627194$ |
$11.40951955$ |
2.926822156 |
\( -\frac{44705920}{43923} a + \frac{181101808}{43923} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 110 a - 194\) , \( -605 a + 1046\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(110a-194\right){x}-605a+1046$ |
| 2904.1-h4 |
2904.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{8} \cdot 3 \cdot 11^{3} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.444313597$ |
$22.81903911$ |
2.926822156 |
\( -\frac{2723160064}{363} a + \frac{1578383360}{121} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 30 a - 54\) , \( -112 a + 201\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(30a-54\right){x}-112a+201$ |
| 2904.1-h5 |
2904.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 11^{6} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.777254389$ |
$2.852379889$ |
2.926822156 |
\( \frac{82062022000}{131769} a + \frac{143604708532}{131769} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 510 a - 889\) , \( 8125 a - 14077\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(510a-889\right){x}+8125a-14077$ |
| 2904.1-h6 |
2904.1-h |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( - 2^{10} \cdot 3^{8} \cdot 11^{3} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.554508779$ |
$0.713094972$ |
2.926822156 |
\( \frac{13295300649324500}{9801} a + \frac{23028136227748078}{9801} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -590 a + 981\) , \( 35185 a - 61047\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-590a+981\right){x}+35185a-61047$ |
| 2904.1-i1 |
2904.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( - 2^{10} \cdot 3^{2} \cdot 11^{9} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.752390050$ |
$4.874242413$ |
4.234669650 |
\( -\frac{20025234470666780}{643076643} a + \frac{34684175376660278}{643076643} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 8012 a - 13878\) , \( -513414 a + 889260\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(8012a-13878\right){x}-513414a+889260$ |
| 2904.1-i2 |
2904.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{8} \cdot 3 \cdot 11^{9} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.504780100$ |
$2.437121206$ |
4.234669650 |
\( \frac{160107487024}{643076643} a + \frac{174681737980}{214358881} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 32 a + 60\) , \( 122 a + 204\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(32a+60\right){x}+122a+204$ |
| 2904.1-i3 |
2904.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 11^{6} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.752390050$ |
$9.748484827$ |
4.234669650 |
\( -\frac{44705920}{43923} a + \frac{181101808}{43923} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 112 a - 193\) , \( 716 a - 1240\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(112a-193\right){x}+716a-1240$ |
| 2904.1-i4 |
2904.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{8} \cdot 3 \cdot 11^{3} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.504780100$ |
$4.874242413$ |
4.234669650 |
\( -\frac{2723160064}{363} a + \frac{1578383360}{121} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 5944 a - 10295\) , \( 330264 a - 572034\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(5944a-10295\right){x}+330264a-572034$ |
| 2904.1-i5 |
2904.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 11^{6} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$0.376195025$ |
$9.748484827$ |
4.234669650 |
\( \frac{82062022000}{131769} a + \frac{143604708532}{131769} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 512 a - 888\) , \( -7614 a + 13188\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(512a-888\right){x}-7614a+13188$ |
| 2904.1-i6 |
2904.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( - 2^{10} \cdot 3^{8} \cdot 11^{3} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.752390050$ |
$4.874242413$ |
4.234669650 |
\( \frac{13295300649324500}{9801} a + \frac{23028136227748078}{9801} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -588 a + 982\) , \( -35774 a + 62028\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-588a+982\right){x}-35774a+62028$ |
| 2904.1-j1 |
2904.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{10} \cdot 3^{4} \cdot 11^{4} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.183646239$ |
$5.218627477$ |
4.426573668 |
\( \frac{1714750}{1089} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 32 a + 56\) , \( 60 a + 104\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(32a+56\right){x}+60a+104$ |
| 2904.1-j2 |
2904.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 11^{2} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.367292479$ |
$20.87450990$ |
4.426573668 |
\( \frac{62500}{33} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -8 a - 14\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-8a-14\right){x}$ |
| 2904.1-k1 |
2904.1-k |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( - 2^{10} \cdot 3^{8} \cdot 11^{3} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.752390050$ |
$4.874242413$ |
4.234669650 |
\( -\frac{13295300649324500}{9801} a + \frac{23028136227748078}{9801} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 2109 a - 3642\) , \( -70342 a + 121894\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(2109a-3642\right){x}-70342a+121894$ |
| 2904.1-k2 |
2904.1-k |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{8} \cdot 3 \cdot 11^{9} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.504780100$ |
$2.437121206$ |
4.234669650 |
\( -\frac{160107487024}{643076643} a + \frac{174681737980}{214358881} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -31 a + 58\) , \( -64 a + 110\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-31a+58\right){x}-64a+110$ |
| 2904.1-k3 |
2904.1-k |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 11^{6} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.752390050$ |
$9.748484827$ |
4.234669650 |
\( \frac{44705920}{43923} a + \frac{181101808}{43923} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 9 a - 17\) , \( -17 a + 26\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(9a-17\right){x}-17a+26$ |
| 2904.1-k4 |
2904.1-k |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 11^{6} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$0.376195025$ |
$9.748484827$ |
4.234669650 |
\( -\frac{82062022000}{131769} a + \frac{143604708532}{131769} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 129 a - 232\) , \( -1152 a + 1994\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(129a-232\right){x}-1152a+1994$ |
| 2904.1-k5 |
2904.1-k |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( 2^{8} \cdot 3 \cdot 11^{3} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.504780100$ |
$4.874242413$ |
4.234669650 |
\( \frac{2723160064}{363} a + \frac{1578383360}{121} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -30 a - 54\) , \( -112 a - 201\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-30a-54\right){x}-112a-201$ |
| 2904.1-k6 |
2904.1-k |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2904.1 |
\( 2^{3} \cdot 3 \cdot 11^{2} \) |
\( - 2^{10} \cdot 3^{2} \cdot 11^{9} \) |
$2.27237$ |
$(a+1), (a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.752390050$ |
$4.874242413$ |
4.234669650 |
\( \frac{20025234470666780}{643076643} a + \frac{34684175376660278}{643076643} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 69 a - 262\) , \( -1362 a + 2846\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(69a-262\right){x}-1362a+2846$ |
*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.
