| 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 |
| 3072.1-a1 |
3072.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{25} \cdot 3^{12} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$3.551466094$ |
3.075659858 |
\( -\frac{217996}{729} a + \frac{1023628}{729} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 504 a - 872\) , \( -2120 a + 3672\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(504a-872\right){x}-2120a+3672$ |
| 3072.1-a2 |
3072.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{20} \cdot 3^{6} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$7.102932189$ |
3.075659858 |
\( -\frac{770336}{27} a + \frac{1419904}{27} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 284 a - 492\) , \( 3672 a - 6360\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(284a-492\right){x}+3672a-6360$ |
| 3072.1-a3 |
3072.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{25} \cdot 3^{3} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$1.775733047$ |
3.075659858 |
\( -\frac{26639622068}{9} a + \frac{15380474156}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 4544 a - 7872\) , \( 223656 a - 387384\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(4544a-7872\right){x}+223656a-387384$ |
| 3072.1-a4 |
3072.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{10} \cdot 3^{3} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 3 \) |
$1$ |
$14.20586437$ |
3.075659858 |
\( \frac{14225792}{9} a + \frac{8213248}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 4 a - 7\) , \( 134 a - 232\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(4a-7\right){x}+134a-232$ |
| 3072.1-b1 |
3072.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{27} \cdot 3^{8} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.120342961$ |
$2.383075350$ |
2.917314563 |
\( -\frac{443186854}{81} a + \frac{767608522}{81} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -48 a - 112\) , \( 1016 a + 1720\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-48a-112\right){x}+1016a+1720$ |
| 3072.1-b2 |
3072.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{24} \cdot 3 \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.060171480$ |
$9.532301402$ |
2.917314563 |
\( -\frac{132636728}{3} a + 76579552 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 107702 a - 186545\) , \( -25356654 a + 43919013\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(107702a-186545\right){x}-25356654a+43919013$ |
| 3072.1-b3 |
3072.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{18} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.530085740$ |
$19.06460280$ |
2.917314563 |
\( -\frac{9856}{3} a + \frac{22336}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 6862 a - 11885\) , \( -381770 a + 661245\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(6862a-11885\right){x}-381770a+661245$ |
| 3072.1-b4 |
3072.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{18} \cdot 3 \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.060171480$ |
$9.532301402$ |
2.917314563 |
\( \frac{166016}{3} a + 95936 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -23148 a + 40096\) , \( -10988976 a + 19033464\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-23148a+40096\right){x}-10988976a+19033464$ |
| 3072.1-b5 |
3072.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{24} \cdot 3^{4} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.060171480$ |
$9.532301402$ |
2.917314563 |
\( \frac{1122088}{9} a + \frac{1989808}{9} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 116 a - 200\) , \( 756 a - 1308\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(116a-200\right){x}+756a-1308$ |
| 3072.1-b6 |
3072.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{27} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.120342961$ |
$4.766150701$ |
2.917314563 |
\( \frac{164847992914}{3} a + \frac{285525100658}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -244 a + 400\) , \( 4260 a - 7308\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-244a+400\right){x}+4260a-7308$ |
| 3072.1-c1 |
3072.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{23} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$2.252849762$ |
2.601366833 |
\( -\frac{740855896}{3} a + \frac{1283201128}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 96 a - 160\) , \( 632 a - 1096\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(96a-160\right){x}+632a-1096$ |
| 3072.1-c2 |
3072.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{16} \cdot 3^{4} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$9.011399049$ |
2.601366833 |
\( -\frac{61952}{9} a + \frac{162688}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 6 a - 10\) , \( 8 a - 16\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(6a-10\right){x}+8a-16$ |
| 3072.1-c3 |
3072.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{23} \cdot 3^{8} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$4.505699524$ |
2.601366833 |
\( \frac{247496}{81} a + \frac{429112}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -4 a\) , \( 36 a - 60\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-4a{x}+36a-60$ |
| 3072.1-c4 |
3072.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{14} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$9.011399049$ |
2.601366833 |
\( \frac{24993664}{3} a + \frac{43299296}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -32 a - 56\) , \( -142 a - 246\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-32a-56\right){x}-142a-246$ |
| 3072.1-d1 |
3072.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{14} \cdot 3^{4} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.603762616$ |
$6.405092923$ |
4.465406728 |
\( \frac{4000}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -6 a + 13\) , \( 23 a - 39\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-6a+13\right){x}+23a-39$ |
| 3072.1-d2 |
3072.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.207525233$ |
$12.81018584$ |
4.465406728 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -3\) , \( -3\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-3{x}-3$ |
| 3072.1-d3 |
3072.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{23} \cdot 3 \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.415050467$ |
$6.405092923$ |
4.465406728 |
\( -\frac{17879000}{3} a + 10335000 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 10 a - 33\) , \( 50 a - 69\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(10a-33\right){x}+50a-69$ |
| 3072.1-d4 |
3072.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{23} \cdot 3 \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.415050467$ |
$6.405092923$ |
4.465406728 |
\( \frac{17879000}{3} a + 10335000 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -10 a - 33\) , \( -50 a - 69\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-10a-33\right){x}-50a-69$ |
| 3072.1-e1 |
3072.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{28} \cdot 3 \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$1.285289264$ |
2.968248410 |
\( -\frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 430252 a - 745216\) , \( 202069724 a - 349995028\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(430252a-745216\right){x}+202069724a-349995028$ |
| 3072.1-e2 |
3072.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{28} \cdot 3^{16} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.285289264$ |
2.968248410 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -32 a + 64\) , \( -1080 a + 1800\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-32a+64\right){x}-1080a+1800$ |
| 3072.1-e3 |
3072.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{14} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$10.28231411$ |
2.968248410 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -54060 a + 93635\) , \( 11124426 a - 19268071\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-54060a+93635\right){x}+11124426a-19268071$ |
| 3072.1-e4 |
3072.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{22} \cdot 3^{4} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$10.28231411$ |
2.968248410 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 1812 a - 3136\) , \( 40796 a - 70660\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(1812a-3136\right){x}+40796a-70660$ |
| 3072.1-e5 |
3072.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{26} \cdot 3^{8} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$5.141157056$ |
2.968248410 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 48 a - 96\) , \( -216 a + 360\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(48a-96\right){x}-216a+360$ |
| 3072.1-e6 |
3072.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{26} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$5.141157056$ |
2.968248410 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 26892 a - 46576\) , \( 3152252 a - 5459860\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(26892a-46576\right){x}+3152252a-5459860$ |
| 3072.1-e7 |
3072.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{28} \cdot 3^{4} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.570578528$ |
2.968248410 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 768 a - 1536\) , \( -16632 a + 27720\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(768a-1536\right){x}-16632a+27720$ |
| 3072.1-e8 |
3072.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{28} \cdot 3 \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$2.570578528$ |
2.968248410 |
\( \frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 24812 a - 42976\) , \( 3661724 a - 6342292\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(24812a-42976\right){x}+3661724a-6342292$ |
| 3072.1-f1 |
3072.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{28} \cdot 3 \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.719487697$ |
$1.285289264$ |
2.760090861 |
\( -\frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 30890 a - 53505\) , \( 3879118 a - 6718827\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(30890a-53505\right){x}+3879118a-6718827$ |
| 3072.1-f2 |
3072.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{28} \cdot 3^{16} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.719487697$ |
$1.285289264$ |
2.760090861 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 32 a + 64\) , \( -1080 a - 1800\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(32a+64\right){x}-1080a-1800$ |
| 3072.1-f3 |
3072.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{14} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.464935962$ |
$10.28231411$ |
2.760090861 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -3882 a + 6724\) , \( 217892 a - 377400\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-3882a+6724\right){x}+217892a-377400$ |
| 3072.1-f4 |
3072.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{22} \cdot 3^{4} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.929871924$ |
$10.28231411$ |
2.760090861 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 130 a - 225\) , \( 750 a - 1299\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(130a-225\right){x}+750a-1299$ |
| 3072.1-f5 |
3072.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{26} \cdot 3^{8} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.859743848$ |
$5.141157056$ |
2.760090861 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -48 a - 96\) , \( -216 a - 360\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-48a-96\right){x}-216a-360$ |
| 3072.1-f6 |
3072.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{26} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.859743848$ |
$5.141157056$ |
2.760090861 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1930 a - 3345\) , \( 60126 a - 104139\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(1930a-3345\right){x}+60126a-104139$ |
| 3072.1-f7 |
3072.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{28} \cdot 3^{4} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.929871924$ |
$2.570578528$ |
2.760090861 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -768 a - 1536\) , \( -16632 a - 27720\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-768a-1536\right){x}-16632a-27720$ |
| 3072.1-f8 |
3072.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{28} \cdot 3 \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$3.719487697$ |
$2.570578528$ |
2.760090861 |
\( \frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1770 a - 3105\) , \( 69998 a - 121131\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(1770a-3105\right){x}+69998a-121131$ |
| 3072.1-g1 |
3072.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{10} \cdot 3^{3} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$14.20586437$ |
1.025219952 |
\( -\frac{14225792}{9} a + \frac{8213248}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -1\) , \( -4 a - 2\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}-{x}-4a-2$ |
| 3072.1-g2 |
3072.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{25} \cdot 3^{12} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.551466094$ |
1.025219952 |
\( \frac{217996}{729} a + \frac{1023628}{729} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -40 a - 56\) , \( 40 a + 72\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-40a-56\right){x}+40a+72$ |
| 3072.1-g3 |
3072.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{20} \cdot 3^{6} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$7.102932189$ |
1.025219952 |
\( \frac{770336}{27} a + \frac{1419904}{27} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -20 a - 36\) , \( -72 a - 120\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-20a-36\right){x}-72a-120$ |
| 3072.1-g4 |
3072.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{25} \cdot 3^{3} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$1.775733047$ |
1.025219952 |
\( \frac{26639622068}{9} a + \frac{15380474156}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -320 a - 576\) , \( -4296 a - 7464\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-320a-576\right){x}-4296a-7464$ |
| 3072.1-h1 |
3072.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{23} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.252849762$ |
1.300683416 |
\( -\frac{740855896}{3} a + \frac{1283201128}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 1312 a - 2272\) , \( 32872 a - 56936\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(1312a-2272\right){x}+32872a-56936$ |
| 3072.1-h2 |
3072.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{16} \cdot 3^{4} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$9.011399049$ |
1.300683416 |
\( -\frac{61952}{9} a + \frac{162688}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 82 a - 142\) , \( 448 a - 776\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(82a-142\right){x}+448a-776$ |
| 3072.1-h3 |
3072.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{23} \cdot 3^{8} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.505699524$ |
1.300683416 |
\( \frac{247496}{81} a + \frac{429112}{81} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -28 a + 48\) , \( 1836 a - 3180\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-28a+48\right){x}+1836a-3180$ |
| 3072.1-h4 |
3072.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{14} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$9.011399049$ |
1.300683416 |
\( \frac{24993664}{3} a + \frac{43299296}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 2 a - 9\) , \( -3 a + 3\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a-9\right){x}-3a+3$ |
| 3072.1-i1 |
3072.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{27} \cdot 3^{8} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.383075350$ |
2.751738390 |
\( -\frac{443186854}{81} a + \frac{767608522}{81} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 122 a - 225\) , \( 1074 a - 1797\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(122a-225\right){x}+1074a-1797$ |
| 3072.1-i2 |
3072.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{24} \cdot 3 \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$9.532301402$ |
2.751738390 |
\( -\frac{132636728}{3} a + 76579552 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 1500096 a - 2598240\) , \( -1316558104 a + 2280345528\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(1500096a-2598240\right){x}-1316558104a+2280345528$ |
| 3072.1-i3 |
3072.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{18} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$19.06460280$ |
2.751738390 |
\( -\frac{9856}{3} a + \frac{22336}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 95576 a - 165540\) , \( -19749120 a + 34206480\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(95576a-165540\right){x}-19749120a+34206480$ |
| 3072.1-i4 |
3072.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{18} \cdot 3 \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$9.532301402$ |
2.751738390 |
\( \frac{166016}{3} a + 95936 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -322420 a + 558448\) , \( -571215336 a + 989373984\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-322420a+558448\right){x}-571215336a+989373984$ |
| 3072.1-i5 |
3072.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{24} \cdot 3^{4} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$9.532301402$ |
2.751738390 |
\( \frac{1122088}{9} a + \frac{1989808}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 1612 a - 2792\) , \( 39276 a - 68028\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(1612a-2792\right){x}+39276a-68028$ |
| 3072.1-i6 |
3072.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{27} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.766150701$ |
2.751738390 |
\( \frac{164847992914}{3} a + \frac{285525100658}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -3308 a + 5728\) , \( 220380 a - 381708\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3308a+5728\right){x}+220380a-381708$ |
| 3072.1-j1 |
3072.1-j |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{25} \cdot 3^{12} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.551466094$ |
1.025219952 |
\( -\frac{217996}{729} a + \frac{1023628}{729} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 40 a - 56\) , \( -40 a + 72\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(40a-56\right){x}-40a+72$ |
| 3072.1-j2 |
3072.1-j |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{20} \cdot 3^{6} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$7.102932189$ |
1.025219952 |
\( -\frac{770336}{27} a + \frac{1419904}{27} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 20 a - 36\) , \( 72 a - 120\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(20a-36\right){x}+72a-120$ |
*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.
