| 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 |
| 144.1-a1 |
144.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{10} \cdot 3^{7} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.098868579$ |
1.211782339 |
\( -\frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 209 a - 410\) , \( 2494 a - 4159\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(209a-410\right){x}+2494a-4159$ |
| 144.1-a2 |
144.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{22} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.098868579$ |
1.211782339 |
\( \frac{207646}{6561} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -a + 10\) , \( -68 a - 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a+10\right){x}-68a-1$ |
| 144.1-a3 |
144.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$8.395474317$ |
1.211782339 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 8 a + 15\) , \( 25 a + 43\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(8a+15\right){x}+25a+43$ |
| 144.1-a4 |
144.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{10} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$16.79094863$ |
1.211782339 |
\( \frac{35152}{9} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -a - 5\) , \( a - 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-5\right){x}+a-1$ |
| 144.1-a5 |
144.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{14} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$8.395474317$ |
1.211782339 |
\( \frac{1556068}{81} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -a - 20\) , \( -14 a - 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-20\right){x}-14a-1$ |
| 144.1-a6 |
144.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$8.395474317$ |
1.211782339 |
\( \frac{28756228}{3} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -a - 50\) , \( 82 a - 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-50\right){x}+82a-1$ |
| 144.1-a7 |
144.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{10} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.197737158$ |
1.211782339 |
\( \frac{3065617154}{9} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -a - 290\) , \( -1040 a - 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-290\right){x}-1040a-1$ |
| 144.1-a8 |
144.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{10} \cdot 3^{7} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$4.197737158$ |
1.211782339 |
\( \frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -211 a - 410\) , \( 2494 a + 4157\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-211a-410\right){x}+2494a+4157$ |
| 144.1-b1 |
144.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{3} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-36$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$8.530775105$ |
1.231311325 |
\( -44330496 a + 76771008 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 34 a - 60\) , \( -126 a + 218\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(34a-60\right){x}-126a+218$ |
| 144.1-b2 |
144.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{3} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-36$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$8.530775105$ |
1.231311325 |
\( -44330496 a + 76771008 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 34 a - 60\) , \( 126 a - 218\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(34a-60\right){x}+126a-218$ |
| 144.1-b3 |
144.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{9} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 2 \) |
$1$ |
$8.530775105$ |
1.231311325 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -6 a - 9\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-6a-9\right){x}$ |
| 144.1-b4 |
144.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{9} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 2 \) |
$1$ |
$8.530775105$ |
1.231311325 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 6 a - 9\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(6a-9\right){x}$ |
| 144.1-b5 |
144.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{3} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-36$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$8.530775105$ |
1.231311325 |
\( 44330496 a + 76771008 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -34 a - 60\) , \( -126 a - 218\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-34a-60\right){x}-126a-218$ |
| 144.1-b6 |
144.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{3} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-36$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$8.530775105$ |
1.231311325 |
\( 44330496 a + 76771008 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -34 a - 60\) , \( 126 a + 218\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-34a-60\right){x}+126a+218$ |
| 144.1-c1 |
144.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{10} \cdot 3^{7} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$4.197737158$ |
1.211782339 |
\( -\frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 43232 a - 74880\) , \( -6451984 a + 11175164\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(43232a-74880\right){x}-6451984a+11175164$ |
| 144.1-c2 |
144.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{22} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.098868579$ |
1.211782339 |
\( \frac{207646}{6561} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -658 a + 1140\) , \( 88718 a - 153664\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-658a+1140\right){x}+88718a-153664$ |
| 144.1-c3 |
144.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$8.395474317$ |
1.211782339 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -8 a + 15\) , \( -25 a + 43\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-8a+15\right){x}-25a+43$ |
| 144.1-c4 |
144.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{10} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$16.79094863$ |
1.211782339 |
\( \frac{35152}{9} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 182 a - 315\) , \( -1366 a + 2366\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(182a-315\right){x}-1366a+2366$ |
| 144.1-c5 |
144.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{14} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$8.395474317$ |
1.211782339 |
\( \frac{1556068}{81} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 1022 a - 1770\) , \( 22034 a - 38164\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(1022a-1770\right){x}+22034a-38164$ |
| 144.1-c6 |
144.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$8.395474317$ |
1.211782339 |
\( \frac{28756228}{3} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 2702 a - 4680\) , \( -101392 a + 175616\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(2702a-4680\right){x}-101392a+175616$ |
| 144.1-c7 |
144.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{10} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.197737158$ |
1.211782339 |
\( \frac{3065617154}{9} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 16142 a - 27960\) , \( 1464590 a - 2536744\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(16142a-27960\right){x}+1464590a-2536744$ |
| 144.1-c8 |
144.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{10} \cdot 3^{7} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.098868579$ |
1.211782339 |
\( \frac{79558124472974}{3} a + 45932904578280 \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 2492 a - 4320\) , \( -117544 a + 203588\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(2492a-4320\right){x}-117544a+203588$ |
*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.
