| 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 |
$6$ |
$8$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{16} \) |
$2.31645$ |
$(-a+4), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$1$ |
$2.325279868$ |
2.485828742 |
\( \frac{207646}{6561} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 6\) , \( -18\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+6{x}-18$ |
| 144.1-a2 |
144.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$2.31645$ |
$(-a+4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$18.60223895$ |
2.485828742 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 80 a + 304\) , \( 832 a + 3115\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(80a+304\right){x}+832a+3115$ |
| 144.1-a3 |
144.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{4} \) |
$2.31645$ |
$(-a+4), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$37.20447790$ |
2.485828742 |
\( \frac{35152}{9} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+{x}$ |
| 144.1-a4 |
144.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$2.31645$ |
$(-a+4), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$9.301119475$ |
2.485828742 |
\( \frac{1556068}{81} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -4\) , \( -10\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-4{x}-10$ |
| 144.1-a5 |
144.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$2.31645$ |
$(-a+4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$37.20447790$ |
2.485828742 |
\( \frac{28756228}{3} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -14\) , \( 12\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-14{x}+12$ |
| 144.1-a6 |
144.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{4} \) |
$2.31645$ |
$(-a+4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$2.325279868$ |
2.485828742 |
\( \frac{3065617154}{9} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -94\) , \( -442\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-94{x}-442$ |
| 144.1-b1 |
144.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{8} \) |
$2.31645$ |
$(-a+4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.250940088$ |
1.136111527 |
\( \frac{4913}{1296} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 4 a + 21\) , \( -307 a - 1143\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(4a+21\right){x}-307a-1143$ |
| 144.1-b2 |
144.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{16} \) |
$2.31645$ |
$(-a+4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.250940088$ |
1.136111527 |
\( \frac{838561807}{26244} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -316 a - 1179\) , \( -5587 a - 20903\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-316a-1179\right){x}-5587a-20903$ |
| 144.1-c1 |
144.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{4} \) |
$2.31645$ |
$(-a+4), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.754271260$ |
$15.34840951$ |
3.598041044 |
\( \frac{2000}{9} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 4 a + 15\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(4a+15\right){x}$ |
| 144.1-c2 |
144.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$2.31645$ |
$(-a+4), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.877135630$ |
$15.34840951$ |
3.598041044 |
\( \frac{665500}{81} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -16 a - 60\) , \( -116 a - 434\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-16a-60\right){x}-116a-434$ |
| 144.1-d1 |
144.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$2.31645$ |
$(-a+4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$27.22014029$ |
1.818722125 |
\( \frac{16384}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -6 a - 15\) , \( -15 a - 60\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-6a-15\right){x}-15a-60$ |
| 144.1-d2 |
144.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{4} \) |
$2.31645$ |
$(-a+4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$27.22014029$ |
1.818722125 |
\( \frac{109744}{9} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 4 a - 22\) , \( 29 a - 112\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(4a-22\right){x}+29a-112$ |
| 144.1-e1 |
144.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{8} \) |
$2.31645$ |
$(-a+4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.250940088$ |
1.136111527 |
\( \frac{4913}{1296} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -4 a + 21\) , \( 307 a - 1143\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a+21\right){x}+307a-1143$ |
| 144.1-e2 |
144.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{16} \) |
$2.31645$ |
$(-a+4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.250940088$ |
1.136111527 |
\( \frac{838561807}{26244} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 316 a - 1179\) , \( 5587 a - 20903\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(316a-1179\right){x}+5587a-20903$ |
| 144.1-f1 |
144.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{16} \) |
$2.31645$ |
$(-a+4), (3)$ |
$2$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$2.592914450$ |
$5.683508517$ |
3.938589198 |
\( \frac{207646}{6561} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -467 a + 1770\) , \( -78662 a + 294347\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-467a+1770\right){x}-78662a+294347$ |
| 144.1-f2 |
144.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$2.31645$ |
$(-a+4), (3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$2.592914450$ |
$11.36701703$ |
3.938589198 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+{x}$ |
| 144.1-f3 |
144.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{4} \) |
$2.31645$ |
$(-a+4), (3)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$2.592914450$ |
$22.73403407$ |
3.938589198 |
\( \frac{35152}{9} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 133 a - 475\) , \( 1201 a - 4473\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(133a-475\right){x}+1201a-4473$ |
| 144.1-f4 |
144.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$2.31645$ |
$(-a+4), (3)$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$2.592914450$ |
$22.73403407$ |
3.938589198 |
\( \frac{1556068}{81} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -733 a - 2720\) , \( 19624 a + 73447\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-733a-2720\right){x}+19624a+73447$ |
| 144.1-f5 |
144.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$2.31645$ |
$(-a+4), (3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.592914450$ |
$5.683508517$ |
3.938589198 |
\( \frac{28756228}{3} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 1933 a - 7210\) , \( 89758 a - 335823\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(1933a-7210\right){x}+89758a-335823$ |
| 144.1-f6 |
144.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{4} \) |
$2.31645$ |
$(-a+4), (3)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.648228612$ |
$22.73403407$ |
3.938589198 |
\( \frac{3065617154}{9} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 11533 a - 43130\) , \( -1300666 a + 4866667\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(11533a-43130\right){x}-1300666a+4866667$ |
| 144.1-g1 |
144.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{4} \) |
$2.31645$ |
$(-a+4), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.754271260$ |
$15.34840951$ |
3.598041044 |
\( \frac{2000}{9} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -4 a + 15\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-4a+15\right){x}$ |
| 144.1-g2 |
144.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$2.31645$ |
$(-a+4), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.877135630$ |
$15.34840951$ |
3.598041044 |
\( \frac{665500}{81} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( 16 a - 60\) , \( 116 a - 434\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(16a-60\right){x}+116a-434$ |
| 144.1-h1 |
144.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$2.31645$ |
$(-a+4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$27.22014029$ |
1.818722125 |
\( \frac{16384}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 6 a - 15\) , \( 15 a - 60\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(6a-15\right){x}+15a-60$ |
| 144.1-h2 |
144.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{4} \) |
$2.31645$ |
$(-a+4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$27.22014029$ |
1.818722125 |
\( \frac{109744}{9} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -4 a - 22\) , \( -29 a - 112\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-4a-22\right){x}-29a-112$ |
*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.
