| 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 |
$4$ |
$10$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{20} \) |
$0.87554$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2 \) |
$1$ |
$5.977383695$ |
1.056662136 |
\( -\frac{873722816}{59049} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -160 a - 238\) , \( 1458 a + 2072\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-160a-238\right){x}+1458a+2072$ |
| 144.1-a2 |
144.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{4} \) |
$0.87554$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$5.977383695$ |
1.056662136 |
\( \frac{64}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2\) , \( -6 a - 8\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+2{x}-6a-8$ |
| 144.1-a3 |
144.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{2} \) |
$0.87554$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$11.95476739$ |
1.056662136 |
\( \frac{85184}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -8 a - 10\) , \( -14 a - 20\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-8a-10\right){x}-14a-20$ |
| 144.1-a4 |
144.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{10} \) |
$0.87554$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$11.95476739$ |
1.056662136 |
\( \frac{58591911104}{243} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -648 a - 970\) , \( 10986 a + 15740\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-648a-970\right){x}+10986a+15740$ |
| 144.1-b1 |
144.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{11} \cdot 3^{2} \) |
$0.87554$ |
$(a), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$11.36701703$ |
1.004711853 |
\( -\frac{123062343233293457}{3} a + 58012144939294440 \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 510 a - 817\) , \( -7986 a + 11650\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(510a-817\right){x}-7986a+11650$ |
| 144.1-b2 |
144.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{16} \) |
$0.87554$ |
$(a), (3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$5.683508517$ |
1.004711853 |
\( \frac{207646}{6561} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 3\) , \( 22\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+3{x}+22$ |
| 144.1-b3 |
144.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$0.87554$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$11.36701703$ |
1.004711853 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+{x}$ |
| 144.1-b4 |
144.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{4} \) |
$0.87554$ |
$(a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$22.73403407$ |
1.004711853 |
\( \frac{35152}{9} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -2\) , \( -1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-2{x}-1$ |
| 144.1-b5 |
144.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$0.87554$ |
$(a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$22.73403407$ |
1.004711853 |
\( \frac{1556068}{81} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -7\) , \( 4\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-7{x}+4$ |
| 144.1-b6 |
144.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$0.87554$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$5.683508517$ |
1.004711853 |
\( \frac{28756228}{3} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -17\) , \( -28\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-17{x}-28$ |
| 144.1-b7 |
144.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{4} \) |
$0.87554$ |
$(a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$22.73403407$ |
1.004711853 |
\( \frac{3065617154}{9} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -97\) , \( 346\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-97{x}+346$ |
| 144.1-b8 |
144.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{11} \cdot 3^{2} \) |
$0.87554$ |
$(a), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$11.36701703$ |
1.004711853 |
\( \frac{123062343233293457}{3} a + 58012144939294440 \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -510 a - 817\) , \( 7986 a + 11650\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-510a-817\right){x}+7986a+11650$ |
*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.
