| 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 |
| 144.4-a1 |
144.4-a |
$2$ |
$5$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
144.4 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{10} \) |
$1.27630$ |
$(-a+2), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 5 \) |
$1$ |
$2.295286137$ |
2.783443290 |
\( -\frac{13549359104}{243} \) |
\( \bigl[0\) , \( -a - 1\) , \( a\) , \( 1938 a - 4965\) , \( -66328 a + 169901\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1938a-4965\right){x}-66328a+169901$ |
| 144.4-a2 |
144.4-a |
$2$ |
$5$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
144.4 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{2} \) |
$1.27630$ |
$(-a+2), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$11.47643068$ |
2.783443290 |
\( \frac{4096}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( a\) , \( -12 a + 35\) , \( -22 a + 53\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-12a+35\right){x}-22a+53$ |
| 144.4-b1 |
144.4-b |
$1$ |
$1$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
144.4 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{6} \) |
$1.27630$ |
$(-a+2), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$11.39664962$ |
2.764093541 |
\( -\frac{80896}{9} a - \frac{388096}{27} \) |
\( \bigl[0\) , \( -a + 1\) , \( a\) , \( -1\) , \( 2 a - 5\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a+1\right){x}^{2}-{x}+2a-5$ |
| 144.4-c1 |
144.4-c |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
144.4 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{2} \) |
$1.27630$ |
$(-a+2), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$25.59440343$ |
0.775944329 |
\( -\frac{396321250}{3} a + 338397375 \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 117 a - 300\) , \( -876 a + 2244\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(117a-300\right){x}-876a+2244$ |
| 144.4-c2 |
144.4-c |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
144.4 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{2} \) |
$1.27630$ |
$(-a+2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$1.599650214$ |
0.775944329 |
\( -\frac{31564213125250}{3} a + \frac{80853398915125}{3} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 80 a - 192\) , \( 523 a - 1360\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(80a-192\right){x}+523a-1360$ |
| 144.4-c3 |
144.4-c |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
144.4 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{16} \) |
$1.27630$ |
$(-a+2), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$3.199300429$ |
0.775944329 |
\( \frac{5359375}{6561} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -142 a + 365\) , \( 1372 a - 3514\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-142a+365\right){x}+1372a-3514$ |
| 144.4-c4 |
144.4-c |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
144.4 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{8} \) |
$1.27630$ |
$(-a+2), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$12.79720171$ |
0.775944329 |
\( \frac{274625}{81} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 53 a - 135\) , \( 221 a - 566\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(53a-135\right){x}+221a-566$ |
| 144.4-c5 |
144.4-c |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
144.4 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{4} \) |
$1.27630$ |
$(-a+2), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$6.398600858$ |
0.775944329 |
\( -\frac{14326000}{9} a + \frac{36913625}{9} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 5 a - 12\) , \( 4 a - 28\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(5a-12\right){x}+4a-28$ |
| 144.4-c6 |
144.4-c |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
144.4 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{4} \) |
$1.27630$ |
$(-a+2), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$25.59440343$ |
0.775944329 |
\( \frac{14326000}{9} a + \frac{22587625}{9} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -13 a - 23\) , \( 40 a + 62\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-13a-23\right){x}+40a+62$ |
| 144.4-c7 |
144.4-c |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
144.4 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{2} \) |
$1.27630$ |
$(-a+2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.199300429$ |
0.775944329 |
\( \frac{396321250}{3} a + \frac{618870875}{3} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 117 a - 303\) , \( 1468 a - 3762\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(117a-303\right){x}+1468a-3762$ |
| 144.4-c8 |
144.4-c |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
144.4 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{2} \) |
$1.27630$ |
$(-a+2), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$12.79720171$ |
0.775944329 |
\( \frac{31564213125250}{3} a + 16429728596625 \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -208 a - 323\) , \( 2386 a + 3734\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-208a-323\right){x}+2386a+3734$ |
| 144.4-d1 |
144.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
144.4 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{13} \cdot 3^{16} \) |
$1.27630$ |
$(-a+2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.917668247$ |
$2.510307630$ |
2.234848983 |
\( -\frac{150435795683}{4374} a + \frac{1155932622647}{13122} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 741 a - 1903\) , \( -16047 a + 41078\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(741a-1903\right){x}-16047a+41078$ |
| 144.4-d2 |
144.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
144.4 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{14} \cdot 3^{2} \) |
$1.27630$ |
$(-a+2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.835336495$ |
$5.020615261$ |
2.234848983 |
\( -\frac{59090945}{12} a + \frac{151366337}{12} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 6 a + 8\) , \( -33 a - 52\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(6a+8\right){x}-33a-52$ |
| 144.4-d3 |
144.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
144.4 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{20} \cdot 3^{2} \) |
$1.27630$ |
$(-a+2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.458834123$ |
$10.04123052$ |
2.234848983 |
\( \frac{1095125}{768} a + \frac{2055079}{768} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -6 a - 8\) , \( 5 a + 8\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-6a-8\right){x}+5a+8$ |
| 144.4-d4 |
144.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
144.4 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{4} \) |
$1.27630$ |
$(-a+2), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.917668247$ |
$10.04123052$ |
2.234848983 |
\( \frac{173375}{144} a + \frac{1033157}{144} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 11 a - 23\) , \( 17 a - 42\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(11a-23\right){x}+17a-42$ |
| 144.4-d5 |
144.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
144.4 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{8} \) |
$1.27630$ |
$(-a+2), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.835336495$ |
$5.020615261$ |
2.234848983 |
\( \frac{2360605505}{108} a + \frac{11062735109}{324} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 46 a - 123\) , \( -258 a + 634\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(46a-123\right){x}-258a+634$ |
| 144.4-d6 |
144.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
144.4 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{13} \cdot 3^{4} \) |
$1.27630$ |
$(-a+2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.670672990$ |
$1.255153815$ |
2.234848983 |
\( \frac{35465918197138001}{18} a + \frac{55381904319590417}{18} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -89 a + 57\) , \( -1329 a + 2254\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-89a+57\right){x}-1329a+2254$ |
| 144.4-e1 |
144.4-e |
$1$ |
$1$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
144.4 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$1.27630$ |
$(-a+2), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.035029694$ |
$31.07619611$ |
1.056087100 |
\( 77824 a - \frac{598016}{3} \) |
\( \bigl[0\) , \( -a\) , \( a\) , \( 4 a - 8\) , \( -4 a + 8\bigr] \) |
${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(4a-8\right){x}-4a+8$ |
*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.
