| 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 |
| 28899.1-a1 |
28899.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.1 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{7} \cdot 13^{4} \cdot 19 \) |
$2.01799$ |
$(-2a+1), (-4a+1), (-5a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.081331887$ |
$2.428644925$ |
2.737004353 |
\( -\frac{21416}{57} a + \frac{38803}{57} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 6 a - 5\) , \( a + 5\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(6a-5\right){x}+a+5$ |
| 28899.1-b1 |
28899.1-b |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.1 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{9} \cdot 13^{2} \cdot 19^{7} \) |
$2.01799$ |
$(-2a+1), (-4a+1), (-5a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$7$ |
7B |
$1$ |
\( 2 \) |
$1$ |
$0.558756646$ |
1.290393201 |
\( \frac{136071228608512}{8044845651} a - \frac{639859178651648}{8044845651} \) |
\( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( 6 a + 327\) , \( -2577 a + 1503\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6a+327\right){x}-2577a+1503$ |
| 28899.1-b2 |
28899.1-b |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.1 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{27} \cdot 13^{2} \cdot 19 \) |
$2.01799$ |
$(-2a+1), (-4a+1), (-5a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$7$ |
7B |
$1$ |
\( 2 \) |
$1$ |
$0.558756646$ |
1.290393201 |
\( \frac{13731074048}{3365793} a + \frac{6137028608}{3365793} \) |
\( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( -21 a - 183\) , \( 231 a + 684\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-21a-183\right){x}+231a+684$ |
| 28899.1-c1 |
28899.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.1 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{3} \cdot 13^{2} \cdot 19 \) |
$2.01799$ |
$(-2a+1), (-4a+1), (-5a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.132925583$ |
$4.673261579$ |
2.869181529 |
\( \frac{356352}{19} a - \frac{49152}{19} \) |
\( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( -2 a + 4\) , \( 4\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a+4\right){x}+4$ |
| 28899.1-d1 |
28899.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.1 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{9} \cdot 13^{6} \cdot 19^{3} \) |
$2.01799$ |
$(-2a+1), (-4a+1), (-5a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$0.870555393$ |
$0.752488959$ |
3.025700258 |
\( \frac{29840721}{6859} a - \frac{35267232}{6859} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -6 a + 106\) , \( 525 a - 306\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-6a+106\right){x}+525a-306$ |
| 28899.1-d2 |
28899.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.1 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{9} \cdot 13^{6} \cdot 19^{6} \) |
$2.01799$ |
$(-2a+1), (-4a+1), (-5a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1.741110786$ |
$0.376244479$ |
3.025700258 |
\( -\frac{36038181633}{47045881} a - \frac{39546962313}{47045881} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 339 a - 224\) , \( 2607 a + 480\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(339a-224\right){x}+2607a+480$ |
| 28899.1-d3 |
28899.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.1 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{3} \cdot 13^{6} \cdot 19 \) |
$2.01799$ |
$(-2a+1), (-4a+1), (-5a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$0.290185131$ |
$2.257466878$ |
3.025700258 |
\( -\frac{9153}{19} a + \frac{36801}{19} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -a - 9\) , \( -3 a + 8\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-a-9\right){x}-3a+8$ |
| 28899.1-d4 |
28899.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.1 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{3} \cdot 13^{6} \cdot 19^{2} \) |
$2.01799$ |
$(-2a+1), (-4a+1), (-5a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$0.580370262$ |
$1.128733439$ |
3.025700258 |
\( -\frac{363527109}{361} a + \frac{287391186}{361} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 4 a - 124\) , \( -27 a + 560\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(4a-124\right){x}-27a+560$ |
| 28899.1-e1 |
28899.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.1 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{12} \cdot 13^{7} \cdot 19^{2} \) |
$2.01799$ |
$(-2a+1), (-4a+1), (-5a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.430211573$ |
1.987062140 |
\( \frac{40051011701}{126711} a - \frac{59299218065}{126711} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 836 a - 586\) , \( -7991 a + 393\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(836a-586\right){x}-7991a+393$ |
| 28899.1-e2 |
28899.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.1 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{9} \cdot 13^{8} \cdot 19 \) |
$2.01799$ |
$(-2a+1), (-4a+1), (-5a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.860423146$ |
1.987062140 |
\( -\frac{11728499}{28899} a + \frac{16628104}{28899} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 41 a - 46\) , \( -122 a - 102\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(41a-46\right){x}-122a-102$ |
| 28899.1-f1 |
28899.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.1 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{3} \cdot 13^{14} \cdot 19 \) |
$2.01799$ |
$(-2a+1), (-4a+1), (-5a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.567123205$ |
$0.304930389$ |
3.615570049 |
\( \frac{925514327675409}{15498883699} a + \frac{1876332936777504}{15498883699} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -169 a + 1346\) , \( -19095 a + 7440\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-169a+1346\right){x}-19095a+7440$ |
| 28899.1-f2 |
28899.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.1 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{3} \cdot 13^{10} \cdot 19^{2} \) |
$2.01799$ |
$(-2a+1), (-4a+1), (-5a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$5.134246410$ |
$0.152465194$ |
3.615570049 |
\( \frac{184924137783523683}{10310521} a + \frac{112490548570162299}{10310521} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -2699 a + 21511\) , \( -1255884 a + 449949\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2699a+21511\right){x}-1255884a+449949$ |
| 28899.1-g1 |
28899.1-g |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.1 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{9} \cdot 13^{8} \cdot 19^{7} \) |
$2.01799$ |
$(-2a+1), (-4a+1), (-5a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$7$ |
7B |
$1$ |
\( 2^{2} \cdot 7 \) |
$0.325082426$ |
$0.154971210$ |
3.257631187 |
\( \frac{136071228608512}{8044845651} a - \frac{639859178651648}{8044845651} \) |
\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( 2365 a + 2581\) , \( -94696 a + 120453\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2365a+2581\right){x}-94696a+120453$ |
| 28899.1-g2 |
28899.1-g |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.1 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{27} \cdot 13^{8} \cdot 19 \) |
$2.01799$ |
$(-2a+1), (-4a+1), (-5a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$7$ |
7B |
$1$ |
\( 2^{2} \) |
$2.275576984$ |
$0.154971210$ |
3.257631187 |
\( \frac{13731074048}{3365793} a + \frac{6137028608}{3365793} \) |
\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( -1610 a - 1310\) , \( 44351 a + 1383\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1610a-1310\right){x}+44351a+1383$ |
| 28899.1-h1 |
28899.1-h |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.1 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{3} \cdot 13^{8} \cdot 19 \) |
$2.01799$ |
$(-2a+1), (-4a+1), (-5a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$1.296129557$ |
2.993282995 |
\( \frac{356352}{19} a - \frac{49152}{19} \) |
\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( -16 a + 53\) , \( 120 a - 36\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-16a+53\right){x}+120a-36$ |
| 28899.1-i1 |
28899.1-i |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.1 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{7} \cdot 13^{10} \cdot 19 \) |
$2.01799$ |
$(-2a+1), (-4a+1), (-5a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$0.673584908$ |
3.111155425 |
\( -\frac{21416}{57} a + \frac{38803}{57} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( -84 a + 26\) , \( 349 a + 67\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-84a+26\right){x}+349a+67$ |
*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.
