| 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 |
| 28899.2-a1 |
28899.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.2 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{6} \cdot 13^{8} \cdot 19^{3} \) |
$2.01799$ |
$(-2a+1), (-4a+1), (-5a+2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.913350368$ |
$0.693472547$ |
2.925472642 |
\( \frac{1360395}{6859} a - \frac{2060262}{6859} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 7 a + 49\) , \( -417 a + 387\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(7a+49\right){x}-417a+387$ |
| 28899.2-a2 |
28899.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.2 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{6} \cdot 13^{8} \cdot 19 \) |
$2.01799$ |
$(-2a+1), (-4a+1), (-5a+2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2 \cdot 3 \) |
$2.740051104$ |
$0.693472547$ |
2.925472642 |
\( \frac{23602023}{19} a + \frac{942327}{19} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 322 a - 351\) , \( 2660 a - 1547\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(322a-351\right){x}+2660a-1547$ |
| 28899.2-b1 |
28899.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.2 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{6} \cdot 13^{2} \cdot 19^{3} \) |
$2.01799$ |
$(-2a+1), (-4a+1), (-5a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \cdot 3 \) |
$0.096264587$ |
$2.500350828$ |
3.335171099 |
\( \frac{1360395}{6859} a - \frac{2060262}{6859} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3 a - 2\) , \( -9 a + 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-3a-2\right){x}-9a+3$ |
| 28899.2-b2 |
28899.2-b |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.2 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{6} \cdot 13^{2} \cdot 19 \) |
$2.01799$ |
$(-2a+1), (-4a+1), (-5a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \) |
$0.288793763$ |
$2.500350828$ |
3.335171099 |
\( \frac{23602023}{19} a + \frac{942327}{19} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -12 a + 30\) , \( 51 a - 2\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-12a+30\right){x}+51a-2$ |
| 28899.2-c1 |
28899.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.2 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{3} \cdot 13^{6} \cdot 19^{2} \) |
$2.01799$ |
$(-2a+1), (-4a+1), (-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$1.128733439$ |
2.606698220 |
\( \frac{363527109}{361} a - \frac{76135923}{361} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -118 a - 7\) , \( 564 a - 231\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-118a-7\right){x}+564a-231$ |
| 28899.2-c2 |
28899.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.2 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{9} \cdot 13^{6} \cdot 19^{6} \) |
$2.01799$ |
$(-2a+1), (-4a+1), (-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.376244479$ |
2.606698220 |
\( \frac{36038181633}{47045881} a - \frac{75585143946}{47045881} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -243 a + 333\) , \( 1743 a + 1720\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-243a+333\right){x}+1743a+1720$ |
| 28899.2-c3 |
28899.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.2 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{9} \cdot 13^{6} \cdot 19^{3} \) |
$2.01799$ |
$(-2a+1), (-4a+1), (-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.752488959$ |
2.606698220 |
\( -\frac{29840721}{6859} a - \frac{5426511}{6859} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 102 a + 3\) , \( -54 a + 463\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(102a+3\right){x}-54a+463$ |
| 28899.2-c4 |
28899.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.2 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{3} \cdot 13^{6} \cdot 19 \) |
$2.01799$ |
$(-2a+1), (-4a+1), (-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$2.257466878$ |
2.606698220 |
\( \frac{9153}{19} a + \frac{27648}{19} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -8 a - 2\) , \( 3 a - 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-8a-2\right){x}+3a-3$ |
*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.
