| 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 |
| 28899.5-a1 |
28899.5-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.5 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{6} \cdot 13^{8} \cdot 19^{3} \) |
$2.01799$ |
$(-2a+1), (4a-3), (-5a+3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.913350368$ |
$0.693472547$ |
2.925472642 |
\( -\frac{1360395}{6859} a - \frac{699867}{6859} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -50 a - 7\) , \( 416 a - 29\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-50a-7\right){x}+416a-29$ |
| 28899.5-a2 |
28899.5-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.5 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{6} \cdot 13^{8} \cdot 19 \) |
$2.01799$ |
$(-2a+1), (4a-3), (-5a+3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2 \cdot 3 \) |
$2.740051104$ |
$0.693472547$ |
2.925472642 |
\( -\frac{23602023}{19} a + \frac{24544350}{19} \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 350 a - 322\) , \( -2661 a + 1113\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(350a-322\right){x}-2661a+1113$ |
| 28899.5-b1 |
28899.5-b |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.5 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{6} \cdot 13^{2} \cdot 19^{3} \) |
$2.01799$ |
$(-2a+1), (4a-3), (-5a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \cdot 3 \) |
$0.096264587$ |
$2.500350828$ |
3.335171099 |
\( -\frac{1360395}{6859} a - \frac{699867}{6859} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( a + 3\) , \( 9 a - 6\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(a+3\right){x}+9a-6$ |
| 28899.5-b2 |
28899.5-b |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.5 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{6} \cdot 13^{2} \cdot 19 \) |
$2.01799$ |
$(-2a+1), (4a-3), (-5a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \) |
$0.288793763$ |
$2.500350828$ |
3.335171099 |
\( -\frac{23602023}{19} a + \frac{24544350}{19} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -30 a + 12\) , \( -51 a + 49\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-30a+12\right){x}-51a+49$ |
| 28899.5-c1 |
28899.5-c |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.5 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{9} \cdot 13^{6} \cdot 19^{3} \) |
$2.01799$ |
$(-2a+1), (4a-3), (-5a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.752488959$ |
2.606698220 |
\( \frac{29840721}{6859} a - \frac{35267232}{6859} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -3 a - 102\) , \( 54 a + 409\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-3a-102\right){x}+54a+409$ |
| 28899.5-c2 |
28899.5-c |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.5 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{9} \cdot 13^{6} \cdot 19^{6} \) |
$2.01799$ |
$(-2a+1), (4a-3), (-5a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.376244479$ |
2.606698220 |
\( -\frac{36038181633}{47045881} a - \frac{39546962313}{47045881} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -333 a + 243\) , \( -1743 a + 3463\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-333a+243\right){x}-1743a+3463$ |
| 28899.5-c3 |
28899.5-c |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.5 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{3} \cdot 13^{6} \cdot 19 \) |
$2.01799$ |
$(-2a+1), (4a-3), (-5a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$2.257466878$ |
2.606698220 |
\( -\frac{9153}{19} a + \frac{36801}{19} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 2 a + 8\) , \( -3 a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(2a+8\right){x}-3a$ |
| 28899.5-c4 |
28899.5-c |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.5 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{3} \cdot 13^{6} \cdot 19^{2} \) |
$2.01799$ |
$(-2a+1), (4a-3), (-5a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$1.128733439$ |
2.606698220 |
\( -\frac{363527109}{361} a + \frac{287391186}{361} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 7 a + 118\) , \( -564 a + 333\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(7a+118\right){x}-564a+333$ |
*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.
