| 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 |
| 106875.2-a1 |
106875.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
106875.2 |
\( 3^{2} \cdot 5^{4} \cdot 19 \) |
\( 3^{3} \cdot 5^{12} \cdot 19^{2} \) |
$2.79845$ |
$(-2a+1), (-5a+2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$0.813941258$ |
1.879716818 |
\( \frac{363527109}{361} a - \frac{76135923}{361} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 269 a - 133\) , \( 1143 a + 366\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(269a-133\right){x}+1143a+366$ |
| 106875.2-a2 |
106875.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
106875.2 |
\( 3^{2} \cdot 5^{4} \cdot 19 \) |
\( 3^{9} \cdot 5^{12} \cdot 19^{6} \) |
$2.79845$ |
$(-2a+1), (-5a+2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.271313752$ |
1.879716818 |
\( \frac{36038181633}{47045881} a - \frac{75585143946}{47045881} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 144 a - 633\) , \( -1857 a + 8491\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(144a-633\right){x}-1857a+8491$ |
| 106875.2-a3 |
106875.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
106875.2 |
\( 3^{2} \cdot 5^{4} \cdot 19 \) |
\( 3^{9} \cdot 5^{12} \cdot 19^{3} \) |
$2.79845$ |
$(-2a+1), (-5a+2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.542627505$ |
1.879716818 |
\( -\frac{29840721}{6859} a - \frac{5426511}{6859} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -231 a + 117\) , \( -1107 a + 1366\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-231a+117\right){x}-1107a+1366$ |
| 106875.2-a4 |
106875.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
106875.2 |
\( 3^{2} \cdot 5^{4} \cdot 19 \) |
\( 3^{3} \cdot 5^{12} \cdot 19 \) |
$2.79845$ |
$(-2a+1), (-5a+2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1.627882516$ |
1.879716818 |
\( \frac{9153}{19} a + \frac{27648}{19} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 19 a - 8\) , \( 18 a - 9\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(19a-8\right){x}+18a-9$ |
| 106875.2-b1 |
106875.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
106875.2 |
\( 3^{2} \cdot 5^{4} \cdot 19 \) |
\( 3^{14} \cdot 5^{6} \cdot 19^{4} \) |
$2.79845$ |
$(-2a+1), (-5a+2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.730221149$ |
$0.636163028$ |
4.291233917 |
\( -\frac{2002212455}{10556001} a + \frac{7086162301}{3518667} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -106 a - 25\) , \( -222 a + 33\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-106a-25\right){x}-222a+33$ |
| 106875.2-b2 |
106875.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
106875.2 |
\( 3^{2} \cdot 5^{4} \cdot 19 \) |
\( 3^{22} \cdot 5^{6} \cdot 19^{2} \) |
$2.79845$ |
$(-2a+1), (-5a+2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.460442298$ |
$0.318081514$ |
4.291233917 |
\( -\frac{1149208785995}{2368521} a + \frac{2642092022288}{2368521} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -1306 a - 400\) , \( -26022 a + 5508\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-1306a-400\right){x}-26022a+5508$ |
| 106875.2-c1 |
106875.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
106875.2 |
\( 3^{2} \cdot 5^{4} \cdot 19 \) |
\( 3^{14} \cdot 5^{18} \cdot 19^{4} \) |
$2.79845$ |
$(-2a+1), (-5a+2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$4.583905005$ |
$0.127232605$ |
5.387575708 |
\( -\frac{2002212455}{10556001} a + \frac{7086162301}{3518667} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -625 a + 3257\) , \( -21137 a - 1137\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-625a+3257\right){x}-21137a-1137$ |
| 106875.2-c2 |
106875.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
106875.2 |
\( 3^{2} \cdot 5^{4} \cdot 19 \) |
\( 3^{22} \cdot 5^{18} \cdot 19^{2} \) |
$2.79845$ |
$(-2a+1), (-5a+2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$9.167810010$ |
$0.063616302$ |
5.387575708 |
\( -\frac{1149208785995}{2368521} a + \frac{2642092022288}{2368521} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -10000 a + 42632\) , \( -3167387 a + 623238\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-10000a+42632\right){x}-3167387a+623238$ |
| 106875.2-d1 |
106875.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
106875.2 |
\( 3^{2} \cdot 5^{4} \cdot 19 \) |
\( 3^{6} \cdot 5^{14} \cdot 19^{2} \) |
$2.79845$ |
$(-2a+1), (-5a+2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.709887492$ |
3.278829880 |
\( -\frac{4364943}{1805} a + \frac{1764899}{361} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -75 a + 132\) , \( 238 a + 263\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-75a+132\right){x}+238a+263$ |
| 106875.2-d2 |
106875.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
106875.2 |
\( 3^{2} \cdot 5^{4} \cdot 19 \) |
\( 3^{6} \cdot 5^{16} \cdot 19 \) |
$2.79845$ |
$(-2a+1), (-5a+2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.354943746$ |
3.278829880 |
\( -\frac{6750142089}{475} a + \frac{5194027514}{475} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( -1200 a + 2007\) , \( 18988 a + 14138\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-1200a+2007\right){x}+18988a+14138$ |
*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.
