| 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 |
| 106875.1-a1 |
106875.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
106875.1 |
\( 3^{2} \cdot 5^{4} \cdot 19 \) |
\( 3^{9} \cdot 5^{12} \cdot 19^{3} \) |
$2.79845$ |
$(-2a+1), (-5a+3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.542627505$ |
1.879716818 |
\( \frac{29840721}{6859} a - \frac{35267232}{6859} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -113 a - 117\) , \( 1106 a + 260\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-113a-117\right){x}+1106a+260$ |
| 106875.1-a2 |
106875.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
106875.1 |
\( 3^{2} \cdot 5^{4} \cdot 19 \) |
\( 3^{9} \cdot 5^{12} \cdot 19^{6} \) |
$2.79845$ |
$(-2a+1), (-5a+3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.271313752$ |
1.879716818 |
\( -\frac{36038181633}{47045881} a - \frac{39546962313}{47045881} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -488 a + 633\) , \( 1856 a + 6635\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-488a+633\right){x}+1856a+6635$ |
| 106875.1-a3 |
106875.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
106875.1 |
\( 3^{2} \cdot 5^{4} \cdot 19 \) |
\( 3^{3} \cdot 5^{12} \cdot 19 \) |
$2.79845$ |
$(-2a+1), (-5a+3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1.627882516$ |
1.879716818 |
\( -\frac{9153}{19} a + \frac{36801}{19} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 12 a + 8\) , \( -19 a + 10\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(12a+8\right){x}-19a+10$ |
| 106875.1-a4 |
106875.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
106875.1 |
\( 3^{2} \cdot 5^{4} \cdot 19 \) |
\( 3^{3} \cdot 5^{12} \cdot 19^{2} \) |
$2.79845$ |
$(-2a+1), (-5a+3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$0.813941258$ |
1.879716818 |
\( -\frac{363527109}{361} a + \frac{287391186}{361} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 137 a + 133\) , \( -1144 a + 1510\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(137a+133\right){x}-1144a+1510$ |
| 106875.1-b1 |
106875.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
106875.1 |
\( 3^{2} \cdot 5^{4} \cdot 19 \) |
\( 3^{14} \cdot 5^{6} \cdot 19^{4} \) |
$2.79845$ |
$(-2a+1), (-5a+3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.730221149$ |
$0.636163028$ |
4.291233917 |
\( \frac{2002212455}{10556001} a + \frac{19256274448}{10556001} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -131 a + 26\) , \( 221 a - 188\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-131a+26\right){x}+221a-188$ |
| 106875.1-b2 |
106875.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
106875.1 |
\( 3^{2} \cdot 5^{4} \cdot 19 \) |
\( 3^{22} \cdot 5^{6} \cdot 19^{2} \) |
$2.79845$ |
$(-2a+1), (-5a+3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.460442298$ |
$0.318081514$ |
4.291233917 |
\( \frac{1149208785995}{2368521} a + \frac{497627745431}{789507} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -1706 a + 401\) , \( 26021 a - 20513\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-1706a+401\right){x}+26021a-20513$ |
| 106875.1-c1 |
106875.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
106875.1 |
\( 3^{2} \cdot 5^{4} \cdot 19 \) |
\( 3^{6} \cdot 5^{16} \cdot 19 \) |
$2.79845$ |
$(-2a+1), (-5a+3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.354943746$ |
3.278829880 |
\( \frac{6750142089}{475} a - \frac{62244583}{19} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -2008 a + 1200\) , \( -18989 a + 33127\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-2008a+1200\right){x}-18989a+33127$ |
| 106875.1-c2 |
106875.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
106875.1 |
\( 3^{2} \cdot 5^{4} \cdot 19 \) |
\( 3^{6} \cdot 5^{14} \cdot 19^{2} \) |
$2.79845$ |
$(-2a+1), (-5a+3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.709887492$ |
3.278829880 |
\( \frac{4364943}{1805} a + \frac{4459552}{1805} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -133 a + 75\) , \( -239 a + 502\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-133a+75\right){x}-239a+502$ |
| 106875.1-d1 |
106875.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
106875.1 |
\( 3^{2} \cdot 5^{4} \cdot 19 \) |
\( 3^{14} \cdot 5^{18} \cdot 19^{4} \) |
$2.79845$ |
$(-2a+1), (-5a+3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$4.583905005$ |
$0.127232605$ |
5.387575708 |
\( \frac{2002212455}{10556001} a + \frac{19256274448}{10556001} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 624 a + 2633\) , \( 21136 a - 22273\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(624a+2633\right){x}+21136a-22273$ |
| 106875.1-d2 |
106875.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
106875.1 |
\( 3^{2} \cdot 5^{4} \cdot 19 \) |
\( 3^{22} \cdot 5^{18} \cdot 19^{2} \) |
$2.79845$ |
$(-2a+1), (-5a+3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$9.167810010$ |
$0.063616302$ |
5.387575708 |
\( \frac{1149208785995}{2368521} a + \frac{497627745431}{789507} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 9999 a + 32633\) , \( 3167386 a - 2544148\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(9999a+32633\right){x}+3167386a-2544148$ |
*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.
