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 |
171.2-a2 |
171.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
171.2 |
\( 3^{2} \cdot 19 \) |
\( 3^{9} \cdot 19^{6} \) |
$0.55969$ |
$(-2a+1), (-5a+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.356568763$ |
0.522143560 |
\( \frac{36038181633}{47045881} a - \frac{75585143946}{47045881} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 19 a + 6\) , \( -19 a + 67\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(19a+6\right){x}-19a+67$ |
3249.3-a2 |
3249.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3249.3 |
\( 3^{2} \cdot 19^{2} \) |
\( 3^{3} \cdot 19^{12} \) |
$1.16852$ |
$(-2a+1), (-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$0.539045766$ |
1.244872874 |
\( \frac{36038181633}{47045881} a - \frac{75585143946}{47045881} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -168 a + 94\) , \( 544 a - 1166\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-168a+94\right){x}+544a-1166$ |
8379.2-d2 |
8379.2-d |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
8379.2 |
\( 3^{2} \cdot 7^{2} \cdot 19 \) |
\( 3^{3} \cdot 7^{6} \cdot 19^{6} \) |
$1.48080$ |
$(-2a+1), (-3a+1), (-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$0.888082720$ |
2.050939191 |
\( \frac{36038181633}{47045881} a - \frac{75585143946}{47045881} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( 35 a - 62\) , \( -184 a + 233\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(35a-62\right){x}-184a+233$ |
8379.6-a2 |
8379.6-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
8379.6 |
\( 3^{2} \cdot 7^{2} \cdot 19 \) |
\( 3^{3} \cdot 7^{6} \cdot 19^{6} \) |
$1.48080$ |
$(-2a+1), (3a-2), (-5a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.095475728$ |
$0.888082720$ |
2.349778965 |
\( \frac{36038181633}{47045881} a - \frac{75585143946}{47045881} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -49 a + 58\) , \( 71 a + 168\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-49a+58\right){x}+71a+168$ |
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 |
\( \frac{36038181633}{47045881} a - \frac{75585143946}{47045881} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -243 a + 333\) , \( 1743 a + 1720\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-243a+333\right){x}+1743a+1720$ |
28899.6-d2 |
28899.6-d |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.6 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{9} \cdot 13^{6} \cdot 19^{6} \) |
$2.01799$ |
$(-2a+1), (4a-3), (-5a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1.741110786$ |
$0.376244479$ |
3.025700258 |
\( \frac{36038181633}{47045881} a - \frac{75585143946}{47045881} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 223 a - 339\) , \( -2607 a + 3087\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(223a-339\right){x}-2607a+3087$ |
43776.2-d2 |
43776.2-d |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
43776.2 |
\( 2^{8} \cdot 3^{2} \cdot 19 \) |
\( 2^{24} \cdot 3^{3} \cdot 19^{6} \) |
$2.23876$ |
$(-2a+1), (-5a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.357843503$ |
$0.587411505$ |
2.912635915 |
\( \frac{36038181633}{47045881} a - \frac{75585143946}{47045881} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -103 a - 31\) , \( -951 a + 312\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-103a-31\right){x}-951a+312$ |
43776.2-i2 |
43776.2-i |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
43776.2 |
\( 2^{8} \cdot 3^{2} \cdot 19 \) |
\( 2^{24} \cdot 3^{9} \cdot 19^{6} \) |
$2.23876$ |
$(-2a+1), (-5a+2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$2.390121950$ |
$0.339142190$ |
3.743960357 |
\( \frac{36038181633}{47045881} a - \frac{75585143946}{47045881} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 312 a + 93\) , \( 888 a - 4366\bigr] \) |
${y}^2={x}^{3}+\left(312a+93\right){x}+888a-4366$ |
43776.2-q2 |
43776.2-q |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
43776.2 |
\( 2^{8} \cdot 3^{2} \cdot 19 \) |
\( 2^{24} \cdot 3^{3} \cdot 19^{6} \) |
$2.23876$ |
$(-2a+1), (-5a+2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{4} \) |
$1$ |
$0.587411505$ |
2.713137527 |
\( \frac{36038181633}{47045881} a - \frac{75585143946}{47045881} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -103 a - 31\) , \( 951 a - 312\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-103a-31\right){x}+951a-312$ |
61731.2-c2 |
61731.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
61731.2 |
\( 3^{2} \cdot 19^{3} \) |
\( 3^{3} \cdot 19^{12} \) |
$2.43964$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$0.539045766$ |
1.244872874 |
\( \frac{36038181633}{47045881} a - \frac{75585143946}{47045881} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -a - 145\) , \( -222 a - 909\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-a-145\right){x}-222a-909$ |
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 |
\( \frac{36038181633}{47045881} a - \frac{75585143946}{47045881} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 144 a - 633\) , \( -1857 a + 8491\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(144a-633\right){x}-1857a+8491$ |
*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.