| 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 |
| 171.1-a2 |
171.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
171.1 |
\( 3^{2} \cdot 19 \) |
\( 3^{9} \cdot 19^{6} \) |
$0.55969$ |
$(-2a+1), (-5a+3)$ |
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 |
\( -\frac{36038181633}{47045881} a - \frac{39546962313}{47045881} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -20 a + 25\) , \( 18 a + 48\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-20a+25\right){x}+18a+48$ |
| 3249.1-a2 |
3249.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3249.1 |
\( 3^{2} \cdot 19^{2} \) |
\( 3^{3} \cdot 19^{12} \) |
$1.16852$ |
$(-2a+1), (-5a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$0.539045766$ |
1.244872874 |
\( -\frac{36038181633}{47045881} a - \frac{39546962313}{47045881} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( 168 a - 74\) , \( -544 a - 622\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(168a-74\right){x}-544a-622$ |
| 8379.1-a2 |
8379.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
8379.1 |
\( 3^{2} \cdot 7^{2} \cdot 19 \) |
\( 3^{3} \cdot 7^{6} \cdot 19^{6} \) |
$1.48080$ |
$(-2a+1), (-3a+1), (-5a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.095475728$ |
$0.888082720$ |
2.349778965 |
\( -\frac{36038181633}{47045881} a - \frac{39546962313}{47045881} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 48 a + 9\) , \( -72 a + 239\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(48a+9\right){x}-72a+239$ |
| 8379.5-d2 |
8379.5-d |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
8379.5 |
\( 3^{2} \cdot 7^{2} \cdot 19 \) |
\( 3^{3} \cdot 7^{6} \cdot 19^{6} \) |
$1.48080$ |
$(-2a+1), (3a-2), (-5a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$0.888082720$ |
2.050939191 |
\( -\frac{36038181633}{47045881} a - \frac{39546962313}{47045881} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -36 a - 27\) , \( 183 a + 49\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-36a-27\right){x}+183a+49$ |
| 28899.1-d2 |
28899.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28899.1 |
\( 3^{2} \cdot 13^{2} \cdot 19 \) |
\( 3^{9} \cdot 13^{6} \cdot 19^{6} \) |
$2.01799$ |
$(-2a+1), (-4a+1), (-5a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1.741110786$ |
$0.376244479$ |
3.025700258 |
\( -\frac{36038181633}{47045881} a - \frac{39546962313}{47045881} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 339 a - 224\) , \( 2607 a + 480\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(339a-224\right){x}+2607a+480$ |
| 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 |
\( -\frac{36038181633}{47045881} a - \frac{39546962313}{47045881} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -333 a + 243\) , \( -1743 a + 3463\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-333a+243\right){x}-1743a+3463$ |
| 43776.1-b2 |
43776.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
43776.1 |
\( 2^{8} \cdot 3^{2} \cdot 19 \) |
\( 2^{24} \cdot 3^{3} \cdot 19^{6} \) |
$2.23876$ |
$(-2a+1), (-5a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.357843503$ |
$0.587411505$ |
2.912635915 |
\( -\frac{36038181633}{47045881} a - \frac{39546962313}{47045881} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 32 a + 104\) , \( 816 a - 608\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(32a+104\right){x}+816a-608$ |
| 43776.1-o2 |
43776.1-o |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
43776.1 |
\( 2^{8} \cdot 3^{2} \cdot 19 \) |
\( 2^{24} \cdot 3^{9} \cdot 19^{6} \) |
$2.23876$ |
$(-2a+1), (-5a+3), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$2.390121950$ |
$0.339142190$ |
3.743960357 |
\( -\frac{36038181633}{47045881} a - \frac{39546962313}{47045881} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 405 a - 93\) , \( -888 a - 3478\bigr] \) |
${y}^2={x}^{3}+\left(405a-93\right){x}-888a-3478$ |
| 43776.1-q2 |
43776.1-q |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
43776.1 |
\( 2^{8} \cdot 3^{2} \cdot 19 \) |
\( 2^{24} \cdot 3^{3} \cdot 19^{6} \) |
$2.23876$ |
$(-2a+1), (-5a+3), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{4} \) |
$1$ |
$0.587411505$ |
2.713137527 |
\( -\frac{36038181633}{47045881} a - \frac{39546962313}{47045881} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 105 a - 135\) , \( -847 a + 504\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(105a-135\right){x}-847a+504$ |
| 61731.3-c2 |
61731.3-c |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
61731.3 |
\( 3^{2} \cdot 19^{3} \) |
\( 3^{3} \cdot 19^{12} \) |
$2.43964$ |
$(-2a+1), (-5a+3), (-5a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$0.539045766$ |
1.244872874 |
\( -\frac{36038181633}{47045881} a - \frac{39546962313}{47045881} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -146 a + 145\) , \( 222 a - 1131\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-146a+145\right){x}+222a-1131$ |
| 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 |
\( -\frac{36038181633}{47045881} a - \frac{39546962313}{47045881} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -488 a + 633\) , \( 1856 a + 6635\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-488a+633\right){x}+1856a+6635$ |
*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.
