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
55.1-c2
55.1-c
$4$
$6$
4.4.5125.1
$4$
$[4, 0]$
55.1
\( 5 \cdot 11 \)
\( 5^{2} \cdot 11^{2} \)
$10.55676$
$(-a^3+a^2+4a+1), (-a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$1$
$117.3818148$
1.639660313
\( \frac{131300318}{605} a^{3} + \frac{14981064}{605} a^{2} - \frac{151139983}{121} a - \frac{681395002}{605} \)
\( \bigl[a^{2} - 4\) , \( -a\) , \( 1\) , \( 2 a^{3} - 3 a^{2} - 8 a + 2\) , \( 2 a^{3} - 4 a^{2} - 5 a + 3\bigr] \)
${y}^2+\left(a^{2}-4\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(2a^{3}-3a^{2}-8a+2\right){x}+2a^{3}-4a^{2}-5a+3$
55.1-d1
55.1-d
$4$
$6$
4.4.5125.1
$4$
$[4, 0]$
55.1
\( 5 \cdot 11 \)
\( 5^{2} \cdot 11^{2} \)
$10.55676$
$(-a^3+a^2+4a+1), (-a)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2^{2} \)
$1$
$669.0430099$
1.038399794
\( \frac{131300318}{605} a^{3} + \frac{14981064}{605} a^{2} - \frac{151139983}{121} a - \frac{681395002}{605} \)
\( \bigl[a^{3} - 4 a - 3\) , \( 0\) , \( a^{3} - 4 a - 3\) , \( a^{3} - 4 a - 3\) , \( a^{3} - 4 a - 2\bigr] \)
${y}^2+\left(a^{3}-4a-3\right){x}{y}+\left(a^{3}-4a-3\right){y}={x}^{3}+\left(a^{3}-4a-3\right){x}+a^{3}-4a-2$
275.1-g3
275.1-g
$4$
$6$
4.4.5125.1
$4$
$[4, 0]$
275.1
\( 5^{2} \cdot 11 \)
\( 5^{8} \cdot 11^{2} \)
$12.90928$
$(-a^3+a^2+4a+1), (-a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$0.160887393$
$211.4553706$
3.801752031
\( \frac{131300318}{605} a^{3} + \frac{14981064}{605} a^{2} - \frac{151139983}{121} a - \frac{681395002}{605} \)
\( \bigl[a^{2} - 3\) , \( a\) , \( 1\) , \( 4 a^{3} + a^{2} - 20 a - 17\) , \( 8 a^{3} + a^{2} - 43 a - 36\bigr] \)
${y}^2+\left(a^{2}-3\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(4a^{3}+a^{2}-20a-17\right){x}+8a^{3}+a^{2}-43a-36$
275.1-l1
275.1-l
$4$
$6$
4.4.5125.1
$4$
$[4, 0]$
275.1
\( 5^{2} \cdot 11 \)
\( 5^{8} \cdot 11^{2} \)
$12.90928$
$(-a^3+a^2+4a+1), (-a)$
$0 \le r \le 1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
\( 2^{3} \)
$1$
$74.27901451$
3.977414736
\( \frac{131300318}{605} a^{3} + \frac{14981064}{605} a^{2} - \frac{151139983}{121} a - \frac{681395002}{605} \)
\( \bigl[a^{2} - a - 4\) , \( a^{3} - 2 a^{2} - 4 a + 4\) , \( a^{3} - 4 a - 3\) , \( a^{3} - 6 a^{2} - a + 21\) , \( -54 a^{3} + 165 a^{2} + 136 a - 517\bigr] \)
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{3}-4a-3\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a+4\right){x}^{2}+\left(a^{3}-6a^{2}-a+21\right){x}-54a^{3}+165a^{2}+136a-517$
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*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.