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
55.2-c2
55.2-c
$4$
$6$
4.4.5125.1
$4$
$[4, 0]$
55.2
\( 5 \cdot 11 \)
\( 5^{2} \cdot 11^{2} \)
$10.55676$
$(-a^3+a^2+4a+1), (a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$1$
$117.3818148$
1.639660313
\( -\frac{131300318}{605} a^{3} + \frac{408882018}{605} a^{2} + \frac{331836833}{605} a - \frac{23469337}{11} \)
\( \bigl[a^{2} - 3\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( 1\) , \( -2 a^{3} + 3 a^{2} + 7 a - 7\) , \( -2 a^{3} + 2 a^{2} + 7 a - 4\bigr] \)
${y}^2+\left(a^{2}-3\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(-2a^{3}+3a^{2}+7a-7\right){x}-2a^{3}+2a^{2}+7a-4$
55.2-d1
55.2-d
$4$
$6$
4.4.5125.1
$4$
$[4, 0]$
55.2
\( 5 \cdot 11 \)
\( 5^{2} \cdot 11^{2} \)
$10.55676$
$(-a^3+a^2+4a+1), (a-1)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2^{2} \)
$1$
$669.0430099$
1.038399794
\( -\frac{131300318}{605} a^{3} + \frac{408882018}{605} a^{2} + \frac{331836833}{605} a - \frac{23469337}{11} \)
\( \bigl[a^{3} - a^{2} - 3 a\) , \( -a^{3} + 2 a^{2} + 4 a - 5\) , \( a^{3} - a^{2} - 3 a + 1\) , \( a^{3} - 6 a^{2} + a + 19\) , \( -a^{3} + a^{2} + 5 a - 3\bigr] \)
${y}^2+\left(a^{3}-a^{2}-3a\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-5\right){x}^{2}+\left(a^{3}-6a^{2}+a+19\right){x}-a^{3}+a^{2}+5a-3$
275.2-g2
275.2-g
$4$
$6$
4.4.5125.1
$4$
$[4, 0]$
275.2
\( 5^{2} \cdot 11 \)
\( 5^{8} \cdot 11^{2} \)
$12.90928$
$(-a^3+a^2+4a+1), (a-1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$0.160887393$
$211.4553706$
3.801752031
\( -\frac{131300318}{605} a^{3} + \frac{408882018}{605} a^{2} + \frac{331836833}{605} a - \frac{23469337}{11} \)
\( \bigl[a^{2} - 4\) , \( -a^{3} + 2 a^{2} + 4 a - 5\) , \( a^{3} - a^{2} - 4 a + 1\) , \( -2 a^{3} + 4 a^{2} + 7 a - 10\) , \( -2 a^{3} + 5 a^{2} + 6 a - 14\bigr] \)
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{3}-a^{2}-4a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-5\right){x}^{2}+\left(-2a^{3}+4a^{2}+7a-10\right){x}-2a^{3}+5a^{2}+6a-14$
275.2-l1
275.2-l
$4$
$6$
4.4.5125.1
$4$
$[4, 0]$
275.2
\( 5^{2} \cdot 11 \)
\( 5^{8} \cdot 11^{2} \)
$12.90928$
$(-a^3+a^2+4a+1), (a-1)$
$0 \le r \le 1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
\( 2^{3} \)
$1$
$74.27901451$
3.977414736
\( -\frac{131300318}{605} a^{3} + \frac{408882018}{605} a^{2} + \frac{331836833}{605} a - \frac{23469337}{11} \)
\( \bigl[a^{2} - a - 4\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( a^{3} - a^{2} - 3 a\) , \( -a^{3} - 3 a^{2} + 9 a + 16\) , \( 53 a^{3} + 5 a^{2} - 303 a - 272\bigr] \)
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{3}-a^{2}-3a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-1\right){x}^{2}+\left(-a^{3}-3a^{2}+9a+16\right){x}+53a^{3}+5a^{2}-303a-272$
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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.