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-b2
55.2-b
$2$
$2$
4.4.5125.1
$4$
$[4, 0]$
55.2
\( 5 \cdot 11 \)
\( 5^{8} \cdot 11^{2} \)
$10.55676$
$(-a^3+a^2+4a+1), (a-1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1.537371468$
$30.87409782$
2.652077121
\( \frac{196392867540579}{3025} a^{3} + \frac{27744964314013}{605} a^{2} - \frac{802919148292512}{3025} a - \frac{72567111214406}{275} \)
\( \bigl[a^{2} - a - 4\) , \( -a^{3} + 4 a + 3\) , \( a^{2} - a - 3\) , \( 16 a^{3} - 41 a^{2} - 21 a + 46\) , \( 66 a^{3} - 198 a^{2} - 52 a + 280\bigr] \)
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-a^{3}+4a+3\right){x}^{2}+\left(16a^{3}-41a^{2}-21a+46\right){x}+66a^{3}-198a^{2}-52a+280$
55.2-e1
55.2-e
$2$
$2$
4.4.5125.1
$4$
$[4, 0]$
55.2
\( 5 \cdot 11 \)
\( 5^{8} \cdot 11^{2} \)
$10.55676$
$(-a^3+a^2+4a+1), (a-1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$0.047398503$
$856.4096892$
2.268084662
\( \frac{196392867540579}{3025} a^{3} + \frac{27744964314013}{605} a^{2} - \frac{802919148292512}{3025} a - \frac{72567111214406}{275} \)
\( \bigl[a^{2} - 4\) , \( a^{3} - 5 a - 4\) , \( a^{2} - 3\) , \( -22 a^{3} + 47 a^{2} + 69 a - 141\) , \( 67 a^{3} - 189 a^{2} - 181 a + 592\bigr] \)
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{3}-5a-4\right){x}^{2}+\left(-22a^{3}+47a^{2}+69a-141\right){x}+67a^{3}-189a^{2}-181a+592$
275.2-c2
275.2-c
$2$
$2$
4.4.5125.1
$4$
$[4, 0]$
275.2
\( 5^{2} \cdot 11 \)
\( 5^{14} \cdot 11^{2} \)
$12.90928$
$(-a^3+a^2+4a+1), (a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$1$
$88.18096989$
2.463530435
\( \frac{196392867540579}{3025} a^{3} + \frac{27744964314013}{605} a^{2} - \frac{802919148292512}{3025} a - \frac{72567111214406}{275} \)
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + a^{2} + 3 a + 1\) , \( a^{2} - a - 3\) , \( -1439 a^{3} - 1027 a^{2} + 5839 a + 5812\) , \( 65659 a^{3} + 46438 a^{2} - 268274 a - 266765\bigr] \)
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a+1\right){x}^{2}+\left(-1439a^{3}-1027a^{2}+5839a+5812\right){x}+65659a^{3}+46438a^{2}-268274a-266765$
275.2-m2
275.2-m
$2$
$2$
4.4.5125.1
$4$
$[4, 0]$
275.2
\( 5^{2} \cdot 11 \)
\( 5^{14} \cdot 11^{2} \)
$12.90928$
$(-a^3+a^2+4a+1), (a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$1$
$59.96957518$
1.675382725
\( \frac{196392867540579}{3025} a^{3} + \frac{27744964314013}{605} a^{2} - \frac{802919148292512}{3025} a - \frac{72567111214406}{275} \)
\( \bigl[a^{3} - a^{2} - 4 a\) , \( a^{3} - a^{2} - 4 a - 1\) , \( a^{2} - a - 3\) , \( 5 a^{3} - 42 a^{2} + 32 a + 65\) , \( -83 a^{3} + 230 a^{2} + 33 a - 317\bigr] \)
${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a-1\right){x}^{2}+\left(5a^{3}-42a^{2}+32a+65\right){x}-83a^{3}+230a^{2}+33a-317$
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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.