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-a2
55.2-a
$2$
$2$
4.4.5125.1
$4$
$[4, 0]$
55.2
\( 5 \cdot 11 \)
\( 5^{4} \cdot 11^{4} \)
$10.55676$
$(-a^3+a^2+4a+1), (a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$134.2078364$
1.874696378
\( -\frac{16065231177563}{73205} a^{3} - \frac{11346843517992}{73205} a^{2} + \frac{65679504182957}{73205} a + \frac{5935761172007}{6655} \)
\( \bigl[a^{3} - 4 a - 4\) , \( -a - 1\) , \( a\) , \( -6 a^{3} - a^{2} + 32 a + 28\) , \( 45 a^{3} + 6 a^{2} - 259 a - 235\bigr] \)
${y}^2+\left(a^{3}-4a-4\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6a^{3}-a^{2}+32a+28\right){x}+45a^{3}+6a^{2}-259a-235$
55.2-f2
55.2-f
$2$
$2$
4.4.5125.1
$4$
$[4, 0]$
55.2
\( 5 \cdot 11 \)
\( 5^{4} \cdot 11^{4} \)
$10.55676$
$(-a^3+a^2+4a+1), (a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$70.55402936$
0.985541431
\( -\frac{16065231177563}{73205} a^{3} - \frac{11346843517992}{73205} a^{2} + \frac{65679504182957}{73205} a + \frac{5935761172007}{6655} \)
\( \bigl[1\) , \( -a^{3} + 4 a + 4\) , \( a^{3} - 5 a - 4\) , \( -8 a^{3} - a^{2} + 32 a + 20\) , \( -10 a^{3} - 9 a^{2} + 41 a + 47\bigr] \)
${y}^2+{x}{y}+\left(a^{3}-5a-4\right){y}={x}^{3}+\left(-a^{3}+4a+4\right){x}^{2}+\left(-8a^{3}-a^{2}+32a+20\right){x}-10a^{3}-9a^{2}+41a+47$
275.2-f1
275.2-f
$2$
$2$
4.4.5125.1
$4$
$[4, 0]$
275.2
\( 5^{2} \cdot 11 \)
\( 5^{10} \cdot 11^{4} \)
$12.90928$
$(-a^3+a^2+4a+1), (a-1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{4} \)
$1.315436724$
$13.28471173$
3.905666397
\( -\frac{16065231177563}{73205} a^{3} - \frac{11346843517992}{73205} a^{2} + \frac{65679504182957}{73205} a + \frac{5935761172007}{6655} \)
\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( -a^{2} + a + 3\) , \( a^{2} - 4\) , \( -35 a^{3} + 124 a^{2} + 4 a - 230\) , \( -392 a^{3} + 1442 a^{2} - 81 a - 2575\bigr] \)
${y}^2+\left(a^{3}-a^{2}-4a+1\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-35a^{3}+124a^{2}+4a-230\right){x}-392a^{3}+1442a^{2}-81a-2575$
275.2-q1
275.2-q
$2$
$2$
4.4.5125.1
$4$
$[4, 0]$
275.2
\( 5^{2} \cdot 11 \)
\( 5^{10} \cdot 11^{4} \)
$12.90928$
$(-a^3+a^2+4a+1), (a-1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{4} \)
$0.108096440$
$142.5533925$
3.443990916
\( -\frac{16065231177563}{73205} a^{3} - \frac{11346843517992}{73205} a^{2} + \frac{65679504182957}{73205} a + \frac{5935761172007}{6655} \)
\( \bigl[a + 1\) , \( a^{3} - 4 a - 4\) , \( a + 1\) , \( -7 a^{3} - 3 a^{2} + 28 a + 24\) , \( 13 a^{3} + 4 a^{2} - 62 a - 55\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-4a-4\right){x}^{2}+\left(-7a^{3}-3a^{2}+28a+24\right){x}+13a^{3}+4a^{2}-62a-55$
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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.