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
11.1-a4
11.1-a
$6$
$8$
4.4.2777.1
$4$
$[4, 0]$
11.1
\( 11 \)
\( -11 \)
$6.35478$
$(-a^3+2a^2+2a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$4$
\( 1 \)
$1$
$60.49229427$
1.147921305
\( \frac{1702129469435805324}{11} a^{3} + \frac{2318878776895144329}{11} a^{2} - \frac{1330538175521684262}{11} a - \frac{1441053861737062367}{11} \)
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a\) , \( a^{2} - a - 1\) , \( -5 a^{3} - 27 a^{2} + 4 a + 16\) , \( -36 a^{3} - 102 a^{2} + 35 a + 61\bigr] \)
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}-a{x}^{2}+\left(-5a^{3}-27a^{2}+4a+16\right){x}-36a^{3}-102a^{2}+35a+61$
121.1-a2
121.1-a
$6$
$8$
4.4.2777.1
$4$
$[4, 0]$
121.1
\( 11^{2} \)
\( - 11^{7} \)
$8.57580$
$(-a^3+2a^2+2a-1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$0.242504090$
$185.1681268$
1.704226669
\( \frac{1702129469435805324}{11} a^{3} + \frac{2318878776895144329}{11} a^{2} - \frac{1330538175521684262}{11} a - \frac{1441053861737062367}{11} \)
\( \bigl[a^{3} - 4 a - 1\) , \( -a^{3} + 5 a + 1\) , \( a^{3} - a^{2} - 2 a + 1\) , \( 40 a^{3} - 227 a^{2} + 21 a + 133\) , \( -475 a^{3} + 2195 a^{2} - 35 a - 1188\bigr] \)
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{3}-a^{2}-2a+1\right){y}={x}^{3}+\left(-a^{3}+5a+1\right){x}^{2}+\left(40a^{3}-227a^{2}+21a+133\right){x}-475a^{3}+2195a^{2}-35a-1188$
176.2-h4
176.2-h
$6$
$8$
4.4.2777.1
$4$
$[4, 0]$
176.2
\( 2^{4} \cdot 11 \)
\( - 2^{12} \cdot 11 \)
$8.98702$
$(-a), (-a^3+2a^2+2a-1)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$0.711919547$
$365.9837623$
2.472149892
\( \frac{1702129469435805324}{11} a^{3} + \frac{2318878776895144329}{11} a^{2} - \frac{1330538175521684262}{11} a - \frac{1441053861737062367}{11} \)
\( \bigl[a^{3} - 3 a\) , \( a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 51 a^{3} - 71 a^{2} - 147 a + 106\) , \( -122 a^{3} + 201 a^{2} + 361 a - 318\bigr] \)
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+a{x}^{2}+\left(51a^{3}-71a^{2}-147a+106\right){x}-122a^{3}+201a^{2}+361a-318$
704.3-h2
704.3-h
$6$
$8$
4.4.2777.1
$4$
$[4, 0]$
704.3
\( 2^{6} \cdot 11 \)
\( - 2^{18} \cdot 11 \)
$10.68742$
$(-a), (-a^3+2a^2+2a-1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$4$
\( 2 \)
$0.208742076$
$105.9042588$
3.356027195
\( \frac{1702129469435805324}{11} a^{3} + \frac{2318878776895144329}{11} a^{2} - \frac{1330538175521684262}{11} a - \frac{1441053861737062367}{11} \)
\( \bigl[a^{3} - 4 a\) , \( -a\) , \( a^{3} - 4 a\) , \( 23 a^{3} - 60 a^{2} - 28 a + 16\) , \( 149 a^{3} - 296 a^{2} - 91 a + 122\bigr] \)
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}-a{x}^{2}+\left(23a^{3}-60a^{2}-28a+16\right){x}+149a^{3}-296a^{2}-91a+122$
704.3-m5
704.3-m
$6$
$8$
4.4.2777.1
$4$
$[4, 0]$
704.3
\( 2^{6} \cdot 11 \)
\( - 2^{18} \cdot 11 \)
$10.68742$
$(-a), (-a^3+2a^2+2a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$4$
\( 2^{2} \)
$1$
$28.03993238$
2.128379236
\( \frac{1702129469435805324}{11} a^{3} + \frac{2318878776895144329}{11} a^{2} - \frac{1330538175521684262}{11} a - \frac{1441053861737062367}{11} \)
\( \bigl[a\) , \( -a^{3} + 3 a + 1\) , \( a^{2} - 2\) , \( 25 a^{3} - 41 a^{2} - 71 a + 52\) , \( -33 a^{3} + 75 a^{2} + 67 a - 151\bigr] \)
${y}^2+a{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+3a+1\right){x}^{2}+\left(25a^{3}-41a^{2}-71a+52\right){x}-33a^{3}+75a^{2}+67a-151$
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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.