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-a2
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
$1$
\( 1 \)
$1$
$241.9691770$
1.147921305
\( \frac{143460}{11} a^{3} - \frac{313574}{11} a^{2} - \frac{467081}{11} a + \frac{520237}{11} \)
\( \bigl[a^{3} - 3 a - 1\) , \( a^{2} - 3\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} + 2 a^{2} - a - 1\) , \( a^{3} + 3 a^{2} - 4\bigr] \)
${y}^2+\left(a^{3}-3a-1\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(a^{3}+2a^{2}-a-1\right){x}+a^{3}+3a^{2}-4$
121.1-a6
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
$1$
\( 2^{2} \)
$0.060626022$
$370.3362537$
1.704226669
\( \frac{143460}{11} a^{3} - \frac{313574}{11} a^{2} - \frac{467081}{11} a + \frac{520237}{11} \)
\( \bigl[1\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( a^{3} - a^{2} - 3 a + 2\) , \( -2 a^{3} + 5 a^{2} - 2 a + 2\) , \( -2 a^{3} + 3 a^{2} + 3 a + 1\bigr] \)
${y}^2+{x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+4\right){x}^{2}+\left(-2a^{3}+5a^{2}-2a+2\right){x}-2a^{3}+3a^{2}+3a+1$
176.2-h6
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
$1$
\( 2^{2} \)
$0.177979886$
$731.9675246$
2.472149892
\( \frac{143460}{11} a^{3} - \frac{313574}{11} a^{2} - \frac{467081}{11} a + \frac{520237}{11} \)
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{2} + 2\) , \( 0\) , \( 1\) , \( 0\bigr] \)
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+{x}$
704.3-h4
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
$1$
\( 2 \)
$0.208742076$
$423.6170354$
3.356027195
\( \frac{143460}{11} a^{3} - \frac{313574}{11} a^{2} - \frac{467081}{11} a + \frac{520237}{11} \)
\( \bigl[a^{3} - 3 a\) , \( -a^{3} + 2 a^{2} + 3 a - 4\) , \( a\) , \( 5 a^{2} - 4 a + 1\) , \( a^{3} + a^{2} + a - 2\bigr] \)
${y}^2+\left(a^{3}-3a\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-4\right){x}^{2}+\left(5a^{2}-4a+1\right){x}+a^{3}+a^{2}+a-2$
704.3-m1
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
$1$
\( 2 \)
$1$
$224.3194590$
2.128379236
\( \frac{143460}{11} a^{3} - \frac{313574}{11} a^{2} - \frac{467081}{11} a + \frac{520237}{11} \)
\( \bigl[a^{2} - 2\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 0\) , \( a^{2}\) , \( 0\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(a^{3}-a^{2}-3a+1\right){x}^{2}+a^{2}{x}$
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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.