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
40.1-a1
40.1-a
$4$
$4$
\(\Q(\sqrt{10}) \)
$2$
$[2, 0]$
40.1
\( 2^{3} \cdot 5 \)
\( 2^{8} \cdot 5^{8} \)
$1.42129$
$(2,a), (5,a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$0.722205338$
$4.406960782$
2.012935576
\( \frac{237276}{625} \)
\( \bigl[a\) , \( -1\) , \( a\) , \( -1\) , \( -5\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-{x}-5$
40.1-a2
40.1-a
$4$
$4$
\(\Q(\sqrt{10}) \)
$2$
$[2, 0]$
40.1
\( 2^{3} \cdot 5 \)
\( 2^{4} \cdot 5^{4} \)
$1.42129$
$(2,a), (5,a)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{2} \)
$1.444410676$
$17.62784313$
2.012935576
\( \frac{148176}{25} \)
\( \bigl[a\) , \( -1\) , \( a\) , \( -6\) , \( -4\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-6{x}-4$
40.1-a3
40.1-a
$4$
$4$
\(\Q(\sqrt{10}) \)
$2$
$[2, 0]$
40.1
\( 2^{3} \cdot 5 \)
\( 2^{20} \cdot 5^{2} \)
$1.42129$
$(2,a), (5,a)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$0.722205338$
$35.25568626$
2.012935576
\( \frac{55296}{5} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -8\) , \( 8\bigr] \)
${y}^2={x}^{3}-8{x}+8$
40.1-a4
40.1-a
$4$
$4$
\(\Q(\sqrt{10}) \)
$2$
$[2, 0]$
40.1
\( 2^{3} \cdot 5 \)
\( 2^{8} \cdot 5^{2} \)
$1.42129$
$(2,a), (5,a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$0.722205338$
$4.406960782$
2.012935576
\( \frac{132304644}{5} \)
\( \bigl[a\) , \( -1\) , \( a\) , \( -31\) , \( -69\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-31{x}-69$
40.1-b1
40.1-b
$4$
$4$
\(\Q(\sqrt{10}) \)
$2$
$[2, 0]$
40.1
\( 2^{3} \cdot 5 \)
\( 2^{20} \cdot 5^{8} \)
$1.42129$
$(2,a), (5,a)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{4} \)
$1.548473301$
$4.406960782$
2.157957601
\( \frac{237276}{625} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( -34\bigr] \)
${y}^2={x}^{3}+13{x}-34$
40.1-b2
40.1-b
$4$
$4$
\(\Q(\sqrt{10}) \)
$2$
$[2, 0]$
40.1
\( 2^{3} \cdot 5 \)
\( 2^{16} \cdot 5^{4} \)
$1.42129$
$(2,a), (5,a)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{3} \)
$0.774236650$
$17.62784313$
2.157957601
\( \frac{148176}{25} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( -6\bigr] \)
${y}^2={x}^{3}-7{x}-6$
40.1-b3
40.1-b
$4$
$4$
\(\Q(\sqrt{10}) \)
$2$
$[2, 0]$
40.1
\( 2^{3} \cdot 5 \)
\( 2^{8} \cdot 5^{2} \)
$1.42129$
$(2,a), (5,a)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$0.387118325$
$35.25568626$
2.157957601
\( \frac{55296}{5} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( 1\bigr] \)
${y}^2={x}^{3}-2{x}+1$
40.1-b4
40.1-b
$4$
$4$
\(\Q(\sqrt{10}) \)
$2$
$[2, 0]$
40.1
\( 2^{3} \cdot 5 \)
\( 2^{20} \cdot 5^{2} \)
$1.42129$
$(2,a), (5,a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1.548473301$
$4.406960782$
2.157957601
\( \frac{132304644}{5} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -107\) , \( -426\bigr] \)
${y}^2={x}^{3}-107{x}-426$
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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.