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
4.1-a1
4.1-a
$2$
$5$
\(\Q(\sqrt{85}) \)
$2$
$[2, 0]$
4.1
\( 2^{2} \)
\( 2^{10} \cdot 3^{12} \)
$1.16510$
$(2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$5$
5B.1.3
$25$
\( 1 \)
$1$
$0.769953241$
2.087828865
\( -\frac{18170704189}{32} \)
\( \bigl[a\) , \( 0\) , \( a\) , \( -383 a - 1644\) , \( -9842 a - 40758\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-383a-1644\right){x}-9842a-40758$
4.1-a2
4.1-a
$2$
$5$
\(\Q(\sqrt{85}) \)
$2$
$[2, 0]$
4.1
\( 2^{2} \)
\( 2^{2} \cdot 3^{12} \)
$1.16510$
$(2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$5$
5B.1.4
$1$
\( 1 \)
$1$
$19.24883104$
2.087828865
\( \frac{1331}{2} \)
\( \bigl[a\) , \( 0\) , \( a\) , \( 2 a + 6\) , \( a + 3\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(2a+6\right){x}+a+3$
4.1-b1
4.1-b
$2$
$5$
\(\Q(\sqrt{85}) \)
$2$
$[2, 0]$
4.1
\( 2^{2} \)
\( 2^{10} \)
$1.16510$
$(2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$5$
5B.1.2
$1$
\( 1 \)
$1$
$0.769953241$
0.083513154
\( -\frac{18170704189}{32} \)
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -490 a - 2009\) , \( -14487 a - 59538\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-490a-2009\right){x}-14487a-59538$
4.1-b2
4.1-b
$2$
$5$
\(\Q(\sqrt{85}) \)
$2$
$[2, 0]$
4.1
\( 2^{2} \)
\( 2^{2} \)
$1.16510$
$(2)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$5$
5B.1.1
$1$
\( 1 \)
$1$
$19.24883104$
0.083513154
\( \frac{1331}{2} \)
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 5 a + 26\) , \( 7 a + 30\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(5a+26\right){x}+7a+30$
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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.