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
2.2-a2
2.2-a
$2$
$5$
\(\Q(\sqrt{129}) \)
$2$
$[2, 0]$
2.2
\( 2 \)
\( -2 \)
$1.20695$
$(a+5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.4.2
$1$
\( 1 \)
$1$
$29.18343844$
2.569458482
\( \frac{958464783206251}{2} a + 2481900631453872 \)
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 117348739 a - 725087104\) , \( -1649973791107 a + 10195036828223\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(117348739a-725087104\right){x}-1649973791107a+10195036828223$
2.2-b2
2.2-b
$2$
$5$
\(\Q(\sqrt{129}) \)
$2$
$[2, 0]$
2.2
\( 2 \)
\( -2 \)
$1.20695$
$(a+5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.2
$1$
\( 1 \)
$5.203755382$
$1.150939947$
1.054641065
\( \frac{958464783206251}{2} a + 2481900631453872 \)
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -716 a - 3720\) , \( -28668 a - 148474\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-716a-3720\right){x}-28668a-148474$
18.2-b2
18.2-b
$2$
$5$
\(\Q(\sqrt{129}) \)
$2$
$[2, 0]$
18.2
\( 2 \cdot 3^{2} \)
\( - 2 \cdot 3^{6} \)
$2.09051$
$(a+5), (-28a+173)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$5$
5B.4.2
$25$
\( 1 \)
$1$
$3.831932200$
8.434570447
\( \frac{958464783206251}{2} a + 2481900631453872 \)
\( \bigl[a\) , \( -1\) , \( 1\) , \( 10444 a - 64512\) , \( 1405446 a - 8684101\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(10444a-64512\right){x}+1405446a-8684101$
18.2-g2
18.2-g
$2$
$5$
\(\Q(\sqrt{129}) \)
$2$
$[2, 0]$
18.2
\( 2 \cdot 3^{2} \)
\( - 2 \cdot 3^{6} \)
$2.09051$
$(a+5), (-28a+173)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$5$
5B.4.2
$1$
\( 1 \)
$1.359450876$
$2.921797094$
0.699437177
\( \frac{958464783206251}{2} a + 2481900631453872 \)
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -72960984 a - 377858259\) , \( -808792298143 a - 4188661182876\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-72960984a-377858259\right){x}-808792298143a-4188661182876$
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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.