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
100009.7-a1
100009.7-a
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
100009.7
\( 7^{2} \cdot 13 \cdot 157 \)
\( 7^{12} \cdot 13^{5} \cdot 157 \)
$2.75238$
$(-3a+1), (3a-2), (4a-3), (-13a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$3.842186552$
$0.369863268$
3.281852171
\( \frac{1575191114742206464}{48006792922543} a + \frac{246838974549929984}{48006792922543} \)
\( \bigl[0\) , \( -a\) , \( a\) , \( -744 a + 521\) , \( -2996 a + 7171\bigr] \)
${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(-744a+521\right){x}-2996a+7171$
100009.7-b1
100009.7-b
$2$
$3$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
100009.7
\( 7^{2} \cdot 13 \cdot 157 \)
\( 7^{4} \cdot 13^{3} \cdot 157 \)
$2.75238$
$(-3a+1), (3a-2), (4a-3), (-13a+1)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1[2]
$1$
\( 3^{2} \)
$2.081941336$
$1.326984491$
6.380191282
\( \frac{19432951197696}{118310647} a - \frac{654901160013824}{118310647} \)
\( \bigl[0\) , \( 1\) , \( a\) , \( -84 a + 128\) , \( -289 a - 226\bigr] \)
${y}^2+a{y}={x}^{3}+{x}^{2}+\left(-84a+128\right){x}-289a-226$
100009.7-b2
100009.7-b
$2$
$3$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
100009.7
\( 7^{2} \cdot 13 \cdot 157 \)
\( 7^{12} \cdot 13 \cdot 157^{3} \)
$2.75238$
$(-3a+1), (3a-2), (4a-3), (-13a+1)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1[2]
$1$
\( 3^{4} \)
$0.693980445$
$0.442328163$
6.380191282
\( \frac{3259043377277014016}{2030133836302663} a + \frac{110775144237600768}{2030133836302663} \)
\( \bigl[0\) , \( 1\) , \( a\) , \( -14 a + 238\) , \( 1384 a - 1237\bigr] \)
${y}^2+a{y}={x}^{3}+{x}^{2}+\left(-14a+238\right){x}+1384a-1237$
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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.