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
149769.1-CMc1
149769.1-CMc
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
149769.1
\( 3^{4} \cdot 43^{2} \)
\( 3^{12} \cdot 43^{10} \)
$3.04477$
$(-2a+1), (-7a+1)$
0
$\mathsf{trivial}$
$\textsf{yes}$
$-3$
$\mathrm{U}(1)$
✓
✓
$43$
43Cs.9.1
$9$
\( 1 \)
$1$
$0.203780700$
2.117751159
\( 0 \)
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 2514 a + 14342\bigr] \)
${y}^2+{y}={x}^{3}+2514a+14342$
149769.1-CMb1
149769.1-CMb
$2$
$3$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
149769.1
\( 3^{4} \cdot 43^{2} \)
\( 3^{12} \cdot 43^{6} \)
$3.04477$
$(-2a+1), (-7a+1)$
$2$
$\mathsf{trivial}$
$\textsf{yes}$
$-3$
$\mathrm{U}(1)$
✓
✓
$3, 43$
3Cs[2] , 43Cs.9.1
$1$
\( 2^{2} \)
$0.354237281$
$0.713924910$
4.672358447
\( 0 \)
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 390 a - 337\bigr] \)
${y}^2+{y}={x}^{3}+390a-337$
149769.1-CMb2
149769.1-CMb
$2$
$3$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
149769.1
\( 3^{4} \cdot 43^{2} \)
\( 3^{4} \cdot 43^{6} \)
$3.04477$
$(-2a+1), (-7a+1)$
$2$
$\mathsf{trivial}$
$\textsf{yes}$
$-27$
$\mathrm{U}(1)$
✓
✓
$43$
43Cs.9.1
$1$
\( 2^{2} \)
$0.354237281$
$0.713924910$
4.672358447
\( -12288000 \)
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -479 a + 130\) , \( -3378 a + 2952\bigr] \)
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-479a+130\right){x}-3378a+2952$
149769.1-CMa1
149769.1-CMa
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
149769.1
\( 3^{4} \cdot 43^{2} \)
\( 3^{6} \cdot 43^{4} \)
$3.04477$
$(-2a+1), (-7a+1)$
0
$\Z/3\Z$
$\textsf{yes}$
$-3$
$\mathrm{U}(1)$
✓
✓
$3$
3B.1.1[2]
$1$
\( 3 \)
$1$
$2.314503840$
0.890852943
\( 0 \)
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -12 a + 3\bigr] \)
${y}^2+{y}={x}^{3}-12a+3$
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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.