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
149769.3-CMc1
149769.3-CMc
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
149769.3
\( 3^{4} \cdot 43^{2} \)
\( 3^{12} \cdot 43^{10} \)
$3.04477$
$(-2a+1), (7a-6)$
0
$\mathsf{trivial}$
$\textsf{yes}$
$-3$
$\mathrm{U}(1)$
✓
✓
$43$
43Cs.9.1
$9$
\( 1 \)
$1$
$0.203780700$
2.117751159
\( 0 \)
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -2514 a + 16856\bigr] \)
${y}^2+{y}={x}^{3}-2514a+16856$
149769.3-CMb1
149769.3-CMb
$2$
$3$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
149769.3
\( 3^{4} \cdot 43^{2} \)
\( 3^{12} \cdot 43^{6} \)
$3.04477$
$(-2a+1), (7a-6)$
$2$
$\mathsf{trivial}$
$\textsf{yes}$
$-3$
$\mathrm{U}(1)$
✓
✓
$3, 43$
3Cs[2] , 43Cs.9.1
$1$
\( 2^{2} \)
$0.354237281$
$0.713924910$
4.672358447
\( 0 \)
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -390 a + 53\bigr] \)
${y}^2+{y}={x}^{3}-390a+53$
149769.3-CMb2
149769.3-CMb
$2$
$3$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
149769.3
\( 3^{4} \cdot 43^{2} \)
\( 3^{4} \cdot 43^{6} \)
$3.04477$
$(-2a+1), (7a-6)$
$2$
$\mathsf{trivial}$
$\textsf{yes}$
$-27$
$\mathrm{U}(1)$
✓
✓
$43$
43Cs.9.1
$1$
\( 2^{2} \)
$0.354237281$
$0.713924910$
4.672358447
\( -12288000 \)
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 481 a - 350\) , \( 3858 a - 776\bigr] \)
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(481a-350\right){x}+3858a-776$
149769.3-CMa1
149769.3-CMa
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
149769.3
\( 3^{4} \cdot 43^{2} \)
\( 3^{6} \cdot 43^{4} \)
$3.04477$
$(-2a+1), (7a-6)$
0
$\Z/3\Z$
$\textsf{yes}$
$-3$
$\mathrm{U}(1)$
✓
✓
$3$
3B.1.1[2]
$1$
\( 3 \)
$1$
$2.314503840$
0.890852943
\( 0 \)
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 12 a - 9\bigr] \)
${y}^2+{y}={x}^{3}+12a-9$
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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.