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
49152.1-b2
49152.1-b
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
49152.1
\( 2^{14} \cdot 3 \)
\( 2^{16} \cdot 3^{2} \)
$2.30454$
$(-2a+1), (2)$
$2$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$0.193042724$
$4.292588069$
3.827383780
\( \frac{16000}{3} \)
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 3 a\) , \( 3\bigr] \)
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+3a{x}+3$
49152.1-k2
49152.1-k
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
49152.1
\( 2^{14} \cdot 3 \)
\( 2^{28} \cdot 3^{2} \)
$2.30454$
$(-2a+1), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$2.146294034$
2.478326877
\( \frac{16000}{3} \)
\( \bigl[0\) , \( a\) , \( 0\) , \( -13 a + 13\) , \( -11\bigr] \)
${y}^2={x}^{3}+a{x}^{2}+\left(-13a+13\right){x}-11$
49152.1-o2
49152.1-o
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
49152.1
\( 2^{14} \cdot 3 \)
\( 2^{28} \cdot 3^{2} \)
$2.30454$
$(-2a+1), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$0.848371993$
$2.146294034$
4.205086228
\( \frac{16000}{3} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -13\) , \( 11\bigr] \)
${y}^2={x}^{3}+{x}^{2}-13{x}+11$
49152.1-v2
49152.1-v
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
49152.1
\( 2^{14} \cdot 3 \)
\( 2^{16} \cdot 3^{2} \)
$2.30454$
$(-2a+1), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$0.466122448$
$4.292588069$
4.620815173
\( \frac{16000}{3} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -3\) , \( -3\bigr] \)
${y}^2={x}^{3}+{x}^{2}-3{x}-3$
147456.1-o2
147456.1-o
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
147456.1
\( 2^{14} \cdot 3^{2} \)
\( 2^{28} \cdot 3^{8} \)
$3.03295$
$(-2a+1), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1.401164680$
$1.239163438$
4.009748527
\( \frac{16000}{3} \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 40\) , \( -106 a + 33\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+40\right){x}-106a+33$
147456.1-r2
147456.1-r
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
147456.1
\( 2^{14} \cdot 3^{2} \)
\( 2^{16} \cdot 3^{8} \)
$3.03295$
$(-2a+1), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$2.478326877$
2.861725379
\( \frac{16000}{3} \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -9 a\) , \( -18 a + 9\bigr] \)
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-9a{x}-18a+9$
147456.1-be2
147456.1-be
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
147456.1
\( 2^{14} \cdot 3^{2} \)
\( 2^{28} \cdot 3^{8} \)
$3.03295$
$(-2a+1), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1.401164680$
$1.239163438$
4.009748527
\( \frac{16000}{3} \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 40\) , \( 106 a - 33\bigr] \)
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+40\right){x}+106a-33$
147456.1-bh2
147456.1-bh
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
147456.1
\( 2^{14} \cdot 3^{2} \)
\( 2^{16} \cdot 3^{8} \)
$3.03295$
$(-2a+1), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$2.478326877$
2.861725379
\( \frac{16000}{3} \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 11 a - 10\) , \( 8 a + 1\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(11a-10\right){x}+8a+1$
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Pari/GP
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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.