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
4096.1-a1
4096.1-a
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
4096.1
\( 2^{12} \)
\( 2^{12} \)
$1.23820$
$(2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 1 \)
$0.368673504$
$6.572645946$
1.399012318
\( -1088 a - 2304 \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1\) , \( -a\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+{x}-a$
4096.1-b1
4096.1-b
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
4096.1
\( 2^{12} \)
\( 2^{24} \)
$1.23820$
$(2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$0.184336752$
$3.286322973$
1.399012318
\( -1088 a - 2304 \)
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 5 a - 4\) , \( 4 a - 1\bigr] \)
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(5a-4\right){x}+4a-1$
4096.1-d1
4096.1-d
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
4096.1
\( 2^{12} \)
\( 2^{24} \)
$1.23820$
$(2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2 \)
$1$
$3.286322973$
1.897359453
\( -1088 a - 2304 \)
\( \bigl[0\) , \( a\) , \( 0\) , \( -a + 5\) , \( -4 a + 1\bigr] \)
${y}^2={x}^{3}+a{x}^{2}+\left(-a+5\right){x}-4a+1$
4096.1-e1
4096.1-e
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
4096.1
\( 2^{12} \)
\( 2^{12} \)
$1.23820$
$(2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 1 \)
$1$
$6.572645946$
1.897359453
\( -1088 a - 2304 \)
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( a - 1\) , \( a\bigr] \)
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(a-1\right){x}+a$
36864.1-g2
36864.1-g
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
36864.1
\( 2^{12} \cdot 3^{2} \)
\( 2^{12} \cdot 3^{6} \)
$2.14462$
$(-2a+1), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2 \)
$0.686488085$
$3.794718906$
3.008028754
\( -1088 a - 2304 \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -3 a + 3\) , \( 3 a - 6\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3a+3\right){x}+3a-6$
36864.1-h2
36864.1-h
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
36864.1
\( 2^{12} \cdot 3^{2} \)
\( 2^{24} \cdot 3^{6} \)
$2.14462$
$(-2a+1), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$0.343244042$
$1.897359453$
3.008028754
\( -1088 a - 2304 \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 5 a - 16\) , \( 10 a - 37\bigr] \)
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(5a-16\right){x}+10a-37$
36864.1-r2
36864.1-r
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
36864.1
\( 2^{12} \cdot 3^{2} \)
\( 2^{12} \cdot 3^{6} \)
$2.14462$
$(-2a+1), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2 \)
$1$
$3.794718906$
2.190881982
\( -1088 a - 2304 \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2 a - 4\) , \( -2 a + 2\bigr] \)
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(2a-4\right){x}-2a+2$
36864.1-s2
36864.1-s
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
36864.1
\( 2^{12} \cdot 3^{2} \)
\( 2^{24} \cdot 3^{6} \)
$2.14462$
$(-2a+1), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$1.897359453$
2.190881982
\( -1088 a - 2304 \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -15 a + 12\) , \( -6 a + 21\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-15a+12\right){x}-6a+21$
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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.