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
46.2-a1
46.2-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
46.2
\( 2 \cdot 23 \)
\( 2^{2} \cdot 23 \)
$0.61571$
$(a), (2a+3)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$6.500075531$
0.614199405
\( -\frac{13982353}{92} a - \frac{23126489}{92} \)
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -4\) , \( -1\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}-4{x}-1$
46.2-a2
46.2-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
46.2
\( 2 \cdot 23 \)
\( 2^{2} \cdot 23^{4} \)
$0.61571$
$(a), (2a+3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$3.250037765$
0.614199405
\( \frac{77942691519}{1119364} a - \frac{145858368769}{1119364} \)
\( \bigl[1\) , \( -a\) , \( a\) , \( -6 a + 10\) , \( 2 a + 8\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-6a+10\right){x}+2a+8$
46.2-a3
46.2-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
46.2
\( 2 \cdot 23 \)
\( 2 \cdot 23^{8} \)
$0.61571$
$(a), (2a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$1.625018882$
0.614199405
\( \frac{5221695638593}{156621970562} a + \frac{45422616717183}{156621970562} \)
\( \bigl[1\) , \( -a\) , \( a\) , \( -a + 10\) , \( -8 a + 30\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-a+10\right){x}-8a+30$
46.2-a4
46.2-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
46.2
\( 2 \cdot 23 \)
\( 2^{4} \cdot 23^{2} \)
$0.61571$
$(a), (2a+3)$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$6.500075531$
0.614199405
\( -\frac{1695309}{8464} a + \frac{8874095}{8464} \)
\( \bigl[1\) , \( -a\) , \( a\) , \( -a\) , \( 0\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}-a{x}$
46.2-a5
46.2-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
46.2
\( 2 \cdot 23 \)
\( 2^{8} \cdot 23 \)
$0.61571$
$(a), (2a+3)$
0
$\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{3} \)
$1$
$6.500075531$
0.614199405
\( \frac{2993221}{5888} a + \frac{15291513}{5888} \)
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -a - 2\) , \( -a + 1\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a-2\right){x}-a+1$
46.2-a6
46.2-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
46.2
\( 2 \cdot 23 \)
\( 2 \cdot 23^{2} \)
$0.61571$
$(a), (2a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$1.625018882$
0.614199405
\( -\frac{14178949136401}{1058} a + \frac{7909975811569}{1058} \)
\( \bigl[1\) , \( -a\) , \( a\) , \( -91 a + 170\) , \( 240 a + 618\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-91a+170\right){x}+240a+618$
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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.