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
46.3-a1
46.3-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
46.3
\( 2 \cdot 23 \)
\( 2^{2} \cdot 23 \)
$0.61571$
$(-a+1), (-2a+5)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$6.500075531$
0.614199405
\( \frac{13982353}{92} a - \frac{18554421}{46} \)
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( a - 4\) , \( -a - 4\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a-4\right){x}-a-4$
46.3-a2
46.3-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
46.3
\( 2 \cdot 23 \)
\( 2^{2} \cdot 23^{4} \)
$0.61571$
$(-a+1), (-2a+5)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$3.250037765$
0.614199405
\( -\frac{77942691519}{1119364} a - \frac{33957838625}{559682} \)
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 5 a + 4\) , \( -3 a + 10\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(5a+4\right){x}-3a+10$
46.3-a3
46.3-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
46.3
\( 2 \cdot 23 \)
\( 2 \cdot 23^{8} \)
$0.61571$
$(-a+1), (-2a+5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$1.625018882$
0.614199405
\( -\frac{5221695638593}{156621970562} a + \frac{25322156177888}{78310985281} \)
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 9\) , \( 7 a + 22\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+9{x}+7a+22$
46.3-a4
46.3-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
46.3
\( 2 \cdot 23 \)
\( 2^{4} \cdot 23^{2} \)
$0.61571$
$(-a+1), (-2a+5)$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$6.500075531$
0.614199405
\( \frac{1695309}{8464} a + \frac{3589393}{4232} \)
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -1\) , \( -a\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}-{x}-a$
46.3-a5
46.3-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
46.3
\( 2 \cdot 23 \)
\( 2^{8} \cdot 23 \)
$0.61571$
$(-a+1), (-2a+5)$
0
$\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{3} \)
$1$
$6.500075531$
0.614199405
\( -\frac{2993221}{5888} a + \frac{9142367}{2944} \)
\( \bigl[1\) , \( -a\) , \( a\) , \( -2\) , \( 1\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}-2{x}+1$
46.3-a6
46.3-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
46.3
\( 2 \cdot 23 \)
\( 2 \cdot 23^{2} \)
$0.61571$
$(-a+1), (-2a+5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$1.625018882$
0.614199405
\( \frac{14178949136401}{1058} a - \frac{3134486662416}{529} \)
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 90 a + 79\) , \( -241 a + 858\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(90a+79\right){x}-241a+858$
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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.