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
3584.9-b1
3584.9-b
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
3584.9
\( 2^{9} \cdot 7 \)
\( 2^{16} \cdot 7^{6} \)
$1.82928$
$(a), (-a+1), (-2a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \cdot 3 \)
$0.233635261$
$2.063563427$
2.186696136
\( \frac{31083}{98} a - \frac{338111}{686} \)
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -8\) , \( -14 a - 6\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}-8{x}-14a-6$
3584.9-e1
3584.9-e
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
3584.9
\( 2^{9} \cdot 7 \)
\( 2^{10} \cdot 7^{6} \)
$1.82928$
$(a), (-a+1), (-2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1$
$2.918319385$
2.206042097
\( \frac{31083}{98} a - \frac{338111}{686} \)
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -3 a + 3\) , \( -3 a + 1\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a+3\right){x}-3a+1$
25088.9-c1
25088.9-c
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
25088.9
\( 2^{9} \cdot 7^{2} \)
\( 2^{10} \cdot 7^{12} \)
$2.97546$
$(a), (-a+1), (-2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$1$
$1.103021048$
1.667611077
\( \frac{31083}{98} a - \frac{338111}{686} \)
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 6 a - 28\) , \( -24 a + 108\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(6a-28\right){x}-24a+108$
25088.9-d1
25088.9-d
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
25088.9
\( 2^{9} \cdot 7^{2} \)
\( 2^{16} \cdot 7^{12} \)
$2.97546$
$(a), (-a+1), (-2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$4$
\( 2^{3} \)
$1$
$0.779953663$
4.716716405
\( \frac{31083}{98} a - \frac{338111}{686} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 12 a + 44\) , \( -155 a + 277\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(12a+44\right){x}-155a+277$
28672.9-g1
28672.9-g
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
28672.9
\( 2^{12} \cdot 7 \)
\( 2^{28} \cdot 7^{6} \)
$3.07647$
$(a), (-a+1), (-2a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$1.648402668$
$1.031781713$
5.142710798
\( \frac{31083}{98} a - \frac{338111}{686} \)
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 20 a - 24\) , \( 84 a - 84\bigr] \)
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(20a-24\right){x}+84a-84$
28672.9-i1
28672.9-i
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
28672.9
\( 2^{12} \cdot 7 \)
\( 2^{22} \cdot 7^{6} \)
$3.07647$
$(a), (-a+1), (-2a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{4} \cdot 3 \)
$0.184934948$
$1.459159692$
4.895691373
\( \frac{31083}{98} a - \frac{338111}{686} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -11 a + 2\) , \( 21 a - 42\bigr] \)
${y}^2={x}^{3}+{x}^{2}+\left(-11a+2\right){x}+21a-42$
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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.