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
2.1-a1
2.1-a
$2$
$2$
\(\Q(\sqrt{82}) \)
$2$
$[2, 0]$
2.1
\( 2 \)
\( 2^{16} \cdot 3^{12} \)
$1.92457$
$(2,a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$4$
\( 2 \)
$1$
$9.868400111$
1.089782484
\( \frac{16974593}{256} \)
\( \bigl[1\) , \( -a\) , \( 1\) , \( -43 a - 364\) , \( -332 a - 2988\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-43a-364\right){x}-332a-2988$
2.1-a2
2.1-a
$2$
$2$
\(\Q(\sqrt{82}) \)
$2$
$[2, 0]$
2.1
\( 2 \)
\( 2^{8} \cdot 3^{12} \)
$1.92457$
$(2,a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$16$
\( 2 \)
$1$
$2.467100027$
1.089782484
\( \frac{68769820673}{16} \)
\( \bigl[1\) , \( -a\) , \( 1\) , \( -683 a - 6204\) , \( -27372 a - 248108\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-683a-6204\right){x}-27372a-248108$
2.1-b1
2.1-b
$2$
$2$
\(\Q(\sqrt{82}) \)
$2$
$[2, 0]$
2.1
\( 2 \)
\( 2^{16} \cdot 3^{12} \)
$1.92457$
$(2,a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$4$
\( 2 \)
$1$
$9.868400111$
1.089782484
\( \frac{16974593}{256} \)
\( \bigl[1\) , \( a\) , \( 1\) , \( 43 a - 364\) , \( 332 a - 2988\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(43a-364\right){x}+332a-2988$
2.1-b2
2.1-b
$2$
$2$
\(\Q(\sqrt{82}) \)
$2$
$[2, 0]$
2.1
\( 2 \)
\( 2^{8} \cdot 3^{12} \)
$1.92457$
$(2,a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$16$
\( 2 \)
$1$
$2.467100027$
1.089782484
\( \frac{68769820673}{16} \)
\( \bigl[1\) , \( a\) , \( 1\) , \( 683 a - 6204\) , \( 27372 a - 248108\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(683a-6204\right){x}+27372a-248108$
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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.