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
21.1-a6
21.1-a
$6$
$8$
\(\Q(\sqrt{42}) \)
$2$
$[2, 0]$
21.1
\( 3 \cdot 7 \)
\( 2^{12} \cdot 3^{2} \cdot 7^{4} \)
$2.47941$
$(3,a), (a+7)$
$2$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$20.59050663$
$0.814020435$
5.172585655
\( \frac{53297461115137}{147} \)
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -109913455 a - 712320537\) , \( -1596914887554 a - 10349191303524\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-109913455a-712320537\right){x}-1596914887554a-10349191303524$
21.1-b6
21.1-b
$6$
$8$
\(\Q(\sqrt{42}) \)
$2$
$[2, 0]$
21.1
\( 3 \cdot 7 \)
\( 2^{12} \cdot 3^{2} \cdot 7^{4} \)
$2.47941$
$(3,a), (a+7)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$8.753013071$
$14.60752776$
4.932302010
\( \frac{53297461115137}{147} \)
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -163084 a - 1056802\) , \( 90983532 a + 589640870\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-163084a-1056802\right){x}+90983532a+589640870$
21.1-c6
21.1-c
$6$
$8$
\(\Q(\sqrt{42}) \)
$2$
$[2, 0]$
21.1
\( 3 \cdot 7 \)
\( 3^{2} \cdot 7^{4} \)
$2.47941$
$(3,a), (a+7)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$14.60752776$
1.126995234
\( \frac{53297461115137}{147} \)
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 40772 a - 264187\) , \( -11291398 a + 73176728\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(40772a-264187\right){x}-11291398a+73176728$
21.1-d6
21.1-d
$6$
$8$
\(\Q(\sqrt{42}) \)
$2$
$[2, 0]$
21.1
\( 3 \cdot 7 \)
\( 3^{2} \cdot 7^{4} \)
$2.47941$
$(3,a), (a+7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$23.79400264$
$0.814020435$
2.988671404
\( \frac{53297461115137}{147} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( -784\) , \( -8515\bigr] \)
${y}^2+{x}{y}={x}^{3}-784{x}-8515$
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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.