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
20.1-a4
20.1-a
$4$
$6$
\(\Q(\sqrt{35}) \)
$2$
$[2, 0]$
20.1
\( 2^{2} \cdot 5 \)
\( 2^{20} \cdot 5^{6} \)
$2.23594$
$(2,a+1), (5,a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$1$
\( 2 \cdot 3^{2} \)
$1$
$3.545375530$
1.348375146
\( \frac{488095744}{125} \)
\( \bigl[0\) , \( a\) , \( 0\) , \( 1984 a - 11727\) , \( 113073 a - 668944\bigr] \)
${y}^2={x}^{3}+a{x}^{2}+\left(1984a-11727\right){x}+113073a-668944$
20.1-b4
20.1-b
$4$
$6$
\(\Q(\sqrt{35}) \)
$2$
$[2, 0]$
20.1
\( 2^{2} \cdot 5 \)
\( 2^{20} \cdot 5^{6} \)
$2.23594$
$(2,a+1), (5,a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$1$
\( 2 \cdot 3 \)
$1$
$20.68730941$
2.622595135
\( \frac{488095744}{125} \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1984 a - 11727\) , \( -113073 a + 668944\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+\left(1984a-11727\right){x}-113073a+668944$
20.1-c4
20.1-c
$4$
$6$
\(\Q(\sqrt{35}) \)
$2$
$[2, 0]$
20.1
\( 2^{2} \cdot 5 \)
\( 2^{8} \cdot 5^{6} \)
$2.23594$
$(2,a+1), (5,a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$1$
\( 2 \cdot 3 \)
$0.564791727$
$20.68730941$
2.962440071
\( \frac{488095744}{125} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( -41\) , \( 116\bigr] \)
${y}^2={x}^{3}-{x}^{2}-41{x}+116$
20.1-d4
20.1-d
$4$
$6$
\(\Q(\sqrt{35}) \)
$2$
$[2, 0]$
20.1
\( 2^{2} \cdot 5 \)
\( 2^{8} \cdot 5^{6} \)
$2.23594$
$(2,a+1), (5,a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2 \)
$11.34765536$
$3.545375530$
3.400199212
\( \frac{488095744}{125} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -41\) , \( -116\bigr] \)
${y}^2={x}^{3}+{x}^{2}-41{x}-116$
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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.