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
50020.3-a1
50020.3-a
$2$
$2$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
50020.3
\( 2^{2} \cdot 5 \cdot 41 \cdot 61 \)
\( 2^{8} \cdot 5^{8} \cdot 41^{2} \cdot 61 \)
$2.67273$
$(a+1), (-a-2), (4a+5), (-6a-5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1.916777935$
$1.139809162$
4.369522107
\( -\frac{8774773673436}{40055078125} a + \frac{30383733145352}{40055078125} \)
\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -20 i + 21\) , \( -53 i + 40\bigr] \)
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-i{x}^{2}+\left(-20i+21\right){x}-53i+40$
50020.3-a2
50020.3-a
$2$
$2$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
50020.3
\( 2^{2} \cdot 5 \cdot 41 \cdot 61 \)
\( 2^{4} \cdot 5^{4} \cdot 41 \cdot 61^{2} \)
$2.67273$
$(a+1), (-a-2), (4a+5), (-6a-5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$0.958388967$
$2.279618325$
4.369522107
\( \frac{74717261312}{95350625} a + \frac{326713991216}{95350625} \)
\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( 5 i - 9\) , \( -6 i + 8\bigr] \)
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-i{x}^{2}+\left(5i-9\right){x}-6i+8$
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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.