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
50052.1-a1
50052.1-a
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
50052.1
\( 2^{2} \cdot 3 \cdot 43 \cdot 97 \)
\( 2^{4} \cdot 3^{5} \cdot 43^{3} \cdot 97^{4} \)
$2.31502$
$(-2a+1), (-7a+1), (-11a+3), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \cdot 3 \)
$1$
$0.597249000$
2.068931227
\( \frac{3642965880419332}{190044833700609} a - \frac{37263435726089087}{760179334802436} \)
\( \bigl[1\) , \( -a\) , \( 1\) , \( 23 a - 47\) , \( -387 a + 725\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(23a-47\right){x}-387a+725$
50052.1-a2
50052.1-a
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
50052.1
\( 2^{2} \cdot 3 \cdot 43 \cdot 97 \)
\( 2^{2} \cdot 3^{10} \cdot 43^{6} \cdot 97^{2} \)
$2.31502$
$(-2a+1), (-7a+1), (-11a+3), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{3} \cdot 3 \)
$1$
$0.298624500$
2.068931227
\( -\frac{326779733064320576764}{14453082297513963} a + \frac{791609358879818344421}{28906164595027926} \)
\( \bigl[1\) , \( -a\) , \( 1\) , \( -1097 a + 523\) , \( -9495 a + 11745\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-1097a+523\right){x}-9495a+11745$
50052.1-b1
50052.1-b
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
50052.1
\( 2^{2} \cdot 3 \cdot 43 \cdot 97 \)
\( 2^{8} \cdot 3^{2} \cdot 43 \cdot 97 \)
$2.31502$
$(-2a+1), (-7a+1), (-11a+3), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2^{3} \)
$0.056004196$
$3.566702939$
3.690429034
\( -\frac{20358375}{66736} a + \frac{447346123}{200208} \)
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -5 a - 1\) , \( -2 a + 1\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-5a-1\right){x}-2a+1$
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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.