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
50052.4-a1
50052.4-a
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
50052.4
\( 2^{2} \cdot 3 \cdot 43 \cdot 97 \)
\( 2^{4} \cdot 3^{5} \cdot 43^{3} \cdot 97^{4} \)
$2.31502$
$(-2a+1), (7a-6), (-11a+8), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \cdot 3 \)
$1$
$0.597249000$
2.068931227
\( -\frac{3642965880419332}{190044833700609} a - \frac{22691572204411759}{760179334802436} \)
\( \bigl[a\) , \( -a\) , \( 1\) , \( 46 a - 23\) , \( 387 a + 338\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(46a-23\right){x}+387a+338$
50052.4-a2
50052.4-a
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
50052.4
\( 2^{2} \cdot 3 \cdot 43 \cdot 97 \)
\( 2^{2} \cdot 3^{10} \cdot 43^{6} \cdot 97^{2} \)
$2.31502$
$(-2a+1), (7a-6), (-11a+8), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{3} \cdot 3 \)
$1$
$0.298624500$
2.068931227
\( \frac{326779733064320576764}{14453082297513963} a + \frac{46016630917059063631}{9635388198342642} \)
\( \bigl[a\) , \( -a\) , \( 1\) , \( -524 a + 1097\) , \( 9495 a + 2250\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-524a+1097\right){x}+9495a+2250$
50052.4-b1
50052.4-b
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
50052.4
\( 2^{2} \cdot 3 \cdot 43 \cdot 97 \)
\( 2^{8} \cdot 3^{2} \cdot 43 \cdot 97 \)
$2.31502$
$(-2a+1), (7a-6), (-11a+8), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2^{3} \)
$0.056004196$
$3.566702939$
3.690429034
\( \frac{20358375}{66736} a + \frac{193135499}{100104} \)
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -5 a + 1\) , \( a\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-5a+1\right){x}+a$
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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.