Elliptic curves over \(\Q(\sqrt{-127285811}) \)

Results (unique match)

 

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
1.0.1-a1	1.0.1-a	$1$	$1$	\(\Q(\sqrt{-127285811}) \)	$2$	$[0, 1]$	1.0.1	\( 1 \)	\( 23567^{12} \)	$1008.15788$	$\textsf{none}$		$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓	✓	$2$	2Cn		\( 1 \)	$1$			\( -8441 a - 14002884 \)	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -9990090 a + 21097369555517\) , \( 14191419334208 a - 18651160865299269019\bigr] \)	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-9990090a+21097369555517\right){x}+14191419334208a-18651160865299269019$

 

  *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.