Elliptic curves over \(\Q(\sqrt{-451767203}) \)

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	$1$	$1$	\(\Q(\sqrt{-451767203}) \)	$2$	$[0, 1]$	1.0.1	\( 1 \)	\( 141803^{12} \)	$1899.31021$	$\textsf{none}$		$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓	✓	$2$	2Cn		\( 1 \)	$1$			\( -35297 a + 198547128 \)	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -23163076 a + 266044005933275\) , \( 57560769602038 a - 836483958630700313803\bigr] \)	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-23163076a+266044005933275\right){x}+57560769602038a-836483958630700313803$

 

  *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.