↑

Learn more

The results below are complete, since the LMFDB contains all elliptic curves with conductor at most 500000

Refine search

Conductor	Discriminant	j-invariant	Rank

Bad$\ p$	Curves per isogeny class	Complex multiplication	Torsion

Isogeny class degree	Cyclic isogeny degree	Isogeny class size	Integral points

Analytic order of Ш	$p\ $div$\ $\|Ш\|	Regulator	Reduction	Faltings height

Galois image	Adelic level	Adelic index	Adelic genus

Nonmax$\ \ell$	$abc$ quality	Szpiro ratio	Manin constant

Intrinsic torsion order

			Sort order	Select

Results (displaying both matches)

Download displayed columns for results to

Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	CM	Sato-Tate	Semistable	Potentially good	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Intrinsic torsion order	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
108.a1	108a2	108.a	108a	$2$	$3$	\( 2^{2} \cdot 3^{3} \)	\( - 2^{8} \cdot 3^{9} \)	$0$	$\mathsf{trivial}$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$		✓	$3$	27.648.18.4	3B.1.2				$1$	$1$		$0$	$18$	$-0.035060$	$0$		$4.88825$	$1$	$[0, 0, 0, 0, -108]$	\(y^2=x^3-108\)		$[ ]$	$1$
108.a2	108a1	108.a	108a	$2$	$3$	\( 2^{2} \cdot 3^{3} \)	\( - 2^{8} \cdot 3^{3} \)	$0$	$\Z/3\Z$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$		✓	$3$	27.648.18.1	3B.1.1				$1$	$1$		$2$	$6$	$-0.584366$	$0$		$3.48041$	$1$	$[0, 0, 0, 0, 4]$	\(y^2=x^3+4\)		$[ ]$	$1$

Download displayed columns for results to