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

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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

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Results (4 matches)

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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
33.a1	33a3	33.a	33a	$4$	$4$	\( 3 \cdot 11 \)	\( 3^{3} \cdot 11^{4} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.7	2B	$264$	$48$	$0$	$1$	$1$		$2$	$6$	$-0.012632$	$347873904937/395307$	$1.00913$	$7.60047$	$1$	$[1, 1, 0, -146, 621]$	\(y^2+xy=x^3+x^2-146x+621\)	2.3.0.a.1, 4.12.0-4.c.1.1, 12.24.0-12.h.1.2, 88.24.0.?, 264.48.0.?	$[ ]$	$1$
33.a2	33a1	33.a	33a	$4$	$4$	\( 3 \cdot 11 \)	\( 3^{6} \cdot 11^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.1	2Cs	$132$	$48$	$0$	$1$	$1$		$2$	$3$	$-0.359206$	$169112377/88209$	$1.00669$	$5.41857$	$1$	$[1, 1, 0, -11, 0]$	\(y^2+xy=x^3+x^2-11x\)	2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.a.1.1, 44.24.0-44.b.1.2, 132.48.0.?	$[ ]$	$1$
33.a3	33a2	33.a	33a	$4$	$4$	\( 3 \cdot 11 \)	\( 3^{3} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.6	2B	$264$	$48$	$0$	$1$	$1$		$1$	$6$	$-0.705779$	$30664297/297$	$1.09706$	$4.93024$	$2$	$[1, 1, 0, -6, -9]$	\(y^2+xy=x^3+x^2-6x-9\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 12.12.0-4.c.1.2, 24.24.0-24.ba.1.4, $\ldots$	$[ ]$	$2$
33.a4	33a4	33.a	33a	$4$	$4$	\( 3 \cdot 11 \)	\( - 3^{12} \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.8	2B	$264$	$48$	$0$	$1$	$1$		$0$	$6$	$-0.012632$	$9090072503/5845851$	$1.03763$	$6.55810$	$2$	$[1, 1, 0, 44, 55]$	\(y^2+xy=x^3+x^2+44x+55\)	2.3.0.a.1, 4.12.0-4.c.1.2, 22.6.0.a.1, 24.24.0-24.ba.1.16, 44.24.0-44.g.1.1, $\ldots$	$[ ]$	$1$

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