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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

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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	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
34.a1	34a4	34.a	34a	$4$	$6$	\( 2 \cdot 17 \)	\( 2 \cdot 17^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.6.0.6, 3.8.0.2	2B, 3B.1.2	$408$	$96$	$1$	$1$	$1$		$0$	$12$	$0.179487$	$159661140625/48275138$	$1.06848$	$7.31528$	$[1, 0, 0, -113, -329]$	\(y^2+xy=x^3-113x-329\)	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 8.6.0.b.1, 24.48.0-24.y.1.13, $\ldots$	$[ ]$	$1$
34.a2	34a3	34.a	34a	$4$	$6$	\( 2 \cdot 17 \)	\( 2^{2} \cdot 17^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.6.0.1, 3.8.0.2	2B, 3B.1.2	$408$	$96$	$1$	$1$	$1$		$1$	$6$	$-0.167086$	$120920208625/19652$	$0.98564$	$7.23647$	$[1, 0, 0, -103, -411]$	\(y^2+xy=x^3-103x-411\)	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 8.6.0.c.1, 24.48.0-24.bw.1.11, $\ldots$	$[ ]$	$1$
34.a3	34a2	34.a	34a	$4$	$6$	\( 2 \cdot 17 \)	\( 2^{3} \cdot 17^{2} \)	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.6.0.6, 3.8.0.1	2B, 3B.1.1	$408$	$96$	$1$	$1$	$1$		$4$	$4$	$-0.369819$	$8805624625/2312$	$0.96590$	$6.49357$	$[1, 0, 0, -43, 105]$	\(y^2+xy=x^3-43x+105\)	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 8.6.0.b.1, 24.48.0-24.y.1.15, $\ldots$	$[ ]$	$1$
34.a4	34a1	34.a	34a	$4$	$6$	\( 2 \cdot 17 \)	\( 2^{6} \cdot 17 \)	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2, 3$	8.6.0.1, 3.8.0.1	2B, 3B.1.1	$408$	$96$	$1$	$1$	$1$		$5$	$2$	$-0.716393$	$3048625/1088$	$0.90010$	$4.23388$	$[1, 0, 0, -3, 1]$	\(y^2+xy=x^3-3x+1\)	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 8.6.0.c.1, 24.48.0-24.bw.1.15, $\ldots$	$[ ]$	$1$

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