Elliptic curves over $\Q$ of conductor 17

Conductor	j-invariant	Rank	Torsion	Complex multiplication
Bad$\ p$	Discriminant	Regulator	Analytic order of Ш	Galois image
Isogeny class size	Isogeny class degree	Cyclic isogeny degree	$p\ $div$\ $|Ш|	Nonmax$\ \ell$
Curves per isogeny class	Reduction	Integral points	Faltings height

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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	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
17.a1	17a3	17.a	17a	$4$	$4$	\( 17 \)	\( 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	32.96.0.18	2B	$1$	$1$		$0$	$4$	$-0.376636$	$82483294977/17$	$[1, -1, 1, -91, -310]$	\(y^2+xy+y=x^3-x^2-91x-310\)
17.a2	17a2	17.a	17a	$4$	$4$	\( 17 \)	\( 17^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	16.96.0.13	2Cs	$1$	$1$		$2$	$2$	$-0.723209$	$20346417/289$	$[1, -1, 1, -6, -4]$	\(y^2+xy+y=x^3-x^2-6x-4\)
17.a3	17a1	17.a	17a	$4$	$4$	\( 17 \)	\( - 17^{4} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	16.96.0.32	2B	$1$	$1$		$2$	$1$	$-0.376636$	$-35937/83521$	$[1, -1, 1, -1, -14]$	\(y^2+xy+y=x^3-x^2-x-14\)
17.a4	17a4	17.a	17a	$4$	$4$	\( 17 \)	\( 17 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	32.96.0.10	2B	$1$	$1$		$3$	$4$	$-1.069784$	$35937/17$	$[1, -1, 1, -1, 0]$	\(y^2+xy+y=x^3-x^2-x\)