Elliptic curves over $\Q$ of conductor 58

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

Results (3 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
58.a1	58a1	58.a	58a	$1$	$1$	\( 2 \cdot 29 \)	\( - 2^{2} \cdot 29 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$116$	$2$	$0$	$0.042420307$	$1$		$12$	$4$	$-0.902228$	$-185193/116$	$0.85122$	$3.16780$	$1$	$[1, -1, 0, -1, 1]$	\(y^2+xy=x^3-x^2-x+1\)	116.2.0.?	$[(0, 1)]$	$1$
58.b1	58b2	58.b	58b	$2$	$5$	\( 2 \cdot 29 \)	\( - 2^{2} \cdot 29^{5} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$5$	5.24.0.3	5B.1.2	$580$	$48$	$1$	$1$	$1$		$0$	$20$	$0.347164$	$-10418796526321/82044596$	$0.99481$	$7.38544$	$1$	$[1, 1, 1, -455, -3951]$	\(y^2+xy+y=x^3+x^2-455x-3951\)	5.24.0-5.a.2.2, 116.2.0.?, 580.48.1.?	$[ ]$	$1$
58.b2	58b1	58.b	58b	$2$	$5$	\( 2 \cdot 29 \)	\( - 2^{10} \cdot 29 \)	$0$	$\Z/5\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$5$	5.24.0.1	5B.1.1	$580$	$48$	$1$	$1$	$1$		$4$	$4$	$-0.457555$	$13651919/29696$	$1.08166$	$4.29613$	$1$	$[1, 1, 1, 5, 9]$	\(y^2+xy+y=x^3+x^2+5x+9\)	5.24.0-5.a.1.2, 116.2.0.?, 580.48.1.?	$[ ]$	$1$

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