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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

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Results (8 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
256.a1	256a2	256.a	256a	$2$	$2$	$2^{8}$	$2^{15}$	$1$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓	$2$	16.192.5.624	2B				$0.960251595$	$1$		$5$	$16$	$-0.403973$	$8000$	$0.90298$	$3.49572$	$[0, 1, 0, -13, -21]$	$y^2=x^3+x^2-13x-21$		$[(5, 8)]$
256.a2	256a1	256.a	256a	$2$	$2$	$2^{8}$	$2^{9}$	$1$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓	$2$	16.192.5.607	2B				$0.480125797$	$1$		$7$	$8$	$-0.750546$	$8000$	$0.90298$	$2.74572$	$[0, 1, 0, -3, 1]$	$y^2=x^3+x^2-3x+1$		$[(0, 1)]$
256.b1	256b1	256.b	256b	$2$	$2$	$2^{8}$	$2^{9}$	$1$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$		✓	$2$	16.384.9.831	2B				$0.608709031$	$1$		$7$	$8$	$-0.790672$	$1728$		$2.46936$	$[0, 0, 0, -2, 0]$	$y^2=x^3-2x$		$[(2, 2)]$
256.b2	256b2	256.b	256b	$2$	$2$	$2^{8}$	$- 2^{15}$	$1$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$		✓	$2$	16.384.9.819	2B				$1.217418063$	$1$		$5$	$16$	$-0.444099$	$1728$		$3.21936$	$[0, 0, 0, 8, 0]$	$y^2=x^3+8x$		$[(1, 3)]$
256.c1	256c2	256.c	256c	$2$	$2$	$2^{8}$	$2^{15}$	$0$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$		✓	$2$	16.384.9.829	2B				$1$	$1$		$1$	$16$	$-0.444099$	$1728$		$3.21936$	$[0, 0, 0, -8, 0]$	$y^2=x^3-8x$		$[]$
256.c2	256c1	256.c	256c	$2$	$2$	$2^{8}$	$- 2^{9}$	$0$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$		✓	$2$	16.384.9.817	2B				$1$	$1$		$1$	$8$	$-0.790672$	$1728$		$2.46936$	$[0, 0, 0, 2, 0]$	$y^2=x^3+2x$		$[]$
256.d1	256d2	256.d	256d	$2$	$2$	$2^{8}$	$2^{15}$	$0$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓	$2$	16.192.5.602	2B				$1$	$1$		$1$	$16$	$-0.403973$	$8000$	$0.90298$	$3.49572$	$[0, -1, 0, -13, 21]$	$y^2=x^3-x^2-13x+21$		$[]$
256.d2	256d1	256.d	256d	$2$	$2$	$2^{8}$	$2^{9}$	$0$	$\Z/2\Z$	$\Q(\sqrt{-2})$	$-8$	$N(\mathrm{U}(1))$		✓	$2$	16.192.5.617	2B				$1$	$1$		$1$	$8$	$-0.750546$	$8000$	$0.90298$	$2.74572$	$[0, -1, 0, -3, -1]$	$y^2=x^3-x^2-3x-1$		$[]$

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