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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 (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
49.a1	49a4	49.a	49a	$4$	$14$	\( 7^{2} \)	\( 7^{9} \)	$0$	$\Z/2\Z$	$\Q(\sqrt{-7})$	$-28$	$N(\mathrm{U}(1))$		✓	$7$	7.48.0.3	7B.1.2				$1$	$1$		$0$	$14$	$0.520391$	$16581375$	$1.19804$	$8.77147$	$[1, -1, 0, -1822, 30393]$	\(y^2+xy=x^3-x^2-1822x+30393\)		$[]$
49.a2	49a3	49.a	49a	$4$	$14$	\( 7^{2} \)	\( - 7^{9} \)	$0$	$\Z/2\Z$	$\Q(\sqrt{-7})$	$-7$	$N(\mathrm{U}(1))$		✓	$7$	7.48.0.3	7B.1.2				$1$	$1$		$1$	$7$	$0.173817$	$-3375$	$0.98030$	$6.69373$	$[1, -1, 0, -107, 552]$	\(y^2+xy=x^3-x^2-107x+552\)		$[]$
49.a3	49a2	49.a	49a	$4$	$14$	\( 7^{2} \)	\( 7^{3} \)	$0$	$\Z/2\Z$	$\Q(\sqrt{-7})$	$-28$	$N(\mathrm{U}(1))$		✓	$7$	7.48.0.6	7B.1.5				$1$	$1$		$0$	$2$	$-0.452565$	$16581375$	$1.19804$	$5.77147$	$[1, -1, 0, -37, -78]$	\(y^2+xy=x^3-x^2-37x-78\)		$[]$
49.a4	49a1	49.a	49a	$4$	$14$	\( 7^{2} \)	\( - 7^{3} \)	$0$	$\Z/2\Z$	$\Q(\sqrt{-7})$	$-7$	$N(\mathrm{U}(1))$		✓	$7$	7.48.0.6	7B.1.5				$1$	$1$		$1$	$1$	$-0.799138$	$-3375$	$0.98030$	$3.69373$	$[1, -1, 0, -2, -1]$	\(y^2+xy=x^3-x^2-2x-1\)		$[]$

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