Elliptic curves over $\Q$ of conductor 55

Results (4 matches)

 

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
55.a1	55a3	55.a	55a	$4$	$4$	\( 5 \cdot 11 \)	\( 5^{4} \cdot 11 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.7	2B	$440$	$48$	$0$	$1$	$1$		$2$	$4$	$-0.285666$	$22930509321/6875$	$1.07717$	$5.95302$	$[1, -1, 0, -59, 190]$	\(y^2+xy=x^3-x^2-59x+190\)	2.3.0.a.1, 4.12.0-4.c.1.1, 40.24.0-40.z.1.4, 44.24.0-44.h.1.2, 440.48.0.?	$[]$
55.a2	55a2	55.a	55a	$4$	$4$	\( 5 \cdot 11 \)	\( 5 \cdot 11^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.8	2B	$440$	$48$	$0$	$1$	$1$		$0$	$4$	$-0.285666$	$2749884201/73205$	$0.94591$	$5.42376$	$[1, -1, 0, -29, -52]$	\(y^2+xy=x^3-x^2-29x-52\)	2.3.0.a.1, 4.12.0-4.c.1.2, 10.6.0.a.1, 20.24.0-20.g.1.1, 88.24.0.?, $\ldots$	$[]$
55.a3	55a1	55.a	55a	$4$	$4$	\( 5 \cdot 11 \)	\( 5^{2} \cdot 11^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.1	2Cs	$220$	$48$	$0$	$1$	$1$		$2$	$2$	$-0.632239$	$8120601/3025$	$1.05560$	$3.97020$	$[1, -1, 0, -4, 3]$	\(y^2+xy=x^3-x^2-4x+3\)	2.6.0.a.1, 4.12.0-2.a.1.1, 20.24.0-20.b.1.2, 44.24.0-44.a.1.1, 220.48.0.?	$[]$
55.a4	55a4	55.a	55a	$4$	$4$	\( 5 \cdot 11 \)	\( - 5 \cdot 11 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.6	2B	$440$	$48$	$0$	$1$	$1$		$1$	$4$	$-0.978812$	$59319/55$	$0.79207$	$2.74264$	$[1, -1, 0, 1, 0]$	\(y^2+xy=x^3-x^2+x\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 20.12.0-4.c.1.2, 40.24.0-40.z.1.10, $\ldots$	$[]$