Elliptic curves over $\Q$ of conductor 475

Results (7 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	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
475.a1	475c2	475.a	475c	$2$	$2$	\( 5^{2} \cdot 19 \)	\( 5^{3} \cdot 19^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$0.372858842$	$1$		$8$	$32$	$-0.326658$	$13312053/361$	$[1, -1, 1, -25, 52]$	\(y^2+xy+y=x^3-x^2-25x+52\)
475.a2	475c1	475.a	475c	$2$	$2$	\( 5^{2} \cdot 19 \)	\( - 5^{3} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$0.745717685$	$1$		$5$	$16$	$-0.673232$	$27/19$	$[1, -1, 1, 0, 2]$	\(y^2+xy+y=x^3-x^2+2\)
475.b1	475a3	475.b	475a	$3$	$9$	\( 5^{2} \cdot 19 \)	\( - 5^{6} \cdot 19 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	27.36.0.1	3B	$1$	$9$	$3$	$0$	$324$	$0.838158$	$-50357871050752/19$	$[0, -1, 1, -19233, -1020257]$	\(y^2+y=x^3-x^2-19233x-1020257\)
475.b2	475a2	475.b	475a	$3$	$9$	\( 5^{2} \cdot 19 \)	\( - 5^{6} \cdot 19^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.36.0.2	3Cs	$1$	$1$		$0$	$108$	$0.288852$	$-89915392/6859$	$[0, -1, 1, -233, -1382]$	\(y^2+y=x^3-x^2-233x-1382\)
475.b3	475a1	475.b	475a	$3$	$9$	\( 5^{2} \cdot 19 \)	\( - 5^{6} \cdot 19 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	27.36.0.1	3B	$1$	$1$		$0$	$36$	$-0.260454$	$32768/19$	$[0, -1, 1, 17, -7]$	\(y^2+y=x^3-x^2+17x-7\)
475.c1	475b2	475.c	475b	$2$	$2$	\( 5^{2} \cdot 19 \)	\( 5^{9} \cdot 19^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.365071063$	$1$		$4$	$160$	$0.478061$	$13312053/361$	$[1, -1, 0, -617, 5916]$	\(y^2+xy=x^3-x^2-617x+5916\)
475.c2	475b1	475.c	475b	$2$	$2$	\( 5^{2} \cdot 19 \)	\( - 5^{9} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2.730142127$	$1$		$3$	$80$	$0.131487$	$27/19$	$[1, -1, 0, 8, 291]$	\(y^2+xy=x^3-x^2+8x+291\)