Elliptic curves over $\Q$ of conductor 507

Results (8 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
507.a1	507c3	507.a	507c	$4$	$4$	\( 3 \cdot 13^{2} \)	\( 3^{4} \cdot 13^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$312$	$48$	$0$	$1.267343718$	$1$		$2$	$672$	$0.964108$	$37159393753/1053$	$1.11616$	$6.37844$	$[1, 1, 1, -11749, -495058]$	\(y^2+xy+y=x^3+x^2-11749x-495058\)	2.3.0.a.1, 4.12.0-4.c.1.2, 24.24.0-24.ba.1.1, 26.6.0.b.1, 52.24.0-52.g.1.1, $\ldots$	$[(200, 2181)]$
507.a2	507c4	507.a	507c	$4$	$4$	\( 3 \cdot 13^{2} \)	\( 3 \cdot 13^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$312$	$48$	$0$	$1.267343718$	$1$		$6$	$672$	$0.964108$	$822656953/85683$	$0.96086$	$5.76667$	$[1, 1, 1, -3299, 64670]$	\(y^2+xy+y=x^3+x^2-3299x+64670\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 12.12.0.h.1, 24.24.0-12.h.1.6, $\ldots$	$[(44, 62)]$
507.a3	507c2	507.a	507c	$4$	$4$	\( 3 \cdot 13^{2} \)	\( 3^{2} \cdot 13^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$156$	$48$	$0$	$2.534687436$	$1$		$6$	$336$	$0.617535$	$10218313/1521$	$0.91403$	$5.06211$	$[1, 1, 1, -764, -7324]$	\(y^2+xy+y=x^3+x^2-764x-7324\)	2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.a.1.3, 52.24.0-52.b.1.2, 156.48.0.?	$[(-18, 40)]$
507.a4	507c1	507.a	507c	$4$	$4$	\( 3 \cdot 13^{2} \)	\( - 3 \cdot 13^{7} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$312$	$48$	$0$	$5.069374873$	$1$		$3$	$168$	$0.270961$	$12167/39$	$0.85844$	$4.22394$	$[1, 1, 1, 81, -564]$	\(y^2+xy+y=x^3+x^2+81x-564\)	2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.ba.1.9, 78.6.0.?, 104.24.0.?, $\ldots$	$[(94/3, 913/3)]$
507.b1	507b2	507.b	507b	$2$	$7$	\( 3 \cdot 13^{2} \)	\( - 3^{14} \cdot 13^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 7$	4.2.0.1, 7.8.0.1	7B	$2184$	$192$	$6$	$0.890582876$	$1$		$4$	$168$	$0.390368$	$-276301129/4782969$	$1.06787$	$4.49515$	$[1, 1, 1, -75, -1422]$	\(y^2+xy+y=x^3+x^2-75x-1422\)	4.2.0.a.1, 7.8.0.a.1, 28.16.0.a.1, 91.48.0.?, 168.32.0.?, $\ldots$	$[(106, 1040)]$
507.b2	507b1	507.b	507b	$2$	$7$	\( 3 \cdot 13^{2} \)	\( - 3^{2} \cdot 13^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 7$	4.2.0.1, 7.8.0.1	7B	$2184$	$192$	$6$	$0.127226125$	$1$		$8$	$24$	$-0.582586$	$-658489/9$	$0.91436$	$2.97839$	$[1, 1, 1, -10, 8]$	\(y^2+xy+y=x^3+x^2-10x+8\)	4.2.0.a.1, 7.8.0.a.1, 28.16.0.a.1, 91.48.0.?, 168.32.0.?, $\ldots$	$[(2, 0)]$
507.c1	507a2	507.c	507a	$2$	$7$	\( 3 \cdot 13^{2} \)	\( - 3^{14} \cdot 13^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 7$	4.2.0.1, 7.16.0.2	7B.2.3	$2184$	$192$	$6$	$1.810964640$	$1$		$0$	$2184$	$1.672844$	$-276301129/4782969$	$1.06787$	$6.96599$	$[1, 1, 0, -12678, -3060351]$	\(y^2+xy=x^3+x^2-12678x-3060351\)	4.2.0.a.1, 7.16.0-7.a.1.1, 24.4.0-4.a.1.1, 28.32.0-28.a.1.4, 91.48.0.?, $\ldots$	$[(6144/5, 354243/5)]$
507.c2	507a1	507.c	507a	$2$	$7$	\( 3 \cdot 13^{2} \)	\( - 3^{2} \cdot 13^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 7$	4.2.0.1, 7.16.0.1	7B.2.1	$2184$	$192$	$6$	$0.258709234$	$1$		$4$	$312$	$0.699888$	$-658489/9$	$0.91436$	$5.44924$	$[1, 1, 0, -1693, 26434]$	\(y^2+xy=x^3+x^2-1693x+26434\)	4.2.0.a.1, 7.16.0-7.a.1.2, 24.4.0-4.a.1.1, 28.32.0-28.a.1.2, 91.48.0.?, $\ldots$	$[(70, 472)]$