Elliptic curves over $\Q$ of conductor 1216

Conductor	j-invariant	Rank	Torsion	Complex multiplication
Bad$\ p$	Discriminant	Regulator	Analytic order of Ш	Galois image
Isogeny class size	Isogeny class degree	Cyclic isogeny degree	$p\ $div$\ $|Ш|	Nonmax$\ \ell$
Curves per isogeny class	Reduction	Integral points	Faltings height

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Results (28 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
1216.a1	1216r1	1216.a	1216r	$1$	$1$	\( 2^{6} \cdot 19 \)	\( - 2^{15} \cdot 19 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.225942131$	$1$		$6$	$192$	$-0.199705$	$27000/19$	$[0, 0, 0, 20, 16]$	\(y^2=x^3+20x+16\)
1216.b1	1216q3	1216.b	1216q	$3$	$9$	\( 2^{6} \cdot 19 \)	\( - 2^{6} \cdot 19 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	27.36.0.1	3B	$0.595904332$	$1$		$2$	$432$	$0.380013$	$-50357871050752/19$	$[0, 1, 0, -3077, 64681]$	\(y^2=x^3+x^2-3077x+64681\)
1216.b2	1216q2	1216.b	1216q	$3$	$9$	\( 2^{6} \cdot 19 \)	\( - 2^{6} \cdot 19^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.36.0.2	3Cs	$0.198634777$	$1$		$4$	$144$	$-0.169293$	$-89915392/6859$	$[0, 1, 0, -37, 81]$	\(y^2=x^3+x^2-37x+81\)
1216.b3	1216q1	1216.b	1216q	$3$	$9$	\( 2^{6} \cdot 19 \)	\( - 2^{6} \cdot 19 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	27.36.0.1	3B	$0.595904332$	$1$		$2$	$48$	$-0.718599$	$32768/19$	$[0, 1, 0, 3, 1]$	\(y^2=x^3+x^2+3x+1\)
1216.c1	1216h1	1216.c	1216h	$1$	$1$	\( 2^{6} \cdot 19 \)	\( - 2^{14} \cdot 19 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$192$	$-0.094357$	$-4194304/19$	$[0, 1, 0, -85, -333]$	\(y^2=x^3+x^2-85x-333\)
1216.d1	1216l1	1216.d	1216l	$1$	$1$	\( 2^{6} \cdot 19 \)	\( - 2^{14} \cdot 19 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$128$	$-0.264905$	$-1024/19$	$[0, 1, 0, -5, -29]$	\(y^2=x^3+x^2-5x-29\)
1216.e1	1216b3	1216.e	1216b	$3$	$9$	\( 2^{6} \cdot 19 \)	\( - 2^{45} \cdot 19 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	27.36.0.1	3B	$2.504328284$	$1$		$0$	$3456$	$1.524891$	$-69173457625/2550136832$	$[0, -1, 0, -5473, -1251871]$	\(y^2=x^3-x^2-5473x-1251871\)
1216.e2	1216b1	1216.e	1216b	$3$	$9$	\( 2^{6} \cdot 19 \)	\( - 2^{21} \cdot 19 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	27.36.0.1	3B	$0.278258698$	$1$		$4$	$384$	$0.426278$	$-413493625/152$	$[0, -1, 0, -993, 12385]$	\(y^2=x^3-x^2-993x+12385\)
1216.e3	1216b2	1216.e	1216b	$3$	$9$	\( 2^{6} \cdot 19 \)	\( - 2^{27} \cdot 19^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.36.0.2	3Cs	$0.834776094$	$1$		$4$	$1152$	$0.975584$	$94196375/3511808$	$[0, -1, 0, 607, 45601]$	\(y^2=x^3-x^2+607x+45601\)
1216.f1	1216c1	1216.f	1216c	$1$	$1$	\( 2^{6} \cdot 19 \)	\( - 2^{17} \cdot 19 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.602396728$	$1$		$4$	$128$	$-0.070605$	$-31250/19$	$[0, -1, 0, -33, -95]$	\(y^2=x^3-x^2-33x-95\)
1216.g1	1216j2	1216.g	1216j	$2$	$5$	\( 2^{6} \cdot 19 \)	\( - 2^{19} \cdot 19^{5} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.2	5B.4.2	$1$	$1$		$0$	$1920$	$1.057505$	$-37966934881/4952198$	$[0, -1, 0, -4481, 129313]$	\(y^2=x^3-x^2-4481x+129313\)
1216.g2	1216j1	1216.g	1216j	$2$	$5$	\( 2^{6} \cdot 19 \)	\( - 2^{23} \cdot 19 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.1	5B.4.1	$1$	$1$		$0$	$384$	$0.252787$	$-1/608$	$[0, -1, 0, -1, -607]$	\(y^2=x^3-x^2-x-607\)
1216.h1	1216i1	1216.h	1216i	$1$	$1$	\( 2^{6} \cdot 19 \)	\( - 2^{6} \cdot 19^{5} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.15.0.1	5Ns	$1$	$1$		$0$	$480$	$0.252518$	$-4741632/2476099$	$[0, 0, 0, -14, -606]$	\(y^2=x^3-14x-606\)
1216.i1	1216n1	1216.i	1216n	$1$	$1$	\( 2^{6} \cdot 19 \)	\( - 2^{6} \cdot 19^{5} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.15.0.1	5Ns	$0.328891621$	$1$		$2$	$480$	$0.252518$	$-4741632/2476099$	$[0, 0, 0, -14, 606]$	\(y^2=x^3-14x+606\)
1216.j1	1216a1	1216.j	1216a	$1$	$1$	\( 2^{6} \cdot 19 \)	\( - 2^{6} \cdot 19 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.595835310$	$1$		$2$	$32$	$-0.715568$	$-13824/19$	$[0, 0, 0, -2, 2]$	\(y^2=x^3-2x+2\)
1216.k1	1216e1	1216.k	1216e	$1$	$1$	\( 2^{6} \cdot 19 \)	\( - 2^{6} \cdot 19 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$32$	$-0.715568$	$-13824/19$	$[0, 0, 0, -2, -2]$	\(y^2=x^3-2x-2\)
1216.l1	1216p1	1216.l	1216p	$1$	$1$	\( 2^{6} \cdot 19 \)	\( - 2^{17} \cdot 19 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.294246876$	$1$		$4$	$128$	$-0.070605$	$-31250/19$	$[0, 1, 0, -33, 95]$	\(y^2=x^3+x^2-33x+95\)
1216.m1	1216o3	1216.m	1216o	$3$	$9$	\( 2^{6} \cdot 19 \)	\( - 2^{45} \cdot 19 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	27.36.0.1	3B	$1.698405069$	$1$		$0$	$3456$	$1.524891$	$-69173457625/2550136832$	$[0, 1, 0, -5473, 1251871]$	\(y^2=x^3+x^2-5473x+1251871\)
1216.m2	1216o1	1216.m	1216o	$3$	$9$	\( 2^{6} \cdot 19 \)	\( - 2^{21} \cdot 19 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	27.36.0.1	3B	$1.698405069$	$1$		$2$	$384$	$0.426278$	$-413493625/152$	$[0, 1, 0, -993, -12385]$	\(y^2=x^3+x^2-993x-12385\)
1216.m3	1216o2	1216.m	1216o	$3$	$9$	\( 2^{6} \cdot 19 \)	\( - 2^{27} \cdot 19^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.36.0.2	3Cs	$0.566135023$	$1$		$4$	$1152$	$0.975584$	$94196375/3511808$	$[0, 1, 0, 607, -45601]$	\(y^2=x^3+x^2+607x-45601\)
1216.n1	1216f2	1216.n	1216f	$2$	$5$	\( 2^{6} \cdot 19 \)	\( - 2^{19} \cdot 19^{5} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.2	5B.4.2	$1$	$1$		$0$	$1920$	$1.057505$	$-37966934881/4952198$	$[0, 1, 0, -4481, -129313]$	\(y^2=x^3+x^2-4481x-129313\)
1216.n2	1216f1	1216.n	1216f	$2$	$5$	\( 2^{6} \cdot 19 \)	\( - 2^{23} \cdot 19 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.1	5B.4.1	$1$	$1$		$0$	$384$	$0.252787$	$-1/608$	$[0, 1, 0, -1, 607]$	\(y^2=x^3+x^2-x+607\)
1216.o1	1216d3	1216.o	1216d	$3$	$9$	\( 2^{6} \cdot 19 \)	\( - 2^{6} \cdot 19 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	27.36.0.1	3B	$9.167331319$	$1$		$0$	$432$	$0.380013$	$-50357871050752/19$	$[0, -1, 0, -3077, -64681]$	\(y^2=x^3-x^2-3077x-64681\)
1216.o2	1216d2	1216.o	1216d	$3$	$9$	\( 2^{6} \cdot 19 \)	\( - 2^{6} \cdot 19^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.36.0.2	3Cs	$3.055777106$	$1$		$2$	$144$	$-0.169293$	$-89915392/6859$	$[0, -1, 0, -37, -81]$	\(y^2=x^3-x^2-37x-81\)
1216.o3	1216d1	1216.o	1216d	$3$	$9$	\( 2^{6} \cdot 19 \)	\( - 2^{6} \cdot 19 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	27.36.0.1	3B	$1.018592368$	$1$		$2$	$48$	$-0.718599$	$32768/19$	$[0, -1, 0, 3, -1]$	\(y^2=x^3-x^2+3x-1\)
1216.p1	1216g1	1216.p	1216g	$1$	$1$	\( 2^{6} \cdot 19 \)	\( - 2^{14} \cdot 19 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$128$	$-0.264905$	$-1024/19$	$[0, -1, 0, -5, 29]$	\(y^2=x^3-x^2-5x+29\)
1216.q1	1216k1	1216.q	1216k	$1$	$1$	\( 2^{6} \cdot 19 \)	\( - 2^{14} \cdot 19 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$192$	$-0.094357$	$-4194304/19$	$[0, -1, 0, -85, 333]$	\(y^2=x^3-x^2-85x+333\)
1216.r1	1216m1	1216.r	1216m	$1$	$1$	\( 2^{6} \cdot 19 \)	\( - 2^{15} \cdot 19 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$192$	$-0.199705$	$27000/19$	$[0, 0, 0, 20, -16]$	\(y^2=x^3+20x-16\)