Elliptic curve search results

Results (32 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	Intrinsic torsion order	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
10368.a1	10368be1	10368.a	10368be	$1$	$1$	\( 2^{7} \cdot 3^{4} \)	\( - 2^{8} \cdot 3^{4} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	8.4.0.2		$8$	$4$	$0$	$1.016754877$	$1$		$8$	$768$	$-0.484169$	$1152$	$0.61315$	$1.83734$	$1$	$[0, 0, 0, 6, 4]$	\(y^2=x^3+6x+4\)	4.2.0.a.1, 8.4.0-4.a.1.1	$[(0, 2), (3, 7)]$	$1$
10368.b1	10368m1	10368.b	10368m	$1$	$1$	\( 2^{7} \cdot 3^{4} \)	\( - 2^{14} \cdot 3^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.2.0.1		$12$	$4$	$0$	$1.747393186$	$1$		$2$	$4608$	$0.411710$	$1152$	$0.61315$	$3.00000$	$1$	$[0, 0, 0, 216, -864]$	\(y^2=x^3+216x-864\)	4.2.0.a.1, 12.4.0-4.a.1.1	$[(4, 8)]$	$1$
10368.c1	10368l1	10368.c	10368l	$1$	$1$	\( 2^{7} \cdot 3^{4} \)	\( - 2^{8} \cdot 3^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	8.4.0.2		$8$	$4$	$0$	$0.966289721$	$1$		$2$	$768$	$-0.484169$	$1152$	$0.61315$	$1.83734$	$1$	$[0, 0, 0, 6, -4]$	\(y^2=x^3+6x-4\)	4.2.0.a.1, 8.4.0-4.a.1.1	$[(2, 4)]$	$1$
10368.d1	10368k1	10368.d	10368k	$1$	$1$	\( 2^{7} \cdot 3^{4} \)	\( - 2^{14} \cdot 3^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.2.0.1		$12$	$4$	$0$	$0.674651306$	$1$		$2$	$4608$	$0.411710$	$1152$	$0.61315$	$3.00000$	$1$	$[0, 0, 0, 216, 864]$	\(y^2=x^3+216x+864\)	4.2.0.a.1, 12.4.0-4.a.1.1	$[(12, 72)]$	$1$
10368.bc1	10368j1	10368.bc	10368j	$1$	$1$	\( 2^{7} \cdot 3^{4} \)	\( - 2^{8} \cdot 3^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.2.0.1		$24$	$4$	$0$	$0.711092309$	$1$		$2$	$2304$	$0.065137$	$1152$	$0.61315$	$2.55022$	$1$	$[0, 0, 0, 54, -108]$	\(y^2=x^3+54x-108\)	4.2.0.a.1, 24.4.0-4.a.1.1	$[(3, 9)]$	$1$
10368.bd1	10368bd1	10368.bd	10368bd	$1$	$1$	\( 2^{7} \cdot 3^{4} \)	\( - 2^{14} \cdot 3^{4} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.4.0.3		$4$	$4$	$0$	$1$	$1$		$0$	$1536$	$-0.137596$	$1152$	$0.61315$	$2.28712$	$1$	$[0, 0, 0, 24, 32]$	\(y^2=x^3+24x+32\)	4.4.0-4.a.1.1	$[ ]$	$1$
10368.be1	10368bc1	10368.be	10368bc	$1$	$1$	\( 2^{7} \cdot 3^{4} \)	\( - 2^{8} \cdot 3^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.2.0.1		$24$	$4$	$0$	$1$	$1$		$0$	$2304$	$0.065137$	$1152$	$0.61315$	$2.55022$	$1$	$[0, 0, 0, 54, 108]$	\(y^2=x^3+54x+108\)	4.2.0.a.1, 24.4.0-4.a.1.1	$[ ]$	$1$
10368.bf1	10368bb1	10368.bf	10368bb	$1$	$1$	\( 2^{7} \cdot 3^{4} \)	\( - 2^{14} \cdot 3^{4} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.4.0.3		$4$	$4$	$0$	$1$	$1$		$0$	$1536$	$-0.137596$	$1152$	$0.61315$	$2.28712$	$1$	$[0, 0, 0, 24, -32]$	\(y^2=x^3+24x-32\)	4.4.0-4.a.1.1	$[ ]$	$1$
259200.bm1	259200bm1	259200.bm	259200bm	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \)	\( - 2^{14} \cdot 3^{4} \cdot 5^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.2.0.1		$20$	$4$	$0$	$3.032479947$	$1$		$2$	$165888$	$0.667123$	$1152$	$0.61315$	$2.47120$	$1$	$[0, 0, 0, 600, -4000]$	\(y^2=x^3+600x-4000\)	4.2.0.a.1, 20.4.0-4.a.1.1	$[(44, 328)]$	$1$
259200.bp1	259200bp1	259200.bp	259200bp	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \)	\( - 2^{8} \cdot 3^{10} \cdot 5^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.2.0.1		$120$	$4$	$0$	$1.903050194$	$1$		$2$	$248832$	$0.869856$	$1152$	$0.61315$	$2.66636$	$1$	$[0, 0, 0, 1350, 13500]$	\(y^2=x^3+1350x+13500\)	4.2.0.a.1, 120.4.0.?	$[(-6, 72)]$	$1$
259200.cc1	259200cc1	259200.cc	259200cc	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \)	\( - 2^{14} \cdot 3^{10} \cdot 5^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.2.0.1		$60$	$4$	$0$	$1$	$1$		$0$	$497664$	$1.216429$	$1152$	$0.61315$	$3.00000$	$1$	$[0, 0, 0, 5400, 108000]$	\(y^2=x^3+5400x+108000\)	4.2.0.a.1, 60.4.0-4.a.1.1	$[ ]$	$1$
259200.cf1	259200cf1	259200.cf	259200cf	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \)	\( - 2^{8} \cdot 3^{4} \cdot 5^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.2.0.1		$40$	$4$	$0$	$1$	$1$		$0$	$82944$	$0.320549$	$1152$	$0.61315$	$2.13757$	$1$	$[0, 0, 0, 150, -500]$	\(y^2=x^3+150x-500\)	4.2.0.a.1, 40.4.0-4.a.1.1	$[ ]$	$1$
259200.eo1	259200eo1	259200.eo	259200eo	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \)	\( - 2^{14} \cdot 3^{10} \cdot 5^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.2.0.1		$60$	$4$	$0$	$1$	$1$		$0$	$497664$	$1.216429$	$1152$	$0.61315$	$3.00000$	$1$	$[0, 0, 0, 5400, -108000]$	\(y^2=x^3+5400x-108000\)	4.2.0.a.1, 60.4.0-4.a.1.1	$[ ]$	$1$
259200.er1	259200er1	259200.er	259200er	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \)	\( - 2^{8} \cdot 3^{4} \cdot 5^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.2.0.1		$40$	$4$	$0$	$3.034153645$	$1$		$2$	$82944$	$0.320549$	$1152$	$0.61315$	$2.13757$	$1$	$[0, 0, 0, 150, 500]$	\(y^2=x^3+150x+500\)	4.2.0.a.1, 40.4.0-4.a.1.1	$[(11, 59)]$	$1$
259200.fe1	259200fe1	259200.fe	259200fe	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \)	\( - 2^{14} \cdot 3^{4} \cdot 5^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.2.0.1		$20$	$4$	$0$	$5.665523528$	$1$		$2$	$165888$	$0.667123$	$1152$	$0.61315$	$2.47120$	$1$	$[0, 0, 0, 600, 4000]$	\(y^2=x^3+600x+4000\)	4.2.0.a.1, 20.4.0-4.a.1.1	$[(804, 22808)]$	$1$
259200.fh1	259200fh1	259200.fh	259200fh	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \)	\( - 2^{8} \cdot 3^{10} \cdot 5^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.2.0.1		$120$	$4$	$0$	$1$	$4$	$2$	$0$	$248832$	$0.869856$	$1152$	$0.61315$	$2.66636$	$1$	$[0, 0, 0, 1350, -13500]$	\(y^2=x^3+1350x-13500\)	4.2.0.a.1, 120.4.0.?	$[ ]$	$1$
508032.e1	-	508032.e	-	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 7^{2} \)	\( - 2^{14} \cdot 3^{4} \cdot 7^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.2.0.1		$28$	$4$	$0$	$1.689802659$	$1$		$2$	$552960$	$0.835359$	$1152$	$0.61315$	$2.49829$	$1$	$[0, 0, 0, 1176, 10976]$	\(y^2=x^3+1176x+10976\)	4.2.0.a.1, 28.4.0-4.a.1.1	$[(-7, 49)]$
508032.f1	-	508032.f	-	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 7^{2} \)	\( - 2^{8} \cdot 3^{10} \cdot 7^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.2.0.1		$168$	$4$	$0$	$0.991071640$	$1$		$2$	$829440$	$1.038092$	$1152$	$0.61315$	$2.68345$	$1$	$[0, 0, 0, 2646, -37044]$	\(y^2=x^3+2646x-37044\)	4.2.0.a.1, 168.4.0.?	$[(84, 882)]$
508032.s1	-	508032.s	-	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 7^{2} \)	\( - 2^{14} \cdot 3^{4} \cdot 7^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.2.0.1		$28$	$4$	$0$	$2.873143531$	$1$		$2$	$552960$	$0.835359$	$1152$	$0.61315$	$2.49829$	$1$	$[0, 0, 0, 1176, -10976]$	\(y^2=x^3+1176x-10976\)	4.2.0.a.1, 28.4.0-4.a.1.1	$[(105, 1127)]$
508032.t1	-	508032.t	-	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 7^{2} \)	\( - 2^{8} \cdot 3^{10} \cdot 7^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.2.0.1		$168$	$4$	$0$	$1$	$1$		$0$	$829440$	$1.038092$	$1152$	$0.61315$	$2.68345$	$1$	$[0, 0, 0, 2646, 37044]$	\(y^2=x^3+2646x+37044\)	4.2.0.a.1, 168.4.0.?	$[ ]$
508032.dg1	-	508032.dg	-	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 7^{2} \)	\( - 2^{14} \cdot 3^{10} \cdot 7^{6} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.2.0.1		$84$	$4$	$0$	$4.258705793$	$1$		$6$	$1658880$	$1.384665$	$1152$	$0.61315$	$3.00000$	$1$	$[0, 0, 0, 10584, 296352]$	\(y^2=x^3+10584x+296352\)	4.2.0.a.1, 84.4.0.?	$[(28, 784), (273, 4851)]$
508032.dh1	-	508032.dh	-	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 7^{2} \)	\( - 2^{8} \cdot 3^{4} \cdot 7^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.2.0.1		$56$	$4$	$0$	$3.396048917$	$1$		$2$	$276480$	$0.488785$	$1152$	$0.61315$	$2.18174$	$1$	$[0, 0, 0, 294, -1372]$	\(y^2=x^3+294x-1372\)	4.2.0.a.1, 56.4.0-4.a.1.1	$[(32, 202)]$
508032.du1	-	508032.du	-	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 7^{2} \)	\( - 2^{14} \cdot 3^{10} \cdot 7^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.2.0.1		$84$	$4$	$0$	$1$	$4$	$2$	$0$	$1658880$	$1.384665$	$1152$	$0.61315$	$3.00000$	$1$	$[0, 0, 0, 10584, -296352]$	\(y^2=x^3+10584x-296352\)	4.2.0.a.1, 84.4.0.?	$[ ]$
508032.dv1	-	508032.dv	-	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 7^{2} \)	\( - 2^{8} \cdot 3^{4} \cdot 7^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.2.0.1		$56$	$4$	$0$	$1$	$1$		$0$	$276480$	$0.488785$	$1152$	$0.61315$	$2.18174$	$1$	$[0, 0, 0, 294, 1372]$	\(y^2=x^3+294x+1372\)	4.2.0.a.1, 56.4.0-4.a.1.1	$[ ]$
12700800.da1	-	12700800.da	-	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{8} \cdot 3^{10} \cdot 5^{6} \cdot 7^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.2.0.1		$840$	$4$	$0$	$1$	$1$		$0$	$89579520$	$1.842810$	$1152$	$0.61315$	$2.74575$	$1$	$[0, 0, 0, 66150, -4630500]$	\(y^2=x^3+66150x-4630500\)	4.2.0.a.1, 840.4.0.?	$[ ]$
12700800.db1	-	12700800.db	-	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{8} \cdot 3^{4} \cdot 5^{6} \cdot 7^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.2.0.1		$280$	$4$	$0$	$1$	$1$		$0$	$29859840$	$1.293505$	$1152$	$0.61315$	$2.34276$	$1$	$[0, 0, 0, 7350, -171500]$	\(y^2=x^3+7350x-171500\)	4.2.0.a.1, 280.4.0.?	$[ ]$
12700800.eu1	-	12700800.eu	-	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{14} \cdot 3^{10} \cdot 5^{6} \cdot 7^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.2.0.1		$420$	$4$	$0$	$7.032080557$	$1$		$0$	$179159040$	$2.189384$	$1152$	$0.61315$	$3.00000$	$1$	$[0, 0, 0, 264600, 37044000]$	\(y^2=x^3+264600x+37044000\)	4.2.0.a.1, 420.4.0.?	$[(4249/3, 441343/3)]$
12700800.ev1	-	12700800.ev	-	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{14} \cdot 3^{4} \cdot 5^{6} \cdot 7^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.2.0.1		$140$	$4$	$0$	$1$	$4$	$2$	$0$	$59719680$	$1.640078$	$1152$	$0.61315$	$2.59702$	$1$	$[0, 0, 0, 29400, 1372000]$	\(y^2=x^3+29400x+1372000\)	4.2.0.a.1, 140.4.0.?	$[ ]$
12700800.sw1	-	12700800.sw	-	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{8} \cdot 3^{10} \cdot 5^{6} \cdot 7^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.2.0.1		$840$	$4$	$0$	$5.378888611$	$1$		$2$	$89579520$	$1.842810$	$1152$	$0.61315$	$2.74575$	$1$	$[0, 0, 0, 66150, 4630500]$	\(y^2=x^3+66150x+4630500\)	4.2.0.a.1, 840.4.0.?	$[(16, 2386)]$
12700800.sx1	-	12700800.sx	-	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{8} \cdot 3^{4} \cdot 5^{6} \cdot 7^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.2.0.1		$280$	$4$	$0$	$8.984968930$	$1$		$0$	$29859840$	$1.293505$	$1152$	$0.61315$	$2.34276$	$1$	$[0, 0, 0, 7350, 171500]$	\(y^2=x^3+7350x+171500\)	4.2.0.a.1, 280.4.0.?	$[(58436/19, 16235366/19)]$
12700800.uq1	-	12700800.uq	-	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{14} \cdot 3^{10} \cdot 5^{6} \cdot 7^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.2.0.1		$420$	$4$	$0$	$7.901296639$	$1$		$0$	$179159040$	$2.189384$	$1152$	$0.61315$	$3.00000$	$1$	$[0, 0, 0, 264600, -37044000]$	\(y^2=x^3+264600x-37044000\)	4.2.0.a.1, 420.4.0.?	$[(35049/11, 10640007/11)]$
12700800.ur1	-	12700800.ur	-	$1$	$1$	\( 2^{7} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \)	\( - 2^{14} \cdot 3^{4} \cdot 5^{6} \cdot 7^{6} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.2.0.1		$140$	$4$	$0$	$36.14603613$	$1$		$2$	$59719680$	$1.640078$	$1152$	$0.61315$	$2.59702$	$1$	$[0, 0, 0, 29400, -1372000]$	\(y^2=x^3+29400x-1372000\)	4.2.0.a.1, 140.4.0.?	$[(476, 10976), (183449/37, 112967393/37)]$

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