Elliptic curves over $\Q$ of conductor 3036

Results (15 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
3036.a1	3036e2	3036.a	3036e	$2$	$2$	\( 2^{2} \cdot 3 \cdot 11 \cdot 23 \)	\( 2^{8} \cdot 3 \cdot 11^{6} \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3036$	$12$	$0$	$1.554773864$	$1$		$3$	$5760$	$1.113937$	$461188987116496/2811467307$	$0.98272$	$4.90254$	$[0, -1, 0, -10220, -392184]$	\(y^2=x^3-x^2-10220x-392184\)	2.3.0.a.1, 12.6.0.a.1, 1012.6.0.?, 3036.12.0.?	$[(-59, 44)]$
3036.a2	3036e1	3036.a	3036e	$2$	$2$	\( 2^{2} \cdot 3 \cdot 11 \cdot 23 \)	\( 2^{4} \cdot 3^{2} \cdot 11^{3} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3036$	$12$	$0$	$3.109547729$	$1$		$3$	$2880$	$0.767364$	$7346581704933376/275517$	$1.07368$	$4.90199$	$[0, -1, 0, -10205, -393414]$	\(y^2=x^3-x^2-10205x-393414\)	2.3.0.a.1, 12.6.0.b.1, 506.6.0.?, 3036.12.0.?	$[(134, 792)]$
3036.b1	3036b2	3036.b	3036b	$2$	$2$	\( 2^{2} \cdot 3 \cdot 11 \cdot 23 \)	\( 2^{8} \cdot 3^{11} \cdot 11^{6} \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$1$		$1$	$63360$	$2.403172$	$154672654658139268432/87821582162841747$	$1.13836$	$6.48929$	$[0, -1, 0, -710084, 31864680]$	\(y^2=x^3-x^2-710084x+31864680\)	2.3.0.a.1, 12.6.0.a.1, 44.6.0.c.1, 132.12.0.?	$[]$
3036.b2	3036b1	3036.b	3036b	$2$	$2$	\( 2^{2} \cdot 3 \cdot 11 \cdot 23 \)	\( - 2^{4} \cdot 3^{22} \cdot 11^{3} \cdot 23^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$1$		$1$	$31680$	$2.056595$	$37458737578627432448/22095372689637291$	$1.10917$	$5.96665$	$[0, -1, 0, 175651, 3875454]$	\(y^2=x^3-x^2+175651x+3875454\)	2.3.0.a.1, 12.6.0.b.1, 22.6.0.a.1, 132.12.0.?	$[]$
3036.c1	3036a1	3036.c	3036a	$1$	$1$	\( 2^{2} \cdot 3 \cdot 11 \cdot 23 \)	\( - 2^{4} \cdot 3^{5} \cdot 11^{3} \cdot 23 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1518$	$2$	$0$	$1$	$1$		$0$	$720$	$0.268859$	$-31808383744/7438959$	$0.85851$	$3.40409$	$[0, -1, 0, -166, -923]$	\(y^2=x^3-x^2-166x-923\)	1518.2.0.?	$[]$
3036.d1	3036d2	3036.d	3036d	$2$	$2$	\( 2^{2} \cdot 3 \cdot 11 \cdot 23 \)	\( 2^{8} \cdot 3^{3} \cdot 11^{2} \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3036$	$12$	$0$	$0.578096874$	$1$		$7$	$1152$	$0.361419$	$5142706000/1728243$	$0.84381$	$3.48029$	$[0, -1, 0, -228, 936]$	\(y^2=x^3-x^2-228x+936\)	2.3.0.a.1, 12.6.0.a.1, 1012.6.0.?, 3036.12.0.?	$[(2, 22)]$
3036.d2	3036d1	3036.d	3036d	$2$	$2$	\( 2^{2} \cdot 3 \cdot 11 \cdot 23 \)	\( 2^{4} \cdot 3^{6} \cdot 11 \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3036$	$12$	$0$	$1.156193749$	$1$		$5$	$576$	$0.014845$	$5619712000/184437$	$0.91469$	$3.14557$	$[0, -1, 0, -93, -306]$	\(y^2=x^3-x^2-93x-306\)	2.3.0.a.1, 12.6.0.b.1, 506.6.0.?, 3036.12.0.?	$[(-5, 3)]$
3036.e1	3036c1	3036.e	3036c	$1$	$1$	\( 2^{2} \cdot 3 \cdot 11 \cdot 23 \)	\( - 2^{4} \cdot 3 \cdot 11 \cdot 23 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1518$	$2$	$0$	$1$	$1$		$0$	$240$	$-0.527033$	$1257728/759$	$0.73400$	$2.09738$	$[0, -1, 0, 6, -3]$	\(y^2=x^3-x^2+6x-3\)	1518.2.0.?	$[]$
3036.f1	3036j2	3036.f	3036j	$2$	$2$	\( 2^{2} \cdot 3 \cdot 11 \cdot 23 \)	\( 2^{8} \cdot 3^{5} \cdot 11^{2} \cdot 23^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3036$	$12$	$0$	$0.153785166$	$1$		$13$	$2880$	$0.648108$	$1136150003536/15554187$	$0.88808$	$4.15348$	$[0, 1, 0, -1380, 19044]$	\(y^2=x^3+x^2-1380x+19044\)	2.3.0.a.1, 12.6.0.a.1, 1012.6.0.?, 3036.12.0.?	$[(0, 138)]$
3036.f2	3036j1	3036.f	3036j	$2$	$2$	\( 2^{2} \cdot 3 \cdot 11 \cdot 23 \)	\( 2^{4} \cdot 3^{10} \cdot 11 \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3036$	$12$	$0$	$0.307570333$	$1$		$11$	$1440$	$0.301534$	$31238127616/14939397$	$1.00600$	$3.35950$	$[0, 1, 0, -165, -396]$	\(y^2=x^3+x^2-165x-396\)	2.3.0.a.1, 12.6.0.b.1, 506.6.0.?, 3036.12.0.?	$[(-3, 9)]$
3036.g1	3036i1	3036.g	3036i	$1$	$1$	\( 2^{2} \cdot 3 \cdot 11 \cdot 23 \)	\( - 2^{4} \cdot 3 \cdot 11^{7} \cdot 23 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1518$	$2$	$0$	$0.340508931$	$1$		$4$	$2016$	$0.668839$	$-398556845824/1344614799$	$0.91946$	$3.91667$	$[0, 1, 0, -386, -7767]$	\(y^2=x^3+x^2-386x-7767\)	1518.2.0.?	$[(54, 363)]$
3036.h1	3036h1	3036.h	3036h	$1$	$1$	\( 2^{2} \cdot 3 \cdot 11 \cdot 23 \)	\( - 2^{4} \cdot 3^{11} \cdot 11 \cdot 23^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1518$	$2$	$0$	$0.132811597$	$1$		$6$	$3168$	$0.919744$	$-28649084226304/23708823039$	$0.93433$	$4.32095$	$[0, 1, 0, -1606, 38093]$	\(y^2=x^3+x^2-1606x+38093\)	1518.2.0.?	$[(41, 207)]$
3036.i1	3036f1	3036.i	3036f	$1$	$1$	\( 2^{2} \cdot 3 \cdot 11 \cdot 23 \)	\( - 2^{4} \cdot 3^{3} \cdot 11 \cdot 23 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1518$	$2$	$0$	$0.144793260$	$1$		$8$	$288$	$-0.336202$	$-7626496/6831$	$0.73947$	$2.43879$	$[0, 1, 0, -10, 17]$	\(y^2=x^3+x^2-10x+17\)	1518.2.0.?	$[(2, 3)]$
3036.j1	3036g2	3036.j	3036g	$2$	$2$	\( 2^{2} \cdot 3 \cdot 11 \cdot 23 \)	\( 2^{8} \cdot 3^{3} \cdot 11^{2} \cdot 23^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$1$		$1$	$7488$	$1.241123$	$190930594365830608/1728243$	$0.96973$	$5.65405$	$[0, 1, 0, -76172, 8066388]$	\(y^2=x^3+x^2-76172x+8066388\)	2.3.0.a.1, 12.6.0.a.1, 44.6.0.c.1, 132.12.0.?	$[]$
3036.j2	3036g1	3036.j	3036g	$2$	$2$	\( 2^{2} \cdot 3 \cdot 11 \cdot 23 \)	\( - 2^{4} \cdot 3^{6} \cdot 11 \cdot 23^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$1$		$1$	$3744$	$0.894549$	$-744208243621888/2244044979$	$1.08325$	$4.61708$	$[0, 1, 0, -4757, 125040]$	\(y^2=x^3+x^2-4757x+125040\)	2.3.0.a.1, 12.6.0.b.1, 22.6.0.a.1, 132.12.0.?	$[]$