Elliptic curves over $\Q$ of conductor 10115

Results (16 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
10115.a1	10115d1	10115.a	10115d	$1$	$1$	\( 5 \cdot 7 \cdot 17^{2} \)	\( 5 \cdot 7^{2} \cdot 17^{4} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$10$	$2$	$0$	$0.236232487$	$1$		$18$	$3888$	$0.118017$	$1183744/245$	$0.76333$	$2.74536$	$[0, 1, 1, -96, -324]$	\(y^2+y=x^3+x^2-96x-324\)	10.2.0.a.1	$[(-6, 8), (45, 297)]$
10115.b1	10115j1	10115.b	10115j	$1$	$1$	\( 5 \cdot 7 \cdot 17^{2} \)	\( 5^{5} \cdot 7^{2} \cdot 17^{2} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$10$	$2$	$0$	$0.118928153$	$1$		$22$	$6480$	$0.325503$	$39814672384/153125$	$0.89122$	$3.26119$	$[0, 1, 1, -470, 3756]$	\(y^2+y=x^3+x^2-470x+3756\)	10.2.0.a.1	$[(10, 12), (-15, 87)]$
10115.c1	10115n1	10115.c	10115n	$1$	$1$	\( 5 \cdot 7 \cdot 17^{2} \)	\( - 5^{11} \cdot 7^{3} \cdot 17^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1190$	$2$	$0$	$0.048390597$	$1$		$10$	$494208$	$2.490639$	$-110470393399988224/284716796875$	$0.97379$	$6.09940$	$[0, 1, 1, -2888940, 1893215556]$	\(y^2+y=x^3+x^2-2888940x+1893215556\)	1190.2.0.?	$[(1065, 5057)]$
10115.d1	10115f1	10115.d	10115f	$1$	$1$	\( 5 \cdot 7 \cdot 17^{2} \)	\( 5^{5} \cdot 7^{2} \cdot 17^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$10$	$2$	$0$	$1.077903214$	$1$		$2$	$110160$	$1.742109$	$39814672384/153125$	$0.89122$	$5.10457$	$[0, -1, 1, -135926, 19269832]$	\(y^2+y=x^3-x^2-135926x+19269832\)	10.2.0.a.1	$[(193, 433)]$
10115.e1	10115m1	10115.e	10115m	$1$	$1$	\( 5 \cdot 7 \cdot 17^{2} \)	\( 5 \cdot 7^{2} \cdot 17^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$10$	$2$	$0$	$4.940028586$	$1$		$2$	$66096$	$1.534624$	$1183744/245$	$0.76333$	$4.58874$	$[0, -1, 1, -27840, -1423724]$	\(y^2+y=x^3-x^2-27840x-1423724\)	10.2.0.a.1	$[(-88, 580)]$
10115.f1	10115g3	10115.f	10115g	$3$	$9$	\( 5 \cdot 7 \cdot 17^{2} \)	\( - 5^{9} \cdot 7 \cdot 17^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$10710$	$144$	$3$	$1$	$1$		$0$	$30240$	$1.544069$	$-250523582464/13671875$	$1.02112$	$4.69934$	$[0, -1, 1, -37955, -2964672]$	\(y^2+y=x^3-x^2-37955x-2964672\)	3.4.0.a.1, 9.12.0.a.1, 51.8.0-3.a.1.1, 63.36.0.e.2, 70.2.0.a.1, $\ldots$	$[]$
10115.f2	10115g1	10115.f	10115g	$3$	$9$	\( 5 \cdot 7 \cdot 17^{2} \)	\( - 5 \cdot 7 \cdot 17^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$10710$	$144$	$3$	$1$	$1$		$0$	$3360$	$0.445457$	$-262144/35$	$0.88715$	$3.21885$	$[0, -1, 1, -385, 3358]$	\(y^2+y=x^3-x^2-385x+3358\)	3.4.0.a.1, 9.12.0.a.1, 51.8.0-3.a.1.2, 63.36.0.e.1, 70.2.0.a.1, $\ldots$	$[]$
10115.f3	10115g2	10115.f	10115g	$3$	$9$	\( 5 \cdot 7 \cdot 17^{2} \)	\( - 5^{3} \cdot 7^{3} \cdot 17^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.12.0.1	3Cs	$10710$	$144$	$3$	$1$	$1$		$0$	$10080$	$0.994762$	$71991296/42875$	$1.06493$	$3.80527$	$[0, -1, 1, 2505, -9069]$	\(y^2+y=x^3-x^2+2505x-9069\)	3.12.0.a.1, 51.24.0-3.a.1.1, 63.36.0.b.1, 70.2.0.a.1, 210.24.1.?, $\ldots$	$[]$
10115.g1	10115a1	10115.g	10115a	$1$	$1$	\( 5 \cdot 7 \cdot 17^{2} \)	\( - 5 \cdot 7 \cdot 17^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1190$	$2$	$0$	$1.663699833$	$1$		$2$	$960$	$-0.147536$	$-7077888/35$	$1.01784$	$2.63297$	$[0, 0, 1, -68, -217]$	\(y^2+y=x^3-68x-217\)	1190.2.0.?	$[(17, 59)]$
10115.h1	10115k1	10115.h	10115k	$1$	$1$	\( 5 \cdot 7 \cdot 17^{2} \)	\( - 5 \cdot 7 \cdot 17^{9} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1190$	$2$	$0$	$8.611324984$	$1$		$0$	$16320$	$1.269072$	$-7077888/35$	$1.01784$	$4.47635$	$[0, 0, 1, -19652, -1064893]$	\(y^2+y=x^3-19652x-1064893\)	1190.2.0.?	$[(285821/35, 113834881/35)]$
10115.i1	10115e1	10115.i	10115e	$1$	$1$	\( 5 \cdot 7 \cdot 17^{2} \)	\( 5^{4} \cdot 7^{13} \cdot 17^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$28$	$2$	$0$	$0.227190405$	$1$		$4$	$168480$	$2.290230$	$172032746578729129/60555631504375$	$1.02035$	$5.53248$	$[1, 1, 0, -506478, 86623057]$	\(y^2+xy=x^3+x^2-506478x+86623057\)	28.2.0.a.1	$[(936, 20357)]$
10115.j1	10115l1	10115.j	10115l	$1$	$1$	\( 5 \cdot 7 \cdot 17^{2} \)	\( 5^{8} \cdot 7 \cdot 17^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$28$	$2$	$0$	$0.465808762$	$1$		$2$	$5184$	$0.402950$	$6161940649/2734375$	$0.89123$	$3.05886$	$[1, 1, 0, -252, -851]$	\(y^2+xy=x^3+x^2-252x-851\)	28.2.0.a.1	$[(-12, 31)]$
10115.k1	10115c1	10115.k	10115c	$1$	$1$	\( 5 \cdot 7 \cdot 17^{2} \)	\( 5^{8} \cdot 7 \cdot 17^{8} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$28$	$2$	$0$	$4.026687761$	$1$		$2$	$88128$	$1.819557$	$6161940649/2734375$	$0.89123$	$4.90224$	$[1, 0, 1, -72979, -3670469]$	\(y^2+xy+y=x^3-72979x-3670469\)	28.2.0.a.1	$[(3203, 179023), (-313/2, 10309/2)]$
10115.l1	10115h1	10115.l	10115h	$1$	$1$	\( 5 \cdot 7 \cdot 17^{2} \)	\( 5^{4} \cdot 7^{13} \cdot 17^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$28$	$2$	$0$	$1$	$9$	$3$	$0$	$2864160$	$3.706837$	$172032746578729129/60555631504375$	$1.02035$	$7.37587$	$[1, 0, 1, -146372293, 426603684733]$	\(y^2+xy+y=x^3-146372293x+426603684733\)	28.2.0.a.1	$[]$
10115.m1	10115b1	10115.m	10115b	$1$	$1$	\( 5 \cdot 7 \cdot 17^{2} \)	\( - 5 \cdot 7 \cdot 17^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1190$	$2$	$0$	$1.321955726$	$1$		$0$	$8064$	$0.628382$	$-4096/595$	$0.74386$	$3.34497$	$[0, 1, 1, -96, 5745]$	\(y^2+y=x^3+x^2-96x+5745\)	1190.2.0.?	$[(-75/2, 285/2)]$
10115.n1	10115i1	10115.n	10115i	$1$	$1$	\( 5 \cdot 7 \cdot 17^{2} \)	\( - 5^{5} \cdot 7^{7} \cdot 17^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1190$	$2$	$0$	$1$	$1$		$0$	$282240$	$2.140713$	$9019694698496/43750721875$	$0.95241$	$5.29494$	$[0, 1, 1, 125330, -46357369]$	\(y^2+y=x^3+x^2+125330x-46357369\)	1190.2.0.?	$[]$