Elliptic curve search results

Results (14 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	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
12506.c2	12506a2	12506.c	12506a	$2$	$7$	\( 2 \cdot 13^{2} \cdot 37 \)	\( - 2^{7} \cdot 13^{10} \cdot 37^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.8.0.1	7B	$26936$	$96$	$2$	$49.62685718$	$1$		$0$	$1589952$	$3.332020$	$4918167786495951/12151280273024$	$1.12906$	$6.67437$	$[1, -1, 0, 18302246, 54487812276]$	\(y^2+xy=x^3-x^2+18302246x+54487812276\)	7.8.0.a.1, 91.48.0.?, 296.2.0.?, 2072.16.0.?, 26936.96.2.?	$[(-571182222497435805879/771978401, 87589820078604572488723309877598/771978401)]$
12506.d2	12506d2	12506.d	12506d	$2$	$7$	\( 2 \cdot 13^{2} \cdot 37 \)	\( - 2^{7} \cdot 13^{4} \cdot 37^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.16.0.2	7B.2.3	$26936$	$96$	$2$	$0.221058494$	$1$		$4$	$122304$	$2.049545$	$4918167786495951/12151280273024$	$1.12906$	$5.04307$	$[1, -1, 1, 108297, 24776015]$	\(y^2+xy+y=x^3-x^2+108297x+24776015\)	7.16.0-7.a.1.1, 91.48.0.?, 296.2.0.?, 2072.32.0.?, 26936.96.2.?	$[(75, 5734)]$
100048.e2	100048k2	100048.e	100048k	$2$	$7$	\( 2^{4} \cdot 13^{2} \cdot 37 \)	\( - 2^{19} \cdot 13^{4} \cdot 37^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.8.0.1	7B	$26936$	$96$	$2$	$1.145479482$	$1$		$2$	$2935296$	$2.742691$	$4918167786495951/12151280273024$	$1.12906$	$4.85468$	$[0, 0, 0, 1732757, -1587397734]$	\(y^2=x^3+1732757x-1587397734\)	7.8.0.a.1, 28.16.0-7.a.1.2, 91.24.0.?, 296.2.0.?, 364.48.0.?, $\ldots$	$[(2106, 106782)]$
100048.f2	100048e2	100048.f	100048e	$2$	$7$	\( 2^{4} \cdot 13^{2} \cdot 37 \)	\( - 2^{19} \cdot 13^{10} \cdot 37^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.8.0.1	7B	$26936$	$96$	$2$	$1$	$16$	$2$	$0$	$38158848$	$4.025169$	$4918167786495951/12151280273024$	$1.12906$	$6.19135$	$[0, 0, 0, 292835933, -3487512821598]$	\(y^2=x^3+292835933x-3487512821598\)	7.8.0.a.1, 91.24.0.?, 296.2.0.?, 364.48.0.?, 2072.16.0.?, $\ldots$	$[ ]$
112554.g2	112554f2	112554.g	112554f	$2$	$7$	\( 2 \cdot 3^{2} \cdot 13^{2} \cdot 37 \)	\( - 2^{7} \cdot 3^{6} \cdot 13^{4} \cdot 37^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.8.0.1	7B	$80808$	$96$	$2$	$0.963326410$	$1$		$4$	$3913728$	$2.598850$	$4918167786495951/12151280273024$	$1.12906$	$4.65711$	$[1, -1, 0, 974676, -669927088]$	\(y^2+xy=x^3-x^2+974676x-669927088\)	7.8.0.a.1, 21.16.0-7.a.1.1, 91.24.0.?, 273.48.0.?, 296.2.0.?, $\ldots$	$[(553, 5884)]$
112554.t2	112554s2	112554.t	112554s	$2$	$7$	\( 2 \cdot 3^{2} \cdot 13^{2} \cdot 37 \)	\( - 2^{7} \cdot 3^{6} \cdot 13^{10} \cdot 37^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.8.0.1	7B	$80808$	$96$	$2$	$9.772511791$	$1$		$2$	$50878464$	$3.881325$	$4918167786495951/12151280273024$	$1.12906$	$5.98026$	$[1, -1, 1, 164720212, -1471335651665]$	\(y^2+xy+y=x^3-x^2+164720212x-1471335651665\)	7.8.0.a.1, 91.24.0.?, 273.48.0.?, 296.2.0.?, 2072.16.0.?, $\ldots$	$[(87835, 26236055)]$
312650.o2	312650o2	312650.o	312650o	$2$	$7$	\( 2 \cdot 5^{2} \cdot 13^{2} \cdot 37 \)	\( - 2^{7} \cdot 5^{6} \cdot 13^{4} \cdot 37^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.8.0.1	7B	$134680$	$96$	$2$	$32.15653498$	$1$		$0$	$17122560$	$2.854263$	$4918167786495951/12151280273024$	$1.12906$	$4.52331$	$[1, -1, 0, 2707433, 3099709341]$	\(y^2+xy=x^3-x^2+2707433x+3099709341\)	7.8.0.a.1, 35.16.0-7.a.1.2, 91.24.0.?, 296.2.0.?, 455.48.0.?, $\ldots$	$[(78361692298483/109849, 715047773228717288467/109849)]$
312650.ce2	312650ce2	312650.ce	312650ce	$2$	$7$	\( 2 \cdot 5^{2} \cdot 13^{2} \cdot 37 \)	\( - 2^{7} \cdot 5^{6} \cdot 13^{10} \cdot 37^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.8.0.1	7B	$134680$	$96$	$2$	$12.93096536$	$1$		$0$	$222593280$	$4.136734$	$4918167786495951/12151280273024$	$1.12906$	$5.73961$	$[1, -1, 1, 457556145, 6811434090647]$	\(y^2+xy+y=x^3-x^2+457556145x+6811434090647\)	7.8.0.a.1, 91.24.0.?, 296.2.0.?, 455.48.0.?, 2072.16.0.?, $\ldots$	$[(142715959/55, 1917755781338/55)]$
400192.s2	400192s2	400192.s	400192s	$2$	$7$	\( 2^{6} \cdot 13^{2} \cdot 37 \)	\( - 2^{25} \cdot 13^{10} \cdot 37^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.8.0.1	7B	$26936$	$96$	$2$	$1$	$1$		$0$	$305270784$	$4.371742$	$4918167786495951/12151280273024$	$1.12906$	$5.84839$	$[0, 0, 0, 1171343732, 27900102572784]$	\(y^2=x^3+1171343732x+27900102572784\)	7.8.0.a.1, 91.24.0.?, 296.2.0.?, 728.48.0.?, 2072.16.0.?, $\ldots$	$[ ]$
400192.t2	400192t2	400192.t	400192t	$2$	$7$	\( 2^{6} \cdot 13^{2} \cdot 37 \)	\( - 2^{25} \cdot 13^{10} \cdot 37^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.8.0.1	7B	$26936$	$96$	$2$	$35.67899878$	$1$		$0$	$305270784$	$4.371742$	$4918167786495951/12151280273024$	$1.12906$	$5.84839$	$[0, 0, 0, 1171343732, -27900102572784]$	\(y^2=x^3+1171343732x-27900102572784\)	7.8.0.a.1, 91.24.0.?, 296.2.0.?, 728.48.0.?, 2072.16.0.?, $\ldots$	$[(2290397416409628704/5758003, 3734634229012264923994660764/5758003)]$
400192.u2	400192u2	400192.u	400192u	$2$	$7$	\( 2^{6} \cdot 13^{2} \cdot 37 \)	\( - 2^{25} \cdot 13^{4} \cdot 37^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.8.0.1	7B	$26936$	$96$	$2$	$1$	$1$		$0$	$23482368$	$3.089264$	$4918167786495951/12151280273024$	$1.12906$	$4.65536$	$[0, 0, 0, 6931028, -12699181872]$	\(y^2=x^3+6931028x-12699181872\)	7.8.0.a.1, 56.16.0-7.a.1.4, 91.24.0.?, 296.2.0.?, 518.16.0.?, $\ldots$	$[ ]$
400192.v2	400192v2	400192.v	400192v	$2$	$7$	\( 2^{6} \cdot 13^{2} \cdot 37 \)	\( - 2^{25} \cdot 13^{4} \cdot 37^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.8.0.1	7B	$26936$	$96$	$2$	$67.82413700$	$1$		$0$	$23482368$	$3.089264$	$4918167786495951/12151280273024$	$1.12906$	$4.65536$	$[0, 0, 0, 6931028, 12699181872]$	\(y^2=x^3+6931028x+12699181872\)	7.8.0.a.1, 56.16.0-7.a.1.3, 91.24.0.?, 296.2.0.?, 728.48.0.?, $\ldots$	$[(357231500244064091636189066916/9680222727305, 278888228717819545166118117681834075751498536/9680222727305)]$
462722.e2	462722e2	462722.e	462722e	$2$	$7$	\( 2 \cdot 13^{2} \cdot 37^{2} \)	\( - 2^{7} \cdot 13^{4} \cdot 37^{13} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.8.0.1	7B	$26936$	$96$	$2$	$94.56598462$	$1$		$0$	$167311872$	$3.855003$	$4918167786495951/12151280273024$	$1.12906$	$5.30795$	$[1, -1, 0, 148259021, 1256313832437]$	\(y^2+xy=x^3-x^2+148259021x+1256313832437\)	7.8.0.a.1, 56.16.0-7.a.1.8, 91.24.0.?, 259.16.0.?, 296.2.0.?, $\ldots$	$[(3721501281385665580467489400057522659773277/8540518911473888516, 7397841108626976939161091172580962012894656852012431723315841921/8540518911473888516)]$
462722.m2	462722m2	462722.m	462722m	$2$	$7$	\( 2 \cdot 13^{2} \cdot 37^{2} \)	\( - 2^{7} \cdot 13^{10} \cdot 37^{13} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.8.0.1	7B	$26936$	$96$	$2$	$1$	$1$		$0$	$2175054336$	$5.137474$	$4918167786495951/12151280273024$	$1.12906$	$6.48770$	$[1, -1, 1, 25055774517, 2760196657187675]$	\(y^2+xy+y=x^3-x^2+25055774517x+2760196657187675\)	7.8.0.a.1, 91.24.0.?, 296.2.0.?, 728.48.0.?, 2072.16.0.?, $\ldots$	$[ ]$

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