Elliptic curves over $\Q$ of conductor 68354

Results (10 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
68354.a1	68354e1	68354.a	68354e	$1$	$1$	\( 2 \cdot 11 \cdot 13 \cdot 239 \)	\( - 2^{4} \cdot 11^{3} \cdot 13^{4} \cdot 239 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$10516$	$2$	$0$	$0.200214668$	$1$		$20$	$92160$	$0.885265$	$-1623435815226889/145368178384$	$0.84762$	$3.15898$	$[1, 0, 1, -2449, 49908]$	\(y^2+xy+y=x^3-2449x+49908\)	10516.2.0.?	$[(-41, 306), (47, 174)]$
68354.b1	68354a1	68354.b	68354a	$1$	$1$	\( 2 \cdot 11 \cdot 13 \cdot 239 \)	\( - 2^{16} \cdot 11^{11} \cdot 13^{2} \cdot 239 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$10516$	$2$	$0$	$9.746604403$	$1$		$0$	$2309120$	$2.694435$	$1032313507493888687089959/755238416393758375936$	$0.98090$	$4.96690$	$[1, -1, 0, 2105536, -604975104]$	\(y^2+xy=x^3-x^2+2105536x-604975104\)	10516.2.0.?	$[(70784/13, 40656832/13)]$
68354.c1	68354b1	68354.c	68354b	$1$	$1$	\( 2 \cdot 11 \cdot 13 \cdot 239 \)	\( - 2^{11} \cdot 11 \cdot 13 \cdot 239 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$273416$	$2$	$0$	$4.259987833$	$1$		$2$	$20416$	$0.217745$	$-213525509833/69994496$	$0.77602$	$2.38365$	$[1, 0, 1, -125, -680]$	\(y^2+xy+y=x^3-125x-680\)	273416.2.0.?	$[(64, 472)]$
68354.d1	68354c1	68354.d	68354c	$1$	$1$	\( 2 \cdot 11 \cdot 13 \cdot 239 \)	\( - 2 \cdot 11^{3} \cdot 13 \cdot 239 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$273416$	$2$	$0$	$2.553751238$	$1$		$2$	$10080$	$0.010025$	$2053225511/8270834$	$0.75447$	$2.08650$	$[1, 0, 1, 26, 130]$	\(y^2+xy+y=x^3+26x+130\)	273416.2.0.?	$[(8, 25)]$
68354.e1	68354d1	68354.e	68354d	$1$	$1$	\( 2 \cdot 11 \cdot 13 \cdot 239 \)	\( - 2^{10} \cdot 11^{6} \cdot 13^{7} \cdot 239 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$6214$	$2$	$0$	$2.032098487$	$1$		$2$	$1270080$	$2.415401$	$22884686124047560887047/27205545267695455232$	$0.94640$	$4.62949$	$[1, 0, 1, 591480, -179727402]$	\(y^2+xy+y=x^3+591480x-179727402\)	6214.2.0.?	$[(3081, 174219)]$
68354.f1	68354i2	68354.f	68354i	$2$	$7$	\( 2 \cdot 11 \cdot 13 \cdot 239 \)	\( - 2 \cdot 11 \cdot 13 \cdot 239^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$7$	7.48.0.5	7B.1.3	$1913912$	$96$	$2$	$56.35013333$	$1$		$0$	$21282464$	$3.414261$	$-18433805126765920887235189777569/12739469393917574594$	$1.04268$	$6.46683$	$[1, -1, 1, -550339173, -4969145682177]$	\(y^2+xy+y=x^3-x^2-550339173x-4969145682177\)	7.48.0-7.a.2.2, 273416.2.0.?, 1913912.96.2.?	$[(2064288047994980639759629/8171208780, 1492429052374114276463145804348419023/8171208780)]$
68354.f2	68354i1	68354.f	68354i	$2$	$7$	\( 2 \cdot 11 \cdot 13 \cdot 239 \)	\( - 2^{7} \cdot 11^{7} \cdot 13^{7} \cdot 239 \)	$1$	$\Z/7\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$7$	7.48.0.1	7B.1.1	$1913912$	$96$	$2$	$8.050019047$	$1$		$6$	$3040352$	$2.441307$	$26515285573583988393471/37407624743081250944$	$1.04399$	$4.67059$	$[1, -1, 1, 621237, -226146597]$	\(y^2+xy+y=x^3-x^2+621237x-226146597\)	7.48.0-7.a.1.2, 273416.2.0.?, 1913912.96.2.?	$[(38889/5, 8290302/5)]$
68354.g1	68354h1	68354.g	68354h	$1$	$1$	\( 2 \cdot 11 \cdot 13 \cdot 239 \)	\( - 2^{8} \cdot 11 \cdot 13^{2} \cdot 239 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$10516$	$2$	$0$	$0.384793076$	$1$		$6$	$17920$	$0.227759$	$19748682927/113741056$	$0.82309$	$2.32637$	$[1, -1, 1, 56, -501]$	\(y^2+xy+y=x^3-x^2+56x-501\)	10516.2.0.?	$[(9, 21)]$
68354.h1	68354f1	68354.h	68354f	$1$	$1$	\( 2 \cdot 11 \cdot 13 \cdot 239 \)	\( - 2^{2} \cdot 11^{4} \cdot 13 \cdot 239 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$6214$	$2$	$0$	$1$	$1$		$0$	$20864$	$0.299641$	$-623930478625/181958348$	$0.78612$	$2.47631$	$[1, 0, 0, -178, -1136]$	\(y^2+xy=x^3-178x-1136\)	6214.2.0.?	$[]$
68354.i1	68354g1	68354.i	68354g	$1$	$1$	\( 2 \cdot 11 \cdot 13 \cdot 239 \)	\( - 2^{16} \cdot 11^{3} \cdot 13^{4} \cdot 239 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$10516$	$2$	$0$	$0.666779942$	$1$		$2$	$350208$	$1.515263$	$25736914533034223/595428058660864$	$0.91051$	$3.72332$	$[1, 1, 1, 6151, 1161799]$	\(y^2+xy+y=x^3+x^2+6151x+1161799\)	10516.2.0.?	$[(47, 1224)]$