LMFDB - Elliptic curves over $\Q$ of conductor 26714

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Conductor	Discriminant	j-invariant	Rank

Bad$\ p$	Curves per isogeny class	Complex multiplication	Torsion

Isogeny class degree	Cyclic isogeny degree	Isogeny class size	Integral points

Analytic order of Ш	$p\ $div$\ $\|Ш\|	Regulator	Reduction	Faltings height

Galois image	Adelic level	Adelic index	Adelic genus

Nonmax$\ \ell$	$abc$ quality	Szpiro ratio	Manin constant

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Results (23 matches)

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	Sato-Tate	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	Manin constant
26714.a1	26714d1	26714.a	26714d	$1$	$1$	$ 2 \cdot 19^{2} \cdot 37 $	$ 2^{3} \cdot 19^{9} \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$5624$	$2$	$0$	$7.257445882$	$1$		$0$	$519840$	$2.174110$	$7784759730259/296$	$0.93902$	$5.51196$	$[1, 0, 1, -2832053, -1834661400]$	$y^2+xy+y=x^3-2832053x-1834661400$	5624.2.0.?	$[(-47606/7, 167201/7)]$	$1$
26714.b1	26714j1	26714.b	26714j	$1$	$1$	$ 2 \cdot 19^{2} \cdot 37 $	$ 2^{5} \cdot 19^{11} \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$5624$	$2$	$0$	$5.866432464$	$1$		$2$	$504000$	$2.021011$	$25601949246817/2931701216$	$0.90899$	$4.76215$	$[1, 0, 1, -221662, 35956848]$	$y^2+xy+y=x^3-221662x+35956848$	5624.2.0.?	$[(164, 1923)]$	$1$
26714.c1	26714i1	26714.c	26714i	$1$	$1$	$ 2 \cdot 19^{2} \cdot 37 $	$ - 2^{7} \cdot 19^{7} \cdot 37^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$152$	$2$	$0$	$0.518603588$	$1$		$4$	$80640$	$1.408695$	$-761048497/3329408$	$0.85394$	$3.95017$	$[1, 1, 0, -6866, 637876]$	$y^2+xy=x^3+x^2-6866x+637876$	152.2.0.?	$[(359, 6499)]$	$1$
26714.d1	26714g1	26714.d	26714g	$2$	$3$	$ 2 \cdot 19^{2} \cdot 37 $	$ - 2^{3} \cdot 19^{9} \cdot 37^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$456$	$16$	$0$	$1$	$1$		$0$	$207360$	$1.720922$	$-677993136625/75119768$	$0.88055$	$4.42308$	$[1, 1, 0, -66070, -7162612]$	$y^2+xy=x^3+x^2-66070x-7162612$	3.4.0.a.1, 24.8.0-3.a.1.6, 57.8.0-3.a.1.1, 152.2.0.?, 456.16.0.?	$[ ]$	$1$
26714.d2	26714g2	26714.d	26714g	$2$	$3$	$ 2 \cdot 19^{2} \cdot 37 $	$ - 2 \cdot 19^{7} \cdot 37^{6} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$456$	$16$	$0$	$1$	$1$		$0$	$622080$	$2.270229$	$166874624291375/97497603542$	$1.05957$	$4.94606$	$[1, 1, 0, 414060, 10218094]$	$y^2+xy=x^3+x^2+414060x+10218094$	3.4.0.a.1, 24.8.0-3.a.1.5, 57.8.0-3.a.1.2, 152.2.0.?, 456.16.0.?	$[ ]$	$1$
26714.e1	26714a1	26714.e	26714a	$1$	$1$	$ 2 \cdot 19^{2} \cdot 37 $	$ - 2^{6} \cdot 19^{4} \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$148$	$2$	$0$	$0.497557400$	$1$		$6$	$13608$	$0.353842$	$-12973257/2368$	$0.98369$	$2.78921$	$[1, -1, 0, -248, -1664]$	$y^2+xy=x^3-x^2-248x-1664$	148.2.0.?	$[(24, 64)]$	$1$
26714.f1	26714h1	26714.f	26714h	$1$	$1$	$ 2 \cdot 19^{2} \cdot 37 $	$ 2^{3} \cdot 19^{7} \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$5624$	$2$	$0$	$1.002882544$	$1$		$2$	$25920$	$0.912441$	$33076161/5624$	$0.76994$	$3.43188$	$[1, -1, 0, -2414, -37764]$	$y^2+xy=x^3-x^2-2414x-37764$	5624.2.0.?	$[(81, 501)]$	$1$
26714.g1	26714c1	26714.g	26714c	$1$	$1$	$ 2 \cdot 19^{2} \cdot 37 $	$ - 2^{9} \cdot 19^{9} \cdot 37^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$152$	$2$	$0$	$7.243418397$	$1$		$0$	$656640$	$2.614349$	$221774710877/959570432$	$0.95121$	$5.34616$	$[1, 0, 1, 864948, 788041866]$	$y^2+xy+y=x^3+864948x+788041866$	152.2.0.?	$[(-41612/9, 10705166/9)]$	$1$
26714.h1	26714b1	26714.h	26714b	$1$	$1$	$ 2 \cdot 19^{2} \cdot 37 $	$ - 2^{15} \cdot 19^{3} \cdot 37^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$152$	$2$	$0$	$3.557269893$	$1$		$0$	$76800$	$1.485762$	$906196171733/61412507648$	$1.00310$	$4.03420$	$[1, 0, 1, 3830, 983548]$	$y^2+xy+y=x^3+3830x+983548$	152.2.0.?	$[(-497/6, 209471/6)]$	$1$
26714.i1	26714e1	26714.i	26714e	$1$	$1$	$ 2 \cdot 19^{2} \cdot 37 $	$ 2^{9} \cdot 19^{9} \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$5624$	$2$	$0$	$1$	$1$		$0$	$191520$	$1.720903$	$36264691/18944$	$0.86105$	$4.30752$	$[1, 1, 0, -47298, 1215476]$	$y^2+xy=x^3+x^2-47298x+1215476$	5624.2.0.?	$[ ]$	$1$
26714.j1	26714f2	26714.j	26714f	$2$	$2$	$ 2 \cdot 19^{2} \cdot 37 $	$ 2^{3} \cdot 19^{9} \cdot 37^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$5624$	$12$	$0$	$1$	$25$	$5$	$0$	$597360$	$1.888937$	$8132727331/10952$	$0.88140$	$4.83855$	$[1, 1, 0, -287363, -59342635]$	$y^2+xy=x^3+x^2-287363x-59342635$	2.3.0.a.1, 152.6.0.?, 296.6.0.?, 2812.6.0.?, 5624.12.0.?	$[ ]$	$1$
26714.j2	26714f1	26714.j	26714f	$2$	$2$	$ 2 \cdot 19^{2} \cdot 37 $	$ - 2^{6} \cdot 19^{9} \cdot 37 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$5624$	$12$	$0$	$1$	$25$	$5$	$1$	$298680$	$1.542364$	$-753571/2368$	$0.80668$	$4.11005$	$[1, 1, 0, -13003, -1452675]$	$y^2+xy=x^3+x^2-13003x-1452675$	2.3.0.a.1, 152.6.0.?, 296.6.0.?, 1406.6.0.?, 5624.12.0.?	$[ ]$	$1$
26714.k1	26714k1	26714.k	26714k	$1$	$1$	$ 2 \cdot 19^{2} \cdot 37 $	$ - 2^{15} \cdot 19^{11} \cdot 37^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$152$	$2$	$0$	$12.22513287$	$1$		$0$	$2592000$	$2.846401$	$-186688297520577/111076295671808$	$1.04874$	$5.63758$	$[1, -1, 0, -429838, -3479583916]$	$y^2+xy=x^3-x^2-429838x-3479583916$	152.2.0.?	$[(932076511/51, 28432382453467/51)]$	$1$
26714.l1	26714l1	26714.l	26714l	$1$	$1$	$ 2 \cdot 19^{2} \cdot 37 $	$ 2^{9} \cdot 19^{3} \cdot 37 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$5624$	$2$	$0$	$0.283482386$	$1$		$18$	$10080$	$0.248684$	$36264691/18944$	$0.86105$	$2.57430$	$[1, 0, 0, -131, -191]$	$y^2+xy=x^3-131x-191$	5624.2.0.?	$[(-8, 23), (30, 137)]$	$1$
26714.m1	26714s1	26714.m	26714s	$1$	$1$	$ 2 \cdot 19^{2} \cdot 37 $	$ 2^{17} \cdot 19^{9} \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$5624$	$2$	$0$	$0.292204654$	$1$		$6$	$440640$	$2.264359$	$1007488615738249/33263845376$	$0.93101$	$5.12245$	$[1, 0, 0, -753956, 244624144]$	$y^2+xy=x^3-753956x+244624144$	5624.2.0.?	$[(828, 13304)]$	$1$
26714.n1	26714m2	26714.n	26714m	$2$	$2$	$ 2 \cdot 19^{2} \cdot 37 $	$ 2^{3} \cdot 19^{3} \cdot 37^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$5624$	$12$	$0$	$1$	$1$		$0$	$31440$	$0.416718$	$8132727331/10952$	$0.88140$	$3.10533$	$[1, 0, 0, -796, 8568]$	$y^2+xy=x^3-796x+8568$	2.3.0.a.1, 152.6.0.?, 296.6.0.?, 2812.6.0.?, 5624.12.0.?	$[ ]$	$1$
26714.n2	26714m1	26714.n	26714m	$2$	$2$	$ 2 \cdot 19^{2} \cdot 37 $	$ - 2^{6} \cdot 19^{3} \cdot 37 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$5624$	$12$	$0$	$1$	$1$		$1$	$15720$	$0.070144$	$-753571/2368$	$0.80668$	$2.37683$	$[1, 0, 0, -36, 208]$	$y^2+xy=x^3-36x+208$	2.3.0.a.1, 152.6.0.?, 296.6.0.?, 1406.6.0.?, 5624.12.0.?	$[ ]$	$1$
26714.o1	26714o1	26714.o	26714o	$1$	$1$	$ 2 \cdot 19^{2} \cdot 37 $	$ - 2^{9} \cdot 19^{3} \cdot 37^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$152$	$2$	$0$	$0.202940235$	$1$		$8$	$34560$	$1.142130$	$221774710877/959570432$	$0.95121$	$3.61294$	$[1, 1, 1, 2396, -113883]$	$y^2+xy+y=x^3+x^2+2396x-113883$	152.2.0.?	$[(45, 273)]$	$1$
26714.p1	26714n1	26714.p	26714n	$1$	$1$	$ 2 \cdot 19^{2} \cdot 37 $	$ - 2^{15} \cdot 19^{9} \cdot 37^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$152$	$2$	$0$	$1.203300299$	$1$		$0$	$1459200$	$2.957981$	$906196171733/61412507648$	$1.00310$	$5.76742$	$[1, 1, 1, 1382803, -6743391837]$	$y^2+xy+y=x^3+x^2+1382803x-6743391837$	152.2.0.?	$[(19039/3, 2001692/3)]$	$1$
26714.q1	26714t1	26714.q	26714t	$1$	$1$	$ 2 \cdot 19^{2} \cdot 37 $	$ - 2^{6} \cdot 19^{10} \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$148$	$2$	$0$	$1$	$1$		$0$	$258552$	$1.826061$	$-12973257/2368$	$0.98369$	$4.52244$	$[1, -1, 1, -89596, 11861247]$	$y^2+xy+y=x^3-x^2-89596x+11861247$	148.2.0.?	$[ ]$	$1$
26714.r1	26714r1	26714.r	26714r	$1$	$1$	$ 2 \cdot 19^{2} \cdot 37 $	$ - 2^{7} \cdot 19^{7} \cdot 37^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$152$	$2$	$0$	$0.285316626$	$1$		$6$	$80640$	$1.475554$	$-49552182217/3329408$	$0.85521$	$4.16001$	$[1, 0, 0, -27624, 1864640]$	$y^2+xy=x^3-27624x+1864640$	152.2.0.?	$[(-8, 1448)]$	$1$
26714.s1	26714q1	26714.s	26714q	$1$	$1$	$ 2 \cdot 19^{2} \cdot 37 $	$ - 2 \cdot 19^{9} \cdot 37^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$152$	$2$	$0$	$4.550605827$	$1$		$0$	$103680$	$1.554859$	$18884848247/18779942$	$0.86750$	$4.05460$	$[1, 0, 0, 20028, -923002]$	$y^2+xy=x^3+20028x-923002$	152.2.0.?	$[(16099/2, 2027883/2)]$	$1$
26714.t1	26714p1	26714.t	26714p	$1$	$1$	$ 2 \cdot 19^{2} \cdot 37 $	$ 2^{3} \cdot 19^{3} \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$5624$	$2$	$0$	$0.991094373$	$1$		$0$	$27360$	$0.701893$	$7784759730259/296$	$0.93902$	$3.77874$	$[1, 1, 1, -7845, 264179]$	$y^2+xy+y=x^3+x^2-7845x+264179$	5624.2.0.?	$[(457/3, -680/3)]$	$1$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

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