LMFDB - Elliptic curves over $\Q$ of conductor 8379

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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

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Results (30 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
8379.a1	8379e1	8379.a	8379e	$1$	$1$	$ 3^{2} \cdot 7^{2} \cdot 19 $	$ - 3^{6} \cdot 7^{8} \cdot 19 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$38$	$2$	$0$	$0.544181114$	$1$		$6$	$13104$	$0.792796$	$-28672/19$	$0.67892$	$3.67364$	$[0, 0, 1, -1029, -18608]$	$y^2+y=x^3-1029x-18608$	38.2.0.a.1	$[(49, 220)]$
8379.b1	8379d1	8379.b	8379d	$1$	$1$	$ 3^{2} \cdot 7^{2} \cdot 19 $	$ - 3^{20} \cdot 7^{4} \cdot 19^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$38$	$2$	$0$	$1$	$1$		$0$	$92736$	$1.902113$	$28383712415744/32806384371$	$1.04419$	$5.02045$	$[0, 0, 1, 76587, -8146728]$	$y^2+y=x^3+76587x-8146728$	38.2.0.a.1	$[]$
8379.c1	8379q1	8379.c	8379q	$1$	$1$	$ 3^{2} \cdot 7^{2} \cdot 19 $	$ - 3^{20} \cdot 7^{10} \cdot 19^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$38$	$2$	$0$	$1$	$1$		$0$	$649152$	$2.875069$	$28383712415744/32806384371$	$1.04419$	$6.31291$	$[0, 0, 1, 3752763, 2794327618]$	$y^2+y=x^3+3752763x+2794327618$	38.2.0.a.1	$[]$
8379.d1	8379i1	8379.d	8379i	$1$	$1$	$ 3^{2} \cdot 7^{2} \cdot 19 $	$ - 3^{6} \cdot 7^{2} \cdot 19 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$38$	$2$	$0$	$0.493971539$	$1$		$4$	$1872$	$-0.180159$	$-28672/19$	$0.67892$	$2.38118$	$[0, 0, 1, -21, 54]$	$y^2+y=x^3-21x+54$	38.2.0.a.1	$[(2, 4)]$
8379.e1	8379n3	8379.e	8379n	$4$	$4$	$ 3^{2} \cdot 7^{2} \cdot 19 $	$ 3^{10} \cdot 7^{6} \cdot 19 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$3192$	$48$	$0$	$1.841944016$	$1$		$16$	$18432$	$1.277252$	$115714886617/1539$	$0.98111$	$4.84216$	$[1, -1, 1, -44771, 3657336]$	$y^2+xy+y=x^3-x^2-44771x+3657336$	2.3.0.a.1, 4.6.0.c.1, 24.12.0.z.1, 56.12.0-4.c.1.5, 76.12.0.?, $\ldots$	$[(86, 618), (122, -57)]$
8379.e2	8379n2	8379.e	8379n	$4$	$4$	$ 3^{2} \cdot 7^{2} \cdot 19 $	$ 3^{8} \cdot 7^{6} \cdot 19^{2} $	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$1596$	$48$	$0$	$1.841944016$	$1$		$26$	$9216$	$0.930679$	$30664297/3249$	$0.90727$	$3.93046$	$[1, -1, 1, -2876, 54366]$	$y^2+xy+y=x^3-x^2-2876x+54366$	2.6.0.a.1, 12.12.0.b.1, 28.12.0-2.a.1.1, 76.12.0.?, 84.24.0.?, $\ldots$	$[(2, 219), (51, 170)]$
8379.e3	8379n1	8379.e	8379n	$4$	$4$	$ 3^{2} \cdot 7^{2} \cdot 19 $	$ 3^{7} \cdot 7^{6} \cdot 19 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$3192$	$48$	$0$	$1.841944016$	$1$		$17$	$4608$	$0.584105$	$389017/57$	$0.96267$	$3.44701$	$[1, -1, 1, -671, -5610]$	$y^2+xy+y=x^3-x^2-671x-5610$	2.3.0.a.1, 4.6.0.c.1, 24.12.0.z.1, 28.12.0-4.c.1.2, 114.6.0.?, $\ldots$	$[(-12, 30), (30, 9)]$
8379.e4	8379n4	8379.e	8379n	$4$	$4$	$ 3^{2} \cdot 7^{2} \cdot 19 $	$ - 3^{7} \cdot 7^{6} \cdot 19^{4} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$3192$	$48$	$0$	$0.460486004$	$1$		$24$	$18432$	$1.277252$	$67419143/390963$	$0.97474$	$4.26116$	$[1, -1, 1, 3739, 263400]$	$y^2+xy+y=x^3-x^2+3739x+263400$	2.3.0.a.1, 4.6.0.c.1, 6.6.0.a.1, 12.12.0.g.1, 28.12.0-4.c.1.1, $\ldots$	$[(-12, 471), (-31, 357)]$
8379.f1	8379b1	8379.f	8379b	$2$	$2$	$ 3^{2} \cdot 7^{2} \cdot 19 $	$ 3^{9} \cdot 7^{8} \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$228$	$12$	$0$	$1$	$1$		$1$	$18432$	$1.276878$	$766060875/931$	$0.86309$	$4.65155$	$[1, -1, 1, -25220, -1533626]$	$y^2+xy+y=x^3-x^2-25220x-1533626$	2.3.0.a.1, 12.6.0.c.1, 76.6.0.?, 114.6.0.?, 228.12.0.?	$[]$
8379.f2	8379b2	8379.f	8379b	$2$	$2$	$ 3^{2} \cdot 7^{2} \cdot 19 $	$ - 3^{9} \cdot 7^{10} \cdot 19^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$228$	$12$	$0$	$1$	$1$		$0$	$36864$	$1.623451$	$-307546875/866761$	$1.04147$	$4.74645$	$[1, -1, 1, -18605, -2361824]$	$y^2+xy+y=x^3-x^2-18605x-2361824$	2.3.0.a.1, 6.6.0.a.1, 76.6.0.?, 228.12.0.?	$[]$
8379.g1	8379m2	8379.g	8379m	$2$	$2$	$ 3^{2} \cdot 7^{2} \cdot 19 $	$ 3^{16} \cdot 7^{9} \cdot 19^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1$	$1$		$0$	$92160$	$2.236542$	$789529529265625/7311624327$	$1.01939$	$5.81942$	$[1, -1, 1, -849155, 298974260]$	$y^2+xy+y=x^3-x^2-849155x+298974260$	2.3.0.a.1, 28.6.0.a.1, 228.6.0.?, 1596.12.0.?	$[]$
8379.g2	8379m1	8379.g	8379m	$2$	$2$	$ 3^{2} \cdot 7^{2} \cdot 19 $	$ 3^{11} \cdot 7^{12} \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1$	$1$		$1$	$46080$	$1.889967$	$1031831907625/543185433$	$0.96952$	$5.08436$	$[1, -1, 1, -92840, -3249214]$	$y^2+xy+y=x^3-x^2-92840x-3249214$	2.3.0.a.1, 28.6.0.b.1, 114.6.0.?, 1596.12.0.?	$[]$
8379.h1	8379c1	8379.h	8379c	$1$	$1$	$ 3^{2} \cdot 7^{2} \cdot 19 $	$ - 3^{10} \cdot 7^{8} \cdot 19 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$38$	$2$	$0$	$1$	$1$		$0$	$13440$	$1.155926$	$-1835008/1539$	$0.91010$	$4.14871$	$[0, 0, 1, -4116, 159066]$	$y^2+y=x^3-4116x+159066$	38.2.0.a.1	$[]$
8379.i1	8379j1	8379.i	8379j	$1$	$1$	$ 3^{2} \cdot 7^{2} \cdot 19 $	$ - 3^{10} \cdot 7^{2} \cdot 19 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$38$	$2$	$0$	$1$	$1$		$0$	$1920$	$0.182970$	$-1835008/1539$	$0.91010$	$2.85624$	$[0, 0, 1, -84, -464]$	$y^2+y=x^3-84x-464$	38.2.0.a.1	$[]$
8379.j1	8379f3	8379.j	8379f	$3$	$9$	$ 3^{2} \cdot 7^{2} \cdot 19 $	$ - 3^{6} \cdot 7^{6} \cdot 19 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	27.36.0.1	3B	$7182$	$1296$	$43$	$21.57657708$	$1$		$0$	$27216$	$1.555700$	$-50357871050752/19$	$1.10495$	$5.51474$	$[0, 0, 1, -339276, -76063766]$	$y^2+y=x^3-339276x-76063766$	3.4.0.a.1, 9.12.0.a.1, 21.8.0-3.a.1.1, 27.36.0.a.1, 38.2.0.a.1, $\ldots$	$[(6984302686/415, 583632546429559/415)]$
8379.j2	8379f2	8379.j	8379f	$3$	$9$	$ 3^{2} \cdot 7^{2} \cdot 19 $	$ - 3^{6} \cdot 7^{6} \cdot 19^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.36.0.2	3Cs	$7182$	$1296$	$43$	$7.192192360$	$1$		$0$	$9072$	$1.006393$	$-89915392/6859$	$1.03310$	$4.06325$	$[0, 0, 1, -4116, -108131]$	$y^2+y=x^3-4116x-108131$	3.12.0.a.1, 9.36.0.b.1, 21.24.0-3.a.1.1, 38.2.0.a.1, 63.72.0-9.b.1.1, $\ldots$	$[(3049/5, 137093/5)]$
8379.j3	8379f1	8379.j	8379f	$3$	$9$	$ 3^{2} \cdot 7^{2} \cdot 19 $	$ - 3^{6} \cdot 7^{6} \cdot 19 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	27.36.0.1	3B	$7182$	$1296$	$43$	$2.397397453$	$1$		$2$	$3024$	$0.457088$	$32768/19$	$1.31757$	$3.17312$	$[0, 0, 1, 294, -86]$	$y^2+y=x^3+294x-86$	3.4.0.a.1, 9.12.0.a.1, 21.8.0-3.a.1.2, 27.36.0.a.1, 38.2.0.a.1, $\ldots$	$[(22, 130)]$
8379.k1	8379k2	8379.k	8379k	$2$	$2$	$ 3^{2} \cdot 7^{2} \cdot 19 $	$ 3^{8} \cdot 7^{9} \cdot 19^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1$	$1$		$0$	$28672$	$1.379976$	$7880599/3249$	$0.86684$	$4.42629$	$[1, -1, 0, -12798, 302049]$	$y^2+xy=x^3-x^2-12798x+302049$	2.3.0.a.1, 28.6.0.a.1, 228.6.0.?, 1596.12.0.?	$[]$
8379.k2	8379k1	8379.k	8379k	$2$	$2$	$ 3^{2} \cdot 7^{2} \cdot 19 $	$ - 3^{7} \cdot 7^{9} \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1$	$4$	$2$	$1$	$14336$	$1.033403$	$68921/57$	$0.78914$	$3.90166$	$[1, -1, 0, 2637, 33480]$	$y^2+xy=x^3-x^2+2637x+33480$	2.3.0.a.1, 28.6.0.b.1, 228.6.0.?, 798.6.0.?, 1596.12.0.?	$[]$
8379.l1	8379g2	8379.l	8379g	$2$	$2$	$ 3^{2} \cdot 7^{2} \cdot 19 $	$ 3^{12} \cdot 7^{7} \cdot 19^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1.149787286$	$1$		$4$	$18432$	$1.448627$	$12246522625/1842183$	$0.89725$	$4.59354$	$[1, -1, 0, -21177, 1025730]$	$y^2+xy=x^3-x^2-21177x+1025730$	2.3.0.a.1, 28.6.0.a.1, 228.6.0.?, 1596.12.0.?	$[(142, 860)]$
8379.l2	8379g1	8379.l	8379g	$2$	$2$	$ 3^{2} \cdot 7^{2} \cdot 19 $	$ 3^{9} \cdot 7^{8} \cdot 19 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$2.299574572$	$1$		$3$	$9216$	$1.102055$	$244140625/25137$	$1.08196$	$4.16012$	$[1, -1, 0, -5742, -150417]$	$y^2+xy=x^3-x^2-5742x-150417$	2.3.0.a.1, 28.6.0.b.1, 114.6.0.?, 1596.12.0.?	$[(142, 1301)]$
8379.m1	8379a1	8379.m	8379a	$2$	$2$	$ 3^{2} \cdot 7^{2} \cdot 19 $	$ 3^{3} \cdot 7^{8} \cdot 19 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$228$	$12$	$0$	$1$	$1$		$1$	$6144$	$0.727572$	$766060875/931$	$0.86309$	$3.92186$	$[1, -1, 0, -2802, 57735]$	$y^2+xy=x^3-x^2-2802x+57735$	2.3.0.a.1, 12.6.0.c.1, 76.6.0.?, 114.6.0.?, 228.12.0.?	$[]$
8379.m2	8379a2	8379.m	8379a	$2$	$2$	$ 3^{2} \cdot 7^{2} \cdot 19 $	$ - 3^{3} \cdot 7^{10} \cdot 19^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$228$	$12$	$0$	$1$	$1$		$0$	$12288$	$1.074146$	$-307546875/866761$	$1.04147$	$4.01676$	$[1, -1, 0, -2067, 88164]$	$y^2+xy=x^3-x^2-2067x+88164$	2.3.0.a.1, 6.6.0.a.1, 76.6.0.?, 228.12.0.?	$[]$
8379.n1	8379h2	8379.n	8379h	$2$	$2$	$ 3^{2} \cdot 7^{2} \cdot 19 $	$ 3^{8} \cdot 7^{3} \cdot 19^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1.195268093$	$1$		$4$	$4096$	$0.407021$	$7880599/3249$	$0.86684$	$3.13382$	$[1, -1, 0, -261, -806]$	$y^2+xy=x^3-x^2-261x-806$	2.3.0.a.1, 28.6.0.a.1, 228.6.0.?, 1596.12.0.?	$[(-10, 32)]$
8379.n2	8379h1	8379.n	8379h	$2$	$2$	$ 3^{2} \cdot 7^{2} \cdot 19 $	$ - 3^{7} \cdot 7^{3} \cdot 19 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$2.390536186$	$1$		$3$	$2048$	$0.060447$	$68921/57$	$0.78914$	$2.60919$	$[1, -1, 0, 54, -113]$	$y^2+xy=x^3-x^2+54x-113$	2.3.0.a.1, 28.6.0.b.1, 228.6.0.?, 798.6.0.?, 1596.12.0.?	$[(6, 17)]$
8379.o1	8379l2	8379.o	8379l	$2$	$2$	$ 3^{2} \cdot 7^{2} \cdot 19 $	$ 3^{8} \cdot 7^{7} \cdot 19^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1$	$1$		$0$	$129024$	$2.048302$	$11192824869409/2963890503$	$0.95644$	$5.34826$	$[1, -1, 0, -205515, 26462218]$	$y^2+xy=x^3-x^2-205515x+26462218$	2.3.0.a.1, 28.6.0.a.1, 228.6.0.?, 1596.12.0.?	$[]$
8379.o2	8379l1	8379.o	8379l	$2$	$2$	$ 3^{2} \cdot 7^{2} \cdot 19 $	$ 3^{7} \cdot 7^{8} \cdot 19^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1596$	$12$	$0$	$1$	$1$		$1$	$64512$	$1.701729$	$8855610342769/1008273$	$0.94565$	$5.32233$	$[1, -1, 0, -190080, 31941643]$	$y^2+xy=x^3-x^2-190080x+31941643$	2.3.0.a.1, 28.6.0.b.1, 114.6.0.?, 1596.12.0.?	$[]$
8379.p1	8379p1	8379.p	8379p	$1$	$1$	$ 3^{2} \cdot 7^{2} \cdot 19 $	$ - 3^{8} \cdot 7^{6} \cdot 19 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$38$	$2$	$0$	$1$	$1$		$0$	$7488$	$0.685713$	$-1404928/171$	$0.86512$	$3.61029$	$[0, 0, 1, -1029, 13977]$	$y^2+y=x^3-1029x+13977$	38.2.0.a.1	$[]$
8379.q1	8379o2	8379.q	8379o	$2$	$5$	$ 3^{2} \cdot 7^{2} \cdot 19 $	$ - 3^{8} \cdot 7^{6} \cdot 19^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$3990$	$48$	$1$	$1$	$9$	$3$	$0$	$158400$	$2.173668$	$-9358714467168256/22284891$	$1.06833$	$6.09313$	$[0, 0, 1, -1936137, -1036938821]$	$y^2+y=x^3-1936137x-1036938821$	5.12.0.a.2, 38.2.0.a.1, 105.24.0.?, 190.24.1.?, 3990.48.1.?	$[]$
8379.q2	8379o1	8379.q	8379o	$2$	$5$	$ 3^{2} \cdot 7^{2} \cdot 19 $	$ - 3^{16} \cdot 7^{6} \cdot 19 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.1	5B.4.1	$3990$	$48$	$1$	$1$	$9$	$3$	$0$	$31680$	$1.368950$	$841232384/1121931$	$1.00490$	$4.32650$	$[0, 0, 1, 8673, -355091]$	$y^2+y=x^3+8673x-355091$	5.12.0.a.1, 38.2.0.a.1, 105.24.0.?, 190.24.1.?, 3990.48.1.?	$[]$

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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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