Elliptic curves over Q\Q of conductor 4275

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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
4275.a1	4275i2	4275.a	4275i	$2$	$5$	$3^{2} \cdot 5^{2} \cdot 19$	$- 3^{8} \cdot 5^{6} \cdot 19^{5}$	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.2	5B.4.2	$570$	$48$	$1$	$1$	$1$		$0$	$67200$	$2.005432$	$-9358714467168256/22284891$	$1.06833$	$6.34210$	$[0, 0, 1, -987825, 377893156]$	$y^2+y=x^3-987825x+377893156$	5.12.0.a.2, 15.24.0-5.a.2.2, 38.2.0.a.1, 190.24.1.?, 570.48.1.?	$[]$
4275.a2	4275i1	4275.a	4275i	$2$	$5$	$3^{2} \cdot 5^{2} \cdot 19$	$- 3^{16} \cdot 5^{6} \cdot 19$	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.1	5B.4.1	$570$	$48$	$1$	$1$	$1$		$0$	$13440$	$1.200714$	$841232384/1121931$	$1.00490$	$4.43327$	$[0, 0, 1, 4425, 129406]$	$y^2+y=x^3+4425x+129406$	5.12.0.a.1, 15.24.0-5.a.1.2, 38.2.0.a.1, 190.24.1.?, 570.48.1.?	$[]$
4275.b1	4275j1	4275.b	4275j	$1$	$1$	$3^{2} \cdot 5^{2} \cdot 19$	$- 3^{8} \cdot 5^{6} \cdot 19$	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$38$	$2$	$0$	$1$	$1$		$0$	$3456$	$0.517477$	$-1404928/171$	$0.86512$	$3.65942$	$[0, 0, 1, -525, -5094]$	$y^2+y=x^3-525x-5094$	38.2.0.a.1	$[]$
4275.c1	4275m1	4275.c	4275m	$1$	$1$	$3^{2} \cdot 5^{2} \cdot 19$	$- 3^{7} \cdot 5^{2} \cdot 19$	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$228$	$2$	$0$	$0.169341172$	$1$		$6$	$768$	$0.017835$	$-16539745/57$	$0.84560$	$3.16221$	$[1, -1, 1, -140, 672]$	$y^2+xy+y=x^3-x^2-140x+672$	228.2.0.?	$[(8, 0)]$
4275.d1	4275d2	4275.d	4275d	$2$	$2$	$3^{2} \cdot 5^{2} \cdot 19$	$3^{3} \cdot 5^{3} \cdot 19$	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1140$	$12$	$0$	$0.770266764$	$1$		$4$	$1024$	$0.323141$	$115003963647/19$	$1.06999$	$4.01797$	$[1, -1, 1, -1520, 23182]$	$y^2+xy+y=x^3-x^2-1520x+23182$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 570.6.0.?, 1140.12.0.?	$[(19, 20)]$
4275.d2	4275d1	4275.d	4275d	$2$	$2$	$3^{2} \cdot 5^{2} \cdot 19$	$- 3^{3} \cdot 5^{3} \cdot 19^{2}$	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1140$	$12$	$0$	$0.385133382$	$1$		$9$	$512$	$-0.023433$	$-27818127/361$	$1.00533$	$3.02463$	$[1, -1, 1, -95, 382]$	$y^2+xy+y=x^3-x^2-95x+382$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.?	$[(4, 5)]$
4275.e1	4275q2	4275.e	4275q	$2$	$2$	$3^{2} \cdot 5^{2} \cdot 19$	$3^{6} \cdot 5^{9} \cdot 19^{2}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$380$	$12$	$0$	$1$	$1$		$0$	$5120$	$1.027367$	$13312053/361$	$0.88614$	$4.48306$	$[1, -1, 1, -5555, -154178]$	$y^2+xy+y=x^3-x^2-5555x-154178$	2.3.0.a.1, 10.6.0.a.1, 76.6.0.?, 380.12.0.?	$[]$
4275.e2	4275q1	4275.e	4275q	$2$	$2$	$3^{2} \cdot 5^{2} \cdot 19$	$- 3^{6} \cdot 5^{9} \cdot 19$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$380$	$12$	$0$	$1$	$1$		$1$	$2560$	$0.680793$	$27/19$	$1.11940$	$3.76470$	$[1, -1, 1, 70, -7928]$	$y^2+xy+y=x^3-x^2+70x-7928$	2.3.0.a.1, 20.6.0.c.1, 76.6.0.?, 190.6.0.?, 380.12.0.?	$[]$
4275.f1	4275h1	4275.f	4275h	$1$	$1$	$3^{2} \cdot 5^{2} \cdot 19$	$- 3^{13} \cdot 5^{10} \cdot 19^{3}$	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$228$	$2$	$0$	$1$	$1$		$0$	$40320$	$1.955042$	$17446602575/15000633$	$0.97617$	$5.53415$	$[1, -1, 1, 103945, -9015928]$	$y^2+xy+y=x^3-x^2+103945x-9015928$	228.2.0.?	$[]$
4275.g1	4275c2	4275.g	4275c	$2$	$2$	$3^{2} \cdot 5^{2} \cdot 19$	$3^{9} \cdot 5^{9} \cdot 19$	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1140$	$12$	$0$	$12.74496912$	$1$		$0$	$15360$	$1.677166$	$115003963647/19$	$1.06999$	$5.96142$	$[1, -1, 1, -341930, -76872428]$	$y^2+xy+y=x^3-x^2-341930x-76872428$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 570.6.0.?, 1140.12.0.?	$[(302003/11, 159236060/11)]$
4275.g2	4275c1	4275.g	4275c	$2$	$2$	$3^{2} \cdot 5^{2} \cdot 19$	$- 3^{9} \cdot 5^{9} \cdot 19^{2}$	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1140$	$12$	$0$	$6.372484561$	$1$		$3$	$7680$	$1.330591$	$-27818127/361$	$1.00533$	$4.96808$	$[1, -1, 1, -21305, -1204928]$	$y^2+xy+y=x^3-x^2-21305x-1204928$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.?	$[(2468, 121135)]$
4275.h1	4275l2	4275.h	4275l	$2$	$2$	$3^{2} \cdot 5^{2} \cdot 19$	$3^{16} \cdot 5^{8} \cdot 19$	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1140$	$12$	$0$	$1.424079894$	$1$		$6$	$15360$	$1.472668$	$48587168449/28048275$	$1.03180$	$4.88664$	$[1, -1, 1, -17105, 47022]$	$y^2+xy+y=x^3-x^2-17105x+47022$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 1140.12.0.?	$[(-16, 570)]$
4275.h2	4275l1	4275.h	4275l	$2$	$2$	$3^{2} \cdot 5^{2} \cdot 19$	$- 3^{11} \cdot 5^{7} \cdot 19^{2}$	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1140$	$12$	$0$	$2.848159789$	$1$		$5$	$7680$	$1.126095$	$756058031/438615$	$1.00322$	$4.38870$	$[1, -1, 1, 4270, 4272]$	$y^2+xy+y=x^3-x^2+4270x+4272$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.?	$[(18, 285)]$
4275.i1	4275k3	4275.i	4275k	$3$	$9$	$3^{2} \cdot 5^{2} \cdot 19$	$- 3^{6} \cdot 5^{6} \cdot 19$	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	27.36.0.1	3B	$5130$	$1296$	$43$	$1.452281787$	$1$		$0$	$7776$	$1.387465$	$-50357871050752/19$	$1.10495$	$5.71715$	$[0, 0, 1, -173100, 27720031]$	$y^2+y=x^3-173100x+27720031$	3.4.0.a.1, 9.12.0.a.1, 15.8.0-3.a.1.2, 27.36.0.a.1, 38.2.0.a.1, $\ldots$	$[(961/2, 5/2)]$
4275.i2	4275k2	4275.i	4275k	$3$	$9$	$3^{2} \cdot 5^{2} \cdot 19$	$- 3^{6} \cdot 5^{6} \cdot 19^{3}$	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.36.0.2	3Cs	$5130$	$1296$	$43$	$0.484093929$	$1$		$4$	$2592$	$0.838158$	$-89915392/6859$	$1.03310$	$4.14884$	$[0, 0, 1, -2100, 39406]$	$y^2+y=x^3-2100x+39406$	3.12.0.a.1, 9.36.0.b.1, 15.24.0-3.a.1.1, 38.2.0.a.1, 45.72.0-9.b.1.1, $\ldots$	$[(34, 85)]$
4275.i3	4275k1	4275.i	4275k	$3$	$9$	$3^{2} \cdot 5^{2} \cdot 19$	$- 3^{6} \cdot 5^{6} \cdot 19$	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	27.36.0.1	3B	$5130$	$1296$	$43$	$1.452281787$	$1$		$2$	$864$	$0.288852$	$32768/19$	$1.31757$	$3.18706$	$[0, 0, 1, 150, 31]$	$y^2+y=x^3+150x+31$	3.4.0.a.1, 9.12.0.a.1, 15.8.0-3.a.1.1, 27.36.0.a.1, 38.2.0.a.1, $\ldots$	$[(1, 13)]$
4275.j1	4275g4	4275.j	4275g	$4$	$4$	$3^{2} \cdot 5^{2} \cdot 19$	$3^{8} \cdot 5^{9} \cdot 19^{4}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$2280$	$48$	$0$	$1$	$1$		$0$	$55296$	$2.108166$	$23977812996389881/146611125$	$1.09826$	$6.45463$	$[1, -1, 0, -1351692, 605208591]$	$y^2+xy=x^3-x^2-1351692x+605208591$	2.3.0.a.1, 4.6.0.c.1, 10.6.0.a.1, 12.12.0-4.c.1.1, 20.12.0.g.1, $\ldots$	$[]$
4275.j2	4275g3	4275.j	4275g	$4$	$4$	$3^{2} \cdot 5^{2} \cdot 19$	$3^{8} \cdot 5^{18} \cdot 19$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$2280$	$48$	$0$	$1$	$1$		$0$	$55296$	$2.108166$	$209595169258201/41748046875$	$0.98100$	$5.88772$	$[1, -1, 0, -278442, -45727659]$	$y^2+xy=x^3-x^2-278442x-45727659$	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 40.12.0.z.1, 60.12.0-4.c.1.2, $\ldots$	$[]$
4275.j3	4275g2	4275.j	4275g	$4$	$4$	$3^{2} \cdot 5^{2} \cdot 19$	$3^{10} \cdot 5^{12} \cdot 19^{2}$	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1140$	$48$	$0$	$1$	$1$		$2$	$27648$	$1.761591$	$6189976379881/456890625$	$0.95560$	$5.46642$	$[1, -1, 0, -86067, 9099216]$	$y^2+xy=x^3-x^2-86067x+9099216$	2.6.0.a.1, 12.12.0-2.a.1.1, 20.12.0.b.1, 60.24.0-20.b.1.2, 76.12.0.?, $\ldots$	$[]$
4275.j4	4275g1	4275.j	4275g	$4$	$4$	$3^{2} \cdot 5^{2} \cdot 19$	$- 3^{14} \cdot 5^{9} \cdot 19$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$2280$	$48$	$0$	$1$	$1$		$1$	$13824$	$1.415016$	$1256216039/15582375$	$0.94875$	$4.81032$	$[1, -1, 0, 5058, 624591]$	$y^2+xy=x^3-x^2+5058x+624591$	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 40.12.0.z.1, 120.24.0.?, $\ldots$	$[]$
4275.k1	4275b2	4275.k	4275b	$2$	$2$	$3^{2} \cdot 5^{2} \cdot 19$	$3^{9} \cdot 5^{3} \cdot 19$	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1140$	$12$	$0$	$9.608092465$	$1$		$0$	$3072$	$0.872447$	$115003963647/19$	$1.06999$	$4.80640$	$[1, -1, 0, -13677, -612244]$	$y^2+xy=x^3-x^2-13677x-612244$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 570.6.0.?, 1140.12.0.?	$[(12463/6, 1259593/6)]$
4275.k2	4275b1	4275.k	4275b	$2$	$2$	$3^{2} \cdot 5^{2} \cdot 19$	$- 3^{9} \cdot 5^{3} \cdot 19^{2}$	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1140$	$12$	$0$	$4.804046232$	$1$		$1$	$1536$	$0.525873$	$-27818127/361$	$1.00533$	$3.81306$	$[1, -1, 0, -852, -9469]$	$y^2+xy=x^3-x^2-852x-9469$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.?	$[(382/3, 4063/3)]$
4275.l1	4275n1	4275.l	4275n	$1$	$1$	$3^{2} \cdot 5^{2} \cdot 19$	$- 3^{13} \cdot 5^{4} \cdot 19^{3}$	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$228$	$2$	$0$	$0.869995144$	$1$		$2$	$8064$	$1.150322$	$17446602575/15000633$	$0.97617$	$4.37912$	$[1, -1, 0, 4158, -72959]$	$y^2+xy=x^3-x^2+4158x-72959$	228.2.0.?	$[(104, 1163)]$
4275.m1	4275e3	4275.m	4275e	$4$	$4$	$3^{2} \cdot 5^{2} \cdot 19$	$3^{10} \cdot 5^{6} \cdot 19$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$2280$	$48$	$0$	$1$	$1$		$0$	$6144$	$1.109016$	$115714886617/1539$	$0.98111$	$4.99043$	$[1, -1, 0, -22842, -1323059]$	$y^2+xy=x^3-x^2-22842x-1323059$	2.3.0.a.1, 4.6.0.c.1, 24.12.0.z.1, 40.12.0-4.c.1.5, 60.12.0-4.c.1.2, $\ldots$	$[]$
4275.m2	4275e2	4275.m	4275e	$4$	$4$	$3^{2} \cdot 5^{2} \cdot 19$	$3^{8} \cdot 5^{6} \cdot 19^{2}$	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1140$	$48$	$0$	$1$	$1$		$2$	$3072$	$0.762443$	$30664297/3249$	$0.90727$	$4.00535$	$[1, -1, 0, -1467, -19184]$	$y^2+xy=x^3-x^2-1467x-19184$	2.6.0.a.1, 12.12.0.b.1, 20.12.0-2.a.1.1, 60.24.0-12.b.1.2, 76.12.0.?, $\ldots$	$[]$
4275.m3	4275e1	4275.m	4275e	$4$	$4$	$3^{2} \cdot 5^{2} \cdot 19$	$3^{7} \cdot 5^{6} \cdot 19$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$2280$	$48$	$0$	$1$	$1$		$1$	$1536$	$0.415869$	$389017/57$	$0.96267$	$3.48299$	$[1, -1, 0, -342, 2191]$	$y^2+xy=x^3-x^2-342x+2191$	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 24.12.0.z.1, 114.6.0.?, $\ldots$	$[]$
4275.m4	4275e4	4275.m	4275e	$4$	$4$	$3^{2} \cdot 5^{2} \cdot 19$	$- 3^{7} \cdot 5^{6} \cdot 19^{4}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.1	2B	$2280$	$48$	$0$	$1$	$1$		$0$	$6144$	$1.109016$	$67419143/390963$	$0.97474$	$4.36267$	$[1, -1, 0, 1908, -96809]$	$y^2+xy=x^3-x^2+1908x-96809$	2.3.0.a.1, 4.6.0.c.1, 6.6.0.a.1, 12.12.0.g.1, 20.12.0-4.c.1.1, $\ldots$	$[]$
4275.n1	4275a2	4275.n	4275a	$2$	$2$	$3^{2} \cdot 5^{2} \cdot 19$	$3^{3} \cdot 5^{9} \cdot 19$	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1140$	$12$	$0$	$3.681226927$	$1$		$0$	$5120$	$1.127859$	$115003963647/19$	$1.06999$	$5.17299$	$[1, -1, 0, -37992, 2859791]$	$y^2+xy=x^3-x^2-37992x+2859791$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 570.6.0.?, 1140.12.0.?	$[(455/2, -313/2)]$
4275.n2	4275a1	4275.n	4275a	$2$	$2$	$3^{2} \cdot 5^{2} \cdot 19$	$- 3^{3} \cdot 5^{9} \cdot 19^{2}$	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1140$	$12$	$0$	$1.840613463$	$1$		$3$	$2560$	$0.781286$	$-27818127/361$	$1.00533$	$4.17965$	$[1, -1, 0, -2367, 45416]$	$y^2+xy=x^3-x^2-2367x+45416$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.?	$[(20, 66)]$
4275.o1	4275f2	4275.o	4275f	$2$	$2$	$3^{2} \cdot 5^{2} \cdot 19$	$3^{8} \cdot 5^{12} \cdot 19$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1140$	$12$	$0$	$1$	$1$		$0$	$9216$	$1.364365$	$90458382169/2671875$	$1.09032$	$4.96098$	$[1, -1, 0, -21042, 1149741]$	$y^2+xy=x^3-x^2-21042x+1149741$	2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 1140.12.0.?	$[]$
4275.o2	4275f1	4275.o	4275f	$2$	$2$	$3^{2} \cdot 5^{2} \cdot 19$	$- 3^{7} \cdot 5^{9} \cdot 19^{2}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1140$	$12$	$0$	$1$	$1$		$1$	$4608$	$1.017792$	$357911/135375$	$0.95197$	$4.24821$	$[1, -1, 0, 333, 59616]$	$y^2+xy=x^3-x^2+333x+59616$	2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.?	$[]$
4275.p1	4275o2	4275.p	4275o	$2$	$2$	$3^{2} \cdot 5^{2} \cdot 19$	$3^{6} \cdot 5^{3} \cdot 19^{2}$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$380$	$12$	$0$	$1$	$1$		$0$	$1024$	$0.222648$	$13312053/361$	$0.88614$	$3.32804$	$[1, -1, 0, -222, -1189]$	$y^2+xy=x^3-x^2-222x-1189$	2.3.0.a.1, 10.6.0.a.1, 76.6.0.?, 380.12.0.?	$[]$
4275.p2	4275o1	4275.p	4275o	$2$	$2$	$3^{2} \cdot 5^{2} \cdot 19$	$- 3^{6} \cdot 5^{3} \cdot 19$	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$380$	$12$	$0$	$1$	$1$		$1$	$512$	$-0.123926$	$27/19$	$1.11940$	$2.60968$	$[1, -1, 0, 3, -64]$	$y^2+xy=x^3-x^2+3x-64$	2.3.0.a.1, 20.6.0.c.1, 76.6.0.?, 190.6.0.?, 380.12.0.?	$[]$
4275.q1	4275p1	4275.q	4275p	$1$	$1$	$3^{2} \cdot 5^{2} \cdot 19$	$- 3^{7} \cdot 5^{8} \cdot 19$	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$228$	$2$	$0$	$1$	$1$		$0$	$3840$	$0.822554$	$-16539745/57$	$0.84560$	$4.31723$	$[1, -1, 0, -3492, 80541]$	$y^2+xy=x^3-x^2-3492x+80541$	228.2.0.?	$[]$

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