Elliptic curves over $\Q$ of conductor 2448

Results (44 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	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
2448.a1	2448l2	2448.a	2448l	$2$	$3$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( - 2^{8} \cdot 3^{9} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$0.379978712$	$1$		$4$	$1728$	$0.675154$	$-1517101056/17$	$[0, 0, 0, -4104, 101196]$	\(y^2=x^3-4104x+101196\)
2448.a2	2448l1	2448.a	2448l	$2$	$3$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( - 2^{8} \cdot 3^{3} \cdot 17^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$0.126659570$	$1$		$6$	$576$	$0.125848$	$-221184/4913$	$[0, 0, 0, -24, 284]$	\(y^2=x^3-24x+284\)
2448.b1	2448h1	2448.b	2448h	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( - 2^{8} \cdot 3^{9} \cdot 17^{5} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.322834554$	$1$		$4$	$3840$	$1.155319$	$57530252288/38336139$	$[0, 0, 0, 4596, -46676]$	\(y^2=x^3+4596x-46676\)
2448.c1	2448s2	2448.c	2448s	$2$	$3$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( - 2^{12} \cdot 3^{7} \cdot 17^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$3456$	$0.983230$	$-23100424192/14739$	$[0, 0, 0, -8544, -304144]$	\(y^2=x^3-8544x-304144\)
2448.c2	2448s1	2448.c	2448s	$2$	$3$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( - 2^{12} \cdot 3^{9} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$1152$	$0.433924$	$32768/459$	$[0, 0, 0, 96, -1744]$	\(y^2=x^3+96x-1744\)
2448.d1	2448d3	2448.d	2448d	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( 2^{11} \cdot 3^{14} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$1$	$1$		$1$	$4096$	$1.001610$	$22994537186/111537$	$[0, 0, 0, -6771, -213550]$	\(y^2=x^3-6771x-213550\)
2448.d2	2448d2	2448.d	2448d	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( 2^{10} \cdot 3^{10} \cdot 17^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.4	2Cs	$1$	$1$		$3$	$2048$	$0.655037$	$40873252/23409$	$[0, 0, 0, -651, 650]$	\(y^2=x^3-651x+650\)
2448.d3	2448d1	2448.d	2448d	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( 2^{8} \cdot 3^{8} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$1$	$1$		$1$	$1024$	$0.308464$	$61918288/153$	$[0, 0, 0, -471, 3926]$	\(y^2=x^3-471x+3926\)
2448.d4	2448d4	2448.d	2448d	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( - 2^{11} \cdot 3^{8} \cdot 17^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.16	2B	$1$	$1$		$1$	$4096$	$1.001610$	$1285471294/751689$	$[0, 0, 0, 2589, 5186]$	\(y^2=x^3+2589x+5186\)
2448.e1	2448m1	2448.e	2448m	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( - 2^{8} \cdot 3^{7} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.876888052$	$1$		$4$	$384$	$0.037764$	$-65536/51$	$[0, 0, 0, -48, -196]$	\(y^2=x^3-48x-196\)
2448.f1	2448a1	2448.f	2448a	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( - 2^{8} \cdot 3^{3} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.813040150$	$1$		$2$	$128$	$-0.337991$	$27648/17$	$[0, 0, 0, 12, -4]$	\(y^2=x^3+12x-4\)
2448.g1	2448i1	2448.g	2448i	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( - 2^{12} \cdot 3^{3} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$320$	$-0.067080$	$-110592/17$	$[0, 0, 0, -48, -144]$	\(y^2=x^3-48x-144\)
2448.h1	2448g1	2448.h	2448g	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( 2^{10} \cdot 3^{8} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.4	2B	$1.472924139$	$1$		$7$	$512$	$0.355572$	$12194500/153$	$[0, 0, 0, -435, -3454]$	\(y^2=x^3-435x-3454\)
2448.h2	2448g2	2448.h	2448g	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( - 2^{11} \cdot 3^{10} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$0.736462069$	$1$		$9$	$1024$	$0.702146$	$-31250/23409$	$[0, 0, 0, -75, -8998]$	\(y^2=x^3-75x-8998\)
2448.i1	2448p3	2448.i	2448p	$4$	$6$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( 2^{30} \cdot 3^{8} \cdot 17^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.4, 3.4.0.1	2B, 3B	$1$	$1$		$1$	$13824$	$1.883879$	$46753267515625/11591221248$	$[0, 0, 0, -108075, -10338982]$	\(y^2=x^3-108075x-10338982\)
2448.i2	2448p1	2448.i	2448p	$4$	$6$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( 2^{18} \cdot 3^{12} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.4, 3.4.0.1	2B, 3B	$1$	$1$		$1$	$4608$	$1.334574$	$1845026709625/793152$	$[0, 0, 0, -36795, 2715626]$	\(y^2=x^3-36795x+2715626\)
2448.i3	2448p2	2448.i	2448p	$4$	$6$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( - 2^{15} \cdot 3^{18} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.5, 3.4.0.1	2B, 3B	$1$	$1$		$1$	$9216$	$1.681147$	$-1107111813625/1228691592$	$[0, 0, 0, -31035, 3594602]$	\(y^2=x^3-31035x+3594602\)
2448.i4	2448p4	2448.i	2448p	$4$	$6$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( - 2^{21} \cdot 3^{10} \cdot 17^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.5, 3.4.0.1	2B, 3B	$1$	$1$		$1$	$27648$	$2.230453$	$655215969476375/1001033261568$	$[0, 0, 0, 260565, -65561254]$	\(y^2=x^3+260565x-65561254\)
2448.j1	2448f2	2448.j	2448f	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( 2^{11} \cdot 3^{6} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$0.480566655$	$1$		$9$	$768$	$0.417461$	$6097250/289$	$[0, 0, 0, -435, 3346]$	\(y^2=x^3-435x+3346\)
2448.j2	2448f1	2448.j	2448f	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( 2^{10} \cdot 3^{6} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$0.961133310$	$1$		$7$	$384$	$0.070888$	$62500/17$	$[0, 0, 0, -75, -182]$	\(y^2=x^3-75x-182\)
2448.k1	2448q4	2448.k	2448q	$4$	$6$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( 2^{13} \cdot 3^{6} \cdot 17^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.6, 3.4.0.1	2B, 3B	$1$	$1$		$1$	$6912$	$1.421940$	$159661140625/48275138$	$[0, 0, 0, -16275, -552238]$	\(y^2=x^3-16275x-552238\)
2448.k2	2448q3	2448.k	2448q	$4$	$6$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( 2^{14} \cdot 3^{6} \cdot 17^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.1, 3.4.0.1	2B, 3B	$1$	$1$		$1$	$3456$	$1.075367$	$120920208625/19652$	$[0, 0, 0, -14835, -695374]$	\(y^2=x^3-14835x-695374\)
2448.k3	2448q2	2448.k	2448q	$4$	$6$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( 2^{15} \cdot 3^{6} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.6, 3.4.0.1	2B, 3B	$1$	$1$		$1$	$2304$	$0.872635$	$8805624625/2312$	$[0, 0, 0, -6195, 187634]$	\(y^2=x^3-6195x+187634\)
2448.k4	2448q1	2448.k	2448q	$4$	$6$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( 2^{18} \cdot 3^{6} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.1, 3.4.0.1	2B, 3B	$1$	$1$		$1$	$1152$	$0.526061$	$3048625/1088$	$[0, 0, 0, -435, 2162]$	\(y^2=x^3-435x+2162\)
2448.l1	2448r1	2448.l	2448r	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( - 2^{8} \cdot 3^{17} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$4224$	$1.151207$	$-1841198792704/3011499$	$[0, 0, 0, -14592, -679412]$	\(y^2=x^3-14592x-679412\)
2448.m1	2448k1	2448.m	2448k	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( - 2^{12} \cdot 3^{9} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1.160245252$	$1$		$2$	$960$	$0.482225$	$-110592/17$	$[0, 0, 0, -432, 3888]$	\(y^2=x^3-432x+3888\)
2448.n1	2448b1	2448.n	2448b	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( - 2^{8} \cdot 3^{9} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$384$	$0.211315$	$27648/17$	$[0, 0, 0, 108, 108]$	\(y^2=x^3+108x+108\)
2448.o1	2448o3	2448.o	2448o	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( 2^{12} \cdot 3^{6} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	32.48.0.12	2B	$3.624239889$	$1$		$3$	$2048$	$0.865817$	$82483294977/17$	$[0, 0, 0, -13059, -574398]$	\(y^2=x^3-13059x-574398\)
2448.o2	2448o2	2448.o	2448o	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( 2^{12} \cdot 3^{6} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.20	2Cs	$1.812119944$	$1$		$9$	$1024$	$0.519243$	$20346417/289$	$[0, 0, 0, -819, -8910]$	\(y^2=x^3-819x-8910\)
2448.o3	2448o4	2448.o	2448o	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( - 2^{12} \cdot 3^{6} \cdot 17^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.76	2B	$3.624239889$	$1$		$3$	$2048$	$0.865817$	$-35937/83521$	$[0, 0, 0, -99, -24030]$	\(y^2=x^3-99x-24030\)
2448.o4	2448o1	2448.o	2448o	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( 2^{12} \cdot 3^{6} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	32.48.0.12	2B	$0.906059972$	$1$		$7$	$512$	$0.172670$	$35937/17$	$[0, 0, 0, -99, 162]$	\(y^2=x^3-99x+162\)
2448.p1	2448n5	2448.p	2448n	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( 2^{13} \cdot 3^{8} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.213	2B	$16.06869956$	$1$		$1$	$24576$	$2.089531$	$2361739090258884097/5202$	$[0, 0, 0, -3995139, -3073590142]$	\(y^2=x^3-3995139x-3073590142\)
2448.p2	2448n3	2448.p	2448n	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( 2^{14} \cdot 3^{10} \cdot 17^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.137	2Cs	$8.034349782$	$1$		$3$	$12288$	$1.742958$	$576615941610337/27060804$	$[0, 0, 0, -249699, -48023710]$	\(y^2=x^3-249699x-48023710\)
2448.p3	2448n6	2448.p	2448n	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( - 2^{13} \cdot 3^{8} \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.224	2B	$4.017174891$	$1$		$3$	$24576$	$2.089531$	$-491411892194497/125563633938$	$[0, 0, 0, -236739, -53231038]$	\(y^2=x^3-236739x-53231038\)
2448.p4	2448n2	2448.p	2448n	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( 2^{16} \cdot 3^{14} \cdot 17^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.89	2Cs	$4.017174891$	$1$		$7$	$6144$	$1.396385$	$163936758817/30338064$	$[0, 0, 0, -16419, -667870]$	\(y^2=x^3-16419x-667870\)
2448.p5	2448n1	2448.p	2448n	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( 2^{20} \cdot 3^{10} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.101	2B	$2.008587445$	$1$		$7$	$3072$	$1.049810$	$4354703137/352512$	$[0, 0, 0, -4899, 122402]$	\(y^2=x^3-4899x+122402\)
2448.p6	2448n4	2448.p	2448n	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( - 2^{14} \cdot 3^{22} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.132	2B	$8.034349782$	$1$		$1$	$12288$	$1.742958$	$1276229915423/2927177028$	$[0, 0, 0, 32541, -3889438]$	\(y^2=x^3+32541x-3889438\)
2448.q1	2448c1	2448.q	2448c	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( 2^{8} \cdot 3^{6} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.3	2B	$1$	$1$		$1$	$384$	$-0.058898$	$35152/17$	$[0, 0, 0, -39, 38]$	\(y^2=x^3-39x+38\)
2448.q2	2448c2	2448.q	2448c	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( - 2^{10} \cdot 3^{6} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.5	2B	$1$	$1$		$1$	$768$	$0.287676$	$415292/289$	$[0, 0, 0, 141, 290]$	\(y^2=x^3+141x+290\)
2448.r1	2448j1	2448.r	2448j	$2$	$3$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( - 2^{8} \cdot 3^{3} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$576$	$0.125848$	$-1517101056/17$	$[0, 0, 0, -456, -3748]$	\(y^2=x^3-456x-3748\)
2448.r2	2448j2	2448.r	2448j	$2$	$3$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( - 2^{8} \cdot 3^{9} \cdot 17^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$1728$	$0.675154$	$-221184/4913$	$[0, 0, 0, -216, -7668]$	\(y^2=x^3-216x-7668\)
2448.s1	2448e1	2448.s	2448e	$1$	$1$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( - 2^{8} \cdot 3^{11} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$1280$	$0.395303$	$-2249728/4131$	$[0, 0, 0, -156, 1532]$	\(y^2=x^3-156x+1532\)
2448.t1	2448t1	2448.t	2448t	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( 2^{14} \cdot 3^{8} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.4	2B	$1$	$1$		$1$	$1536$	$0.478925$	$1771561/612$	$[0, 0, 0, -363, 1690]$	\(y^2=x^3-363x+1690\)
2448.t2	2448t2	2448.t	2448t	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 17 \)	\( - 2^{13} \cdot 3^{10} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$1$	$1$		$1$	$3072$	$0.825499$	$46268279/46818$	$[0, 0, 0, 1077, 11770]$	\(y^2=x^3+1077x+11770\)