LMFDB - Elliptic curves over $\Q$ of conductor 2601

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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 (20 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	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
2601.a1	2601l2	2601.a	2601l	$2$	$5$	$ 3^{2} \cdot 17^{2} $	$ - 3^{11} \cdot 17^{3} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$5$	5.6.0.1	5B	$510$	$48$	$1$	$0.160897783$	$1$		$24$	$3840$	$0.842180$	$-13549359104/243$	$1.07715$	$4.88589$	$[0, 0, 1, -7599, 254970]$	$y^2+y=x^3-7599x+254970$	5.6.0.a.1, 30.12.0.a.1, 85.12.0.?, 102.2.0.?, 170.24.0.?, $\ldots$	$[(47, 40), (-34, 688)]$
2601.a2	2601l1	2601.a	2601l	$2$	$5$	$ 3^{2} \cdot 17^{2} $	$ - 3^{7} \cdot 17^{3} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$5$	5.6.0.1	5B	$510$	$48$	$1$	$0.160897783$	$1$		$26$	$768$	$0.037462$	$4096/3$	$0.95016$	$2.97687$	$[0, 0, 1, 51, 72]$	$y^2+y=x^3+51x+72$	5.6.0.a.1, 30.12.0.a.2, 85.12.0.?, 102.2.0.?, 170.24.0.?, $\ldots$	$[(17, 76), (-1, 4)]$
2601.b1	2601d1	2601.b	2601d	$1$	$1$	$ 3^{2} \cdot 17^{2} $	$ - 3^{3} \cdot 17^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$					$102$	$2$	$0$	$0.196951747$	$1$		$6$	$2304$	$0.656379$	$-110592/17$	$0.95016$	$4.08770$	$[0, 0, 1, -867, 11054]$	$y^2+y=x^3-867x+11054$	102.2.0.?	$[(-17, 144)]$
2601.c1	2601k2	2601.c	2601k	$2$	$5$	$ 3^{2} \cdot 17^{2} $	$ - 3^{11} \cdot 17^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$5$	5.6.0.1	5B	$510$	$48$	$1$	$1$	$1$		$0$	$65280$	$2.258789$	$-13549359104/243$	$1.07715$	$7.04765$	$[0, 0, 1, -2196111, 1252668838]$	$y^2+y=x^3-2196111x+1252668838$	5.6.0.a.1, 30.12.0.a.1, 85.12.0.?, 102.2.0.?, 170.24.0.?, $\ldots$	$[]$
2601.c2	2601k1	2601.c	2601k	$2$	$5$	$ 3^{2} \cdot 17^{2} $	$ - 3^{7} \cdot 17^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$5$	5.6.0.1	5B	$510$	$48$	$1$	$1$	$1$		$0$	$13056$	$1.454069$	$4096/3$	$0.95016$	$5.13863$	$[0, 0, 1, 14739, 354964]$	$y^2+y=x^3+14739x+354964$	5.6.0.a.1, 30.12.0.a.2, 85.12.0.?, 102.2.0.?, 170.24.0.?, $\ldots$	$[]$
2601.d1	2601f1	2601.d	2601f	$1$	$1$	$ 3^{2} \cdot 17^{2} $	$ - 3^{9} \cdot 17^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓				$6$	$6$	$0$	$1$	$1$		$0$	$7344$	$1.401564$	$-459$	$0.95016$	$5.11766$	$[1, -1, 1, -8291, 636310]$	$y^2+xy+y=x^3-x^2-8291x+636310$	6.6.0.b.1	$[]$
2601.e1	2601b1	2601.e	2601b	$1$	$1$	$ 3^{2} \cdot 17^{2} $	$ - 3^{9} \cdot 17^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓				$6$	$6$	$0$	$0.519407854$	$1$		$4$	$432$	$-0.015044$	$-459$	$0.95016$	$2.95591$	$[1, -1, 1, -29, 136]$	$y^2+xy+y=x^3-x^2-29x+136$	6.6.0.b.1	$[(-2, 14)]$
2601.f1	2601g2	2601.f	2601g	$2$	$3$	$ 3^{2} \cdot 17^{2} $	$ - 3^{7} \cdot 17^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$3$	3.4.0.1	3B	$102$	$16$	$0$	$1$	$1$		$0$	$13824$	$1.706690$	$-23100424192/14739$	$1.03897$	$6.03475$	$[0, 0, 1, -154326, 23347804]$	$y^2+y=x^3-154326x+23347804$	3.4.0.a.1, 6.8.0-3.a.1.2, 51.8.0-3.a.1.2, 102.16.0.?	$[]$
2601.f2	2601g1	2601.f	2601g	$2$	$3$	$ 3^{2} \cdot 17^{2} $	$ - 3^{9} \cdot 17^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$3$	3.4.0.1	3B	$102$	$16$	$0$	$1$	$1$		$0$	$4608$	$1.157383$	$32768/459$	$1.01165$	$4.72205$	$[0, 0, 1, 1734, 133879]$	$y^2+y=x^3+1734x+133879$	3.4.0.a.1, 6.8.0-3.a.1.1, 51.8.0-3.a.1.1, 102.16.0.?	$[]$
2601.g1	2601j3	2601.g	2601j	$4$	$4$	$ 3^{2} \cdot 17^{2} $	$ 3^{6} \cdot 17^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	32.48.0.12	2B	$3264$	$1536$	$53$	$1$	$1$		$0$	$9216$	$1.589277$	$82483294977/17$	$1.03131$	$6.19646$	$[1, -1, 0, -235878, 44152991]$	$y^2+xy=x^3-x^2-235878x+44152991$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.o.1, 12.12.0-4.c.1.1, 16.24.0.j.1, $\ldots$	$[]$
2601.g2	2601j2	2601.g	2601j	$4$	$4$	$ 3^{2} \cdot 17^{2} $	$ 3^{6} \cdot 17^{8} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	16.48.0.20	2Cs	$1632$	$1536$	$53$	$1$	$1$		$2$	$4608$	$1.242702$	$20346417/289$	$1.02963$	$5.14003$	$[1, -1, 0, -14793, 687680]$	$y^2+xy=x^3-x^2-14793x+687680$	2.6.0.a.1, 4.12.0.a.1, 8.24.0.f.1, 12.24.0-4.a.1.2, 16.48.0.c.2, $\ldots$	$[]$
2601.g3	2601j1	2601.g	2601j	$4$	$4$	$ 3^{2} \cdot 17^{2} $	$ 3^{6} \cdot 17^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	32.48.0.12	2B	$3264$	$1536$	$53$	$1$	$1$		$1$	$2304$	$0.896130$	$35937/17$	$1.02432$	$4.33393$	$[1, -1, 0, -1788, -11989]$	$y^2+xy=x^3-x^2-1788x-11989$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.o.1, 12.12.0-4.c.1.2, 16.24.0.j.1, $\ldots$	$[]$
2601.g4	2601j4	2601.g	2601j	$4$	$4$	$ 3^{2} \cdot 17^{2} $	$ - 3^{6} \cdot 17^{10} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	16.48.0.76	2B	$3264$	$1536$	$53$	$1$	$1$		$0$	$9216$	$1.589277$	$-35937/83521$	$1.18071$	$5.38920$	$[1, -1, 0, -1788, 1845125]$	$y^2+xy=x^3-x^2-1788x+1845125$	2.3.0.a.1, 4.12.0.d.1, 8.24.0.t.1, 16.48.0.m.2, 24.48.0-8.t.1.3, $\ldots$	$[]$
2601.h1	2601a1	2601.h	2601a	$1$	$1$	$ 3^{2} \cdot 17^{2} $	$ - 3^{3} \cdot 17^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓				$6$	$6$	$0$	$1.058379456$	$1$		$2$	$144$	$-0.564350$	$-459$	$0.95016$	$2.11766$	$[1, -1, 0, -3, -4]$	$y^2+xy=x^3-x^2-3x-4$	6.6.0.b.1	$[(4, 4)]$
2601.i1	2601i1	2601.i	2601i	$2$	$2$	$ 3^{2} \cdot 17^{2} $	$ 3^{10} \cdot 17^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.84	2B	$816$	$192$	$5$	$1$	$1$		$1$	$768$	$0.329570$	$274625/81$	$0.94244$	$3.51166$	$[1, -1, 0, -207, -752]$	$y^2+xy=x^3-x^2-207x-752$	2.3.0.a.1, 4.12.0.f.1, 8.24.0.bh.1, 34.6.0.a.1, 48.48.1.gv.1, $\ldots$	$[]$
2601.i2	2601i2	2601.i	2601i	$2$	$2$	$ 3^{2} \cdot 17^{2} $	$ - 3^{14} \cdot 17^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.127	2B	$816$	$192$	$5$	$1$	$1$		$0$	$1536$	$0.676144$	$5359375/6561$	$1.11521$	$3.90339$	$[1, -1, 0, 558, -5495]$	$y^2+xy=x^3-x^2+558x-5495$	2.3.0.a.1, 4.6.0.e.1, 8.24.0.bj.1, 48.48.1.gx.1, 68.12.0.l.1, $\ldots$	$[]$
2601.j1	2601h1	2601.j	2601h	$2$	$2$	$ 3^{2} \cdot 17^{2} $	$ 3^{10} \cdot 17^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.84	2B	$816$	$192$	$5$	$1$	$9$	$3$	$1$	$13056$	$1.746176$	$274625/81$	$0.94244$	$5.67341$	$[1, -1, 0, -59877, -3934008]$	$y^2+xy=x^3-x^2-59877x-3934008$	2.3.0.a.1, 4.12.0.f.1, 8.24.0.bh.1, 34.6.0.a.1, 48.48.1.gv.1, $\ldots$	$[]$
2601.j2	2601h2	2601.j	2601h	$2$	$2$	$ 3^{2} \cdot 17^{2} $	$ - 3^{14} \cdot 17^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.24.0.127	2B	$816$	$192$	$5$	$1$	$9$	$3$	$0$	$26112$	$2.092751$	$5359375/6561$	$1.11521$	$6.06515$	$[1, -1, 0, 161208, -26352027]$	$y^2+xy=x^3-x^2+161208x-26352027$	2.3.0.a.1, 4.6.0.e.1, 8.24.0.bj.1, 48.48.1.gx.1, 68.12.0.l.1, $\ldots$	$[]$
2601.k1	2601e1	2601.k	2601e	$1$	$1$	$ 3^{2} \cdot 17^{2} $	$ - 3^{3} \cdot 17^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓				$6$	$6$	$0$	$1$	$1$		$0$	$2448$	$0.852257$	$-459$	$0.95016$	$4.27942$	$[1, -1, 0, -921, -23260]$	$y^2+xy=x^3-x^2-921x-23260$	6.6.0.b.1	$[]$
2601.l1	2601c1	2601.l	2601c	$1$	$1$	$ 3^{2} \cdot 17^{2} $	$ - 3^{9} \cdot 17^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$					$102$	$2$	$0$	$5.674412284$	$1$		$0$	$6912$	$1.205685$	$-110592/17$	$0.95016$	$4.92595$	$[0, 0, 1, -7803, -298465]$	$y^2+y=x^3-7803x-298465$	102.2.0.?	$[(1305/2, 45167/2)]$

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Elliptic curves over $\Q$
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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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