LMFDB - Elliptic curve search results

Refine search

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

		Sort order	Select

Results (34 matches)

Download displayed columns for results to

Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	Sato-Tate	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
2720.c1	2720b1	2720.c	2720b	$1$	$1$	$ 2^{5} \cdot 5 \cdot 17 $	$ - 2^{9} \cdot 5^{5} \cdot 17 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$1$	$1$	$0$	$480$	$0.113687$	$55742968/53125$	$0.84898$	$3.04418$	$[0, -1, 0, 64, 136]$	$y^2=x^3-x^2+64x+136$	680.2.0.?	$[]$
2720.d1	2720e1	2720.d	2720e	$1$	$1$	$ 2^{5} \cdot 5 \cdot 17 $	$ - 2^{9} \cdot 5^{5} \cdot 17 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$1.497324305$	$1$	$4$	$480$	$0.113687$	$55742968/53125$	$0.84898$	$3.04418$	$[0, 1, 0, 64, -136]$	$y^2=x^3+x^2+64x-136$	680.2.0.?	$[(2, 2)]$
5440.j1	5440k1	5440.j	5440k	$1$	$1$	$ 2^{6} \cdot 5 \cdot 17 $	$ - 2^{15} \cdot 5^{5} \cdot 17 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$0.186992389$	$1$	$6$	$1920$	$0.460260$	$55742968/53125$	$0.84898$	$3.28238$	$[0, -1, 0, 255, -1343]$	$y^2=x^3-x^2+255x-1343$	680.2.0.?	$[(9, 40)]$
5440.s1	5440j1	5440.s	5440j	$1$	$1$	$ 2^{6} \cdot 5 \cdot 17 $	$ - 2^{15} \cdot 5^{5} \cdot 17 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$0.248219807$	$1$	$4$	$1920$	$0.460260$	$55742968/53125$	$0.84898$	$3.28238$	$[0, 1, 0, 255, 1343]$	$y^2=x^3+x^2+255x+1343$	680.2.0.?	$[(31, 200)]$
13600.k1	13600a1	13600.k	13600a	$1$	$1$	$ 2^{5} \cdot 5^{2} \cdot 17 $	$ - 2^{9} \cdot 5^{11} \cdot 17 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$1.790992906$	$1$	$2$	$11520$	$0.918406$	$55742968/53125$	$0.84898$	$3.54400$	$[0, -1, 0, 1592, -20188]$	$y^2=x^3-x^2+1592x-20188$	680.2.0.?	$[(32, 250)]$
13600.n1	13600n1	13600.n	13600n	$1$	$1$	$ 2^{5} \cdot 5^{2} \cdot 17 $	$ - 2^{9} \cdot 5^{11} \cdot 17 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$1$	$1$	$0$	$11520$	$0.918406$	$55742968/53125$	$0.84898$	$3.54400$	$[0, 1, 0, 1592, 20188]$	$y^2=x^3+x^2+1592x+20188$	680.2.0.?	$[]$
24480.v1	24480n1	24480.v	24480n	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 17 $	$ - 2^{9} \cdot 3^{6} \cdot 5^{5} \cdot 17 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$0.695371050$	$1$	$4$	$14400$	$0.662993$	$55742968/53125$	$0.84898$	$3.03458$	$[0, 0, 0, 573, 4246]$	$y^2=x^3+573x+4246$	680.2.0.?	$[(-3, 50)]$
24480.be1	24480be1	24480.be	24480be	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 17 $	$ - 2^{9} \cdot 3^{6} \cdot 5^{5} \cdot 17 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$1$	$1$	$0$	$14400$	$0.662993$	$55742968/53125$	$0.84898$	$3.03458$	$[0, 0, 0, 573, -4246]$	$y^2=x^3+573x-4246$	680.2.0.?	$[]$
27200.t1	27200g1	27200.t	27200g	$1$	$1$	$ 2^{6} \cdot 5^{2} \cdot 17 $	$ - 2^{15} \cdot 5^{11} \cdot 17 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$1.077467210$	$1$	$2$	$46080$	$1.264980$	$55742968/53125$	$0.84898$	$3.71072$	$[0, -1, 0, 6367, 155137]$	$y^2=x^3-x^2+6367x+155137$	680.2.0.?	$[(32, 625)]$
27200.ce1	27200d1	27200.ce	27200d	$1$	$1$	$ 2^{6} \cdot 5^{2} \cdot 17 $	$ - 2^{15} \cdot 5^{11} \cdot 17 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$2.485123224$	$1$	$0$	$46080$	$1.264980$	$55742968/53125$	$0.84898$	$3.71072$	$[0, 1, 0, 6367, -155137]$	$y^2=x^3+x^2+6367x-155137$	680.2.0.?	$[(337/3, 10000/3)]$
46240.p1	46240ba1	46240.p	46240ba	$1$	$1$	$ 2^{5} \cdot 5 \cdot 17^{2} $	$ - 2^{9} \cdot 5^{5} \cdot 17^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$1.028286027$	$1$	$4$	$138240$	$1.530294$	$55742968/53125$	$0.84898$	$3.82381$	$[0, -1, 0, 18400, -778748]$	$y^2=x^3-x^2+18400x-778748$	680.2.0.?	$[(584, 14450)]$
46240.u1	46240i1	46240.u	46240i	$1$	$1$	$ 2^{5} \cdot 5 \cdot 17^{2} $	$ - 2^{9} \cdot 5^{5} \cdot 17^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$1$	$1$	$0$	$138240$	$1.530294$	$55742968/53125$	$0.84898$	$3.82381$	$[0, 1, 0, 18400, 778748]$	$y^2=x^3+x^2+18400x+778748$	680.2.0.?	$[]$
48960.s1	48960bo1	48960.s	48960bo	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 17 $	$ - 2^{15} \cdot 3^{6} \cdot 5^{5} \cdot 17 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$1$	$1$	$0$	$57600$	$1.009567$	$55742968/53125$	$0.84898$	$3.22492$	$[0, 0, 0, 2292, 33968]$	$y^2=x^3+2292x+33968$	680.2.0.?	$[]$
48960.cj1	48960bj1	48960.cj	48960bj	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 17 $	$ - 2^{15} \cdot 3^{6} \cdot 5^{5} \cdot 17 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$1$	$1$	$0$	$57600$	$1.009567$	$55742968/53125$	$0.84898$	$3.22492$	$[0, 0, 0, 2292, -33968]$	$y^2=x^3+2292x-33968$	680.2.0.?	$[]$
92480.bm1	92480j1	92480.bm	92480j	$1$	$1$	$ 2^{6} \cdot 5 \cdot 17^{2} $	$ - 2^{15} \cdot 5^{5} \cdot 17^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$1.376549533$	$1$	$4$	$552960$	$1.876867$	$55742968/53125$	$0.84898$	$3.95573$	$[0, -1, 0, 73599, 6156385]$	$y^2=x^3-x^2+73599x+6156385$	680.2.0.?	$[(-11, 2312)]$
92480.cw1	92480f1	92480.cw	92480f	$1$	$1$	$ 2^{6} \cdot 5 \cdot 17^{2} $	$ - 2^{15} \cdot 5^{5} \cdot 17^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$4.237532230$	$1$	$2$	$552960$	$1.876867$	$55742968/53125$	$0.84898$	$3.95573$	$[0, 1, 0, 73599, -6156385]$	$y^2=x^3+x^2+73599x-6156385$	680.2.0.?	$[(115, 1960)]$
122400.bf1	122400bh1	122400.bf	122400bh	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 17 $	$ - 2^{9} \cdot 3^{6} \cdot 5^{11} \cdot 17 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$4.524171648$	$1$	$2$	$345600$	$1.467712$	$55742968/53125$	$0.84898$	$3.44197$	$[0, 0, 0, 14325, -530750]$	$y^2=x^3+14325x-530750$	680.2.0.?	$[(3390, 197500)]$
122400.cw1	122400dp1	122400.cw	122400dp	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 17 $	$ - 2^{9} \cdot 3^{6} \cdot 5^{11} \cdot 17 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$1$	$1$	$0$	$345600$	$1.467712$	$55742968/53125$	$0.84898$	$3.44197$	$[0, 0, 0, 14325, 530750]$	$y^2=x^3+14325x+530750$	680.2.0.?	$[]$
133280.s1	133280j1	133280.s	133280j	$1$	$1$	$ 2^{5} \cdot 5 \cdot 7^{2} \cdot 17 $	$ - 2^{9} \cdot 5^{5} \cdot 7^{6} \cdot 17 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$1.024977852$	$1$	$10$	$172800$	$1.086641$	$55742968/53125$	$0.84898$	$3.02961$	$[0, -1, 0, 3120, 52900]$	$y^2=x^3-x^2+3120x+52900$	680.2.0.?	$[(40, 490), (285, 4900)]$
133280.bq1	133280bz1	133280.bq	133280bz	$1$	$1$	$ 2^{5} \cdot 5 \cdot 7^{2} \cdot 17 $	$ - 2^{9} \cdot 5^{5} \cdot 7^{6} \cdot 17 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$1.702405169$	$1$	$0$	$172800$	$1.086641$	$55742968/53125$	$0.84898$	$3.02961$	$[0, 1, 0, 3120, -52900]$	$y^2=x^3+x^2+3120x-52900$	680.2.0.?	$[(85/2, 1225/2)]$
231200.y1	231200y1	231200.y	231200y	$1$	$1$	$ 2^{5} \cdot 5^{2} \cdot 17^{2} $	$ - 2^{9} \cdot 5^{11} \cdot 17^{7} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$5.145490928$	$1$	$6$	$3317760$	$2.335014$	$55742968/53125$	$0.84898$	$4.10739$	$[0, -1, 0, 459992, 96423512]$	$y^2=x^3-x^2+459992x+96423512$	680.2.0.?	$[(737, 28900), (-43, 8750)]$
231200.by1	231200by1	231200.by	231200by	$1$	$1$	$ 2^{5} \cdot 5^{2} \cdot 17^{2} $	$ - 2^{9} \cdot 5^{11} \cdot 17^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$1.429051491$	$1$	$2$	$3317760$	$2.335014$	$55742968/53125$	$0.84898$	$4.10739$	$[0, 1, 0, 459992, -96423512]$	$y^2=x^3+x^2+459992x-96423512$	680.2.0.?	$[(5043, 361250)]$
244800.fj1	244800fj1	244800.fj	244800fj	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 17 $	$ - 2^{15} \cdot 3^{6} \cdot 5^{11} \cdot 17 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$4.042237426$	$1$	$2$	$1382400$	$1.814285$	$55742968/53125$	$0.84898$	$3.58487$	$[0, 0, 0, 57300, -4246000]$	$y^2=x^3+57300x-4246000$	680.2.0.?	$[(74, 632)]$
244800.oo1	244800oo1	244800.oo	244800oo	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 17 $	$ - 2^{15} \cdot 3^{6} \cdot 5^{11} \cdot 17 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$4.932056475$	$1$	$0$	$1382400$	$1.814285$	$55742968/53125$	$0.84898$	$3.58487$	$[0, 0, 0, 57300, 4246000]$	$y^2=x^3+57300x+4246000$	680.2.0.?	$[(1390/3, 110600/3)]$
266560.bq1	266560bq1	266560.bq	266560bq	$1$	$1$	$ 2^{6} \cdot 5 \cdot 7^{2} \cdot 17 $	$ - 2^{15} \cdot 5^{5} \cdot 7^{6} \cdot 17 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$1$	$1$	$0$	$691200$	$1.433216$	$55742968/53125$	$0.84898$	$3.19441$	$[0, -1, 0, 12479, -435679]$	$y^2=x^3-x^2+12479x-435679$	680.2.0.?	$[]$
266560.fi1	266560fi1	266560.fi	266560fi	$1$	$1$	$ 2^{6} \cdot 5 \cdot 7^{2} \cdot 17 $	$ - 2^{15} \cdot 5^{5} \cdot 7^{6} \cdot 17 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$1$	$1$	$0$	$691200$	$1.433216$	$55742968/53125$	$0.84898$	$3.19441$	$[0, 1, 0, 12479, 435679]$	$y^2=x^3+x^2+12479x+435679$	680.2.0.?	$[]$
329120.i1	329120i1	329120.i	329120i	$1$	$1$	$ 2^{5} \cdot 5 \cdot 11^{2} \cdot 17 $	$ - 2^{9} \cdot 5^{5} \cdot 11^{6} \cdot 17 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$2.551926467$	$1$	$2$	$691200$	$1.312635$	$55742968/53125$	$0.84898$	$3.02750$	$[0, -1, 0, 7704, -211880]$	$y^2=x^3-x^2+7704x-211880$	680.2.0.?	$[(81, 968)]$
329120.w1	329120w1	329120.w	329120w	$1$	$1$	$ 2^{5} \cdot 5 \cdot 11^{2} \cdot 17 $	$ - 2^{9} \cdot 5^{5} \cdot 11^{6} \cdot 17 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$1$	$1$	$0$	$691200$	$1.312635$	$55742968/53125$	$0.84898$	$3.02750$	$[0, 1, 0, 7704, 211880]$	$y^2=x^3+x^2+7704x+211880$	680.2.0.?	$[]$
416160.r1	416160r1	416160.r	416160r	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 17^{2} $	$ - 2^{9} \cdot 3^{6} \cdot 5^{5} \cdot 17^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$12.52153478$	$1$	$0$	$4147200$	$2.079601$	$55742968/53125$	$0.84898$	$3.68392$	$[0, 0, 0, 165597, -20860598]$	$y^2=x^3+165597x-20860598$	680.2.0.?	$[(5881014/115, 18041140588/115)]$
416160.bo1	416160bo1	416160.bo	416160bo	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 17^{2} $	$ - 2^{9} \cdot 3^{6} \cdot 5^{5} \cdot 17^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$1$	$1$	$0$	$4147200$	$2.079601$	$55742968/53125$	$0.84898$	$3.68392$	$[0, 0, 0, 165597, 20860598]$	$y^2=x^3+165597x+20860598$	680.2.0.?	$[]$
459680.k1	459680k1	459680.k	459680k	$1$	$1$	$ 2^{5} \cdot 5 \cdot 13^{2} \cdot 17 $	$ - 2^{9} \cdot 5^{5} \cdot 13^{6} \cdot 17 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$1$	$1$	$0$	$984960$	$1.396162$	$55742968/53125$	$0.84898$	$3.02680$	$[0, -1, 0, 10760, 341912]$	$y^2=x^3-x^2+10760x+341912$	680.2.0.?	$[]$
459680.t1	459680t1	459680.t	459680t	$1$	$1$	$ 2^{5} \cdot 5 \cdot 13^{2} \cdot 17 $	$ - 2^{9} \cdot 5^{5} \cdot 13^{6} \cdot 17 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$3.917047875$	$1$	$2$	$984960$	$1.396162$	$55742968/53125$	$0.84898$	$3.02680$	$[0, 1, 0, 10760, -341912]$	$y^2=x^3+x^2+10760x-341912$	680.2.0.?	$[(306, 5630)]$
462400.cw1	462400cw1	462400.cw	462400cw	$1$	$1$	$ 2^{6} \cdot 5^{2} \cdot 17^{2} $	$ - 2^{15} \cdot 5^{11} \cdot 17^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$4.099040169$	$1$	$2$	$13271040$	$2.681587$	$55742968/53125$	$0.84898$	$4.20796$	$[0, -1, 0, 1839967, -773228063]$	$y^2=x^3-x^2+1839967x-773228063$	680.2.0.?	$[(1128, 52309)]$
462400.gq1	462400gq1	462400.gq	462400gq	$1$	$1$	$ 2^{6} \cdot 5^{2} \cdot 17^{2} $	$ - 2^{15} \cdot 5^{11} \cdot 17^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$680$	$2$	$0$	$7.015312289$	$1$	$0$	$13271040$	$2.681587$	$55742968/53125$	$0.84898$	$4.20796$	$[0, 1, 0, 1839967, 773228063]$	$y^2=x^3+x^2+1839967x+773228063$	680.2.0.?	$[(69901/3, 18776908/3)]$

Download displayed columns for results to

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (34 matches)

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

Learn more

Refine search Advanced search options

Results (34 matches)

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

Refine search