LMFDB - Elliptic curve search results

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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	Manin constant

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Results (28 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
7392.g2	7392m1	7392.g	7392m	$2$	$2$	$ 2^{5} \cdot 3 \cdot 7 \cdot 11 $	$ - 2^{6} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$616$	$12$	$0$	$1$	$1$		$1$	$1280$	$-0.223597$	$4410944/7623$	$0.81189$	$2.26139$	$[0, -1, 0, 14, -32]$	$y^2=x^3-x^2+14x-32$	2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.?	$[ ]$
7392.n2	7392d1	7392.n	7392d	$2$	$2$	$ 2^{5} \cdot 3 \cdot 7 \cdot 11 $	$ - 2^{6} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$616$	$12$	$0$	$1$	$1$		$1$	$1280$	$-0.223597$	$4410944/7623$	$0.81189$	$2.26139$	$[0, 1, 0, 14, 32]$	$y^2=x^3+x^2+14x+32$	2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.?	$[ ]$
14784.a2	14784m1	14784.a	14784m	$2$	$2$	$ 2^{6} \cdot 3 \cdot 7 \cdot 11 $	$ - 2^{12} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$616$	$12$	$0$	$0.825720167$	$1$		$23$	$5120$	$0.122977$	$4410944/7623$	$0.81189$	$2.53129$	$[0, -1, 0, 55, 201]$	$y^2=x^3-x^2+55x+201$	2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.?	$[(8, 33), (-1, 12)]$
14784.bj2	14784bh1	14784.bj	14784bh	$2$	$2$	$ 2^{6} \cdot 3 \cdot 7 \cdot 11 $	$ - 2^{12} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$616$	$12$	$0$	$0.950010937$	$1$		$5$	$5120$	$0.122977$	$4410944/7623$	$0.81189$	$2.53129$	$[0, 1, 0, 55, -201]$	$y^2=x^3+x^2+55x-201$	2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.?	$[(7, 24)]$
22176.b2	22176r1	22176.b	22176r	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 7 \cdot 11 $	$ - 2^{6} \cdot 3^{8} \cdot 7 \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$616$	$12$	$0$	$1$	$1$		$1$	$10240$	$0.325709$	$4410944/7623$	$0.81189$	$2.67184$	$[0, 0, 0, 123, -740]$	$y^2=x^3+123x-740$	2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.?	$[ ]$
22176.c2	22176g1	22176.c	22176g	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 7 \cdot 11 $	$ - 2^{6} \cdot 3^{8} \cdot 7 \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$616$	$12$	$0$	$1.707267630$	$1$		$5$	$10240$	$0.325709$	$4410944/7623$	$0.81189$	$2.67184$	$[0, 0, 0, 123, 740]$	$y^2=x^3+123x+740$	2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.?	$[(4, 36)]$
44352.ey2	44352bb1	44352.ey	44352bb	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11 $	$ - 2^{12} \cdot 3^{8} \cdot 7 \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$616$	$12$	$0$	$1$	$1$		$1$	$40960$	$0.672283$	$4410944/7623$	$0.81189$	$2.88744$	$[0, 0, 0, 492, -5920]$	$y^2=x^3+492x-5920$	2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.?	$[ ]$
44352.fc2	44352ct1	44352.fc	44352ct	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11 $	$ - 2^{12} \cdot 3^{8} \cdot 7 \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$616$	$12$	$0$	$1$	$1$		$1$	$40960$	$0.672283$	$4410944/7623$	$0.81189$	$2.88744$	$[0, 0, 0, 492, 5920]$	$y^2=x^3+492x+5920$	2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.?	$[ ]$
51744.a2	51744n1	51744.a	51744n	$2$	$2$	$ 2^{5} \cdot 3 \cdot 7^{2} \cdot 11 $	$ - 2^{6} \cdot 3^{2} \cdot 7^{7} \cdot 11^{2} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$616$	$12$	$0$	$1.306233271$	$1$		$19$	$61440$	$0.749358$	$4410944/7623$	$0.81189$	$2.93164$	$[0, -1, 0, 670, -9624]$	$y^2=x^3-x^2+670x-9624$	2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.?	$[(68, 588), (19, 98)]$
51744.bk2	51744ct1	51744.bk	51744ct	$2$	$2$	$ 2^{5} \cdot 3 \cdot 7^{2} \cdot 11 $	$ - 2^{6} \cdot 3^{2} \cdot 7^{7} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$616$	$12$	$0$	$1.571057265$	$1$		$5$	$61440$	$0.749358$	$4410944/7623$	$0.81189$	$2.93164$	$[0, 1, 0, 670, 9624]$	$y^2=x^3+x^2+670x+9624$	2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.?	$[(10, 132)]$
81312.y2	81312i1	81312.y	81312i	$2$	$2$	$ 2^{5} \cdot 3 \cdot 7 \cdot 11^{2} $	$ - 2^{6} \cdot 3^{2} \cdot 7 \cdot 11^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$616$	$12$	$0$	$1$	$1$		$1$	$153600$	$0.975350$	$4410944/7623$	$0.81189$	$3.05431$	$[0, -1, 0, 1654, 35928]$	$y^2=x^3-x^2+1654x+35928$	2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.?	$[ ]$
81312.bx2	81312bx1	81312.bx	81312bx	$2$	$2$	$ 2^{5} \cdot 3 \cdot 7 \cdot 11^{2} $	$ - 2^{6} \cdot 3^{2} \cdot 7 \cdot 11^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$616$	$12$	$0$	$5.996615590$	$1$		$1$	$153600$	$0.975350$	$4410944/7623$	$0.81189$	$3.05431$	$[0, 1, 0, 1654, -35928]$	$y^2=x^3+x^2+1654x-35928$	2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.?	$[(9682/7, 972840/7)]$
103488.ej2	103488bj1	103488.ej	103488bj	$2$	$2$	$ 2^{6} \cdot 3 \cdot 7^{2} \cdot 11 $	$ - 2^{12} \cdot 3^{2} \cdot 7^{7} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$616$	$12$	$0$	$1$	$1$		$1$	$245760$	$1.095932$	$4410944/7623$	$0.81189$	$3.11583$	$[0, -1, 0, 2679, 74313]$	$y^2=x^3-x^2+2679x+74313$	2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.?	$[ ]$
103488.ix2	103488em1	103488.ix	103488em	$2$	$2$	$ 2^{6} \cdot 3 \cdot 7^{2} \cdot 11 $	$ - 2^{12} \cdot 3^{2} \cdot 7^{7} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$616$	$12$	$0$	$1$	$1$		$1$	$245760$	$1.095932$	$4410944/7623$	$0.81189$	$3.11583$	$[0, 1, 0, 2679, -74313]$	$y^2=x^3+x^2+2679x-74313$	2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.?	$[ ]$
155232.eo2	155232ei1	155232.eo	155232ei	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{6} \cdot 3^{8} \cdot 7^{7} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$616$	$12$	$0$	$7.021347754$	$1$		$1$	$491520$	$1.298664$	$4410944/7623$	$0.81189$	$3.21367$	$[0, 0, 0, 6027, -253820]$	$y^2=x^3+6027x-253820$	2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.?	$[(2265/7, 120560/7)]$
155232.es2	155232ck1	155232.es	155232ck	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{6} \cdot 3^{8} \cdot 7^{7} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$616$	$12$	$0$	$2.863863690$	$1$		$3$	$491520$	$1.298664$	$4410944/7623$	$0.81189$	$3.21367$	$[0, 0, 0, 6027, 253820]$	$y^2=x^3+6027x+253820$	2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.?	$[(140, 1960)]$
162624.d2	162624gw1	162624.d	162624gw	$2$	$2$	$ 2^{6} \cdot 3 \cdot 7 \cdot 11^{2} $	$ - 2^{12} \cdot 3^{2} \cdot 7 \cdot 11^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$616$	$12$	$0$	$1.768974701$	$1$		$5$	$614400$	$1.321924$	$4410944/7623$	$0.81189$	$3.22447$	$[0, -1, 0, 6615, -294039]$	$y^2=x^3-x^2+6615x-294039$	2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.?	$[(48, 363)]$
162624.eq2	162624eg1	162624.eq	162624eg	$2$	$2$	$ 2^{6} \cdot 3 \cdot 7 \cdot 11^{2} $	$ - 2^{12} \cdot 3^{2} \cdot 7 \cdot 11^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$616$	$12$	$0$	$1.924903567$	$1$		$3$	$614400$	$1.321924$	$4410944/7623$	$0.81189$	$3.22447$	$[0, 1, 0, 6615, 294039]$	$y^2=x^3+x^2+6615x+294039$	2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.?	$[(315, 5808)]$
184800.bs2	184800cq1	184800.bs	184800cq	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{6} \cdot 3^{2} \cdot 5^{6} \cdot 7 \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$616$	$12$	$0$	$1.504919877$	$1$		$5$	$102400$	$0.581122$	$4410944/7623$	$0.81189$	$2.45744$	$[0, -1, 0, 342, 3312]$	$y^2=x^3-x^2+342x+3312$	2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.?	$[(3, 66)]$
184800.eh2	184800fc1	184800.eh	184800fc	$2$	$2$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{6} \cdot 3^{2} \cdot 5^{6} \cdot 7 \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$616$	$12$	$0$	$2.637811988$	$1$		$5$	$102400$	$0.581122$	$4410944/7623$	$0.81189$	$2.45744$	$[0, 1, 0, 342, -3312]$	$y^2=x^3+x^2+342x-3312$	2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.?	$[(9, 24)]$
243936.a2	243936a1	243936.a	243936a	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{6} \cdot 3^{8} \cdot 7 \cdot 11^{8} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$616$	$12$	$0$	$8.778839365$	$1$		$9$	$1228800$	$1.524656$	$4410944/7623$	$0.81189$	$3.31519$	$[0, 0, 0, 14883, -984940]$	$y^2=x^3+14883x-984940$	2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.?	$[(176, 2662), (1463, 56144)]$
243936.c2	243936c1	243936.c	243936c	$2$	$2$	$ 2^{5} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{6} \cdot 3^{8} \cdot 7 \cdot 11^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$616$	$12$	$0$	$1$	$1$		$1$	$1228800$	$1.524656$	$4410944/7623$	$0.81189$	$3.31519$	$[0, 0, 0, 14883, 984940]$	$y^2=x^3+14883x+984940$	2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.?	$[ ]$
310464.m2	310464m1	310464.m	310464m	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{12} \cdot 3^{8} \cdot 7^{7} \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$616$	$12$	$0$	$1.182614647$	$1$		$7$	$1966080$	$1.645237$	$4410944/7623$	$0.81189$	$3.36639$	$[0, 0, 0, 24108, 2030560]$	$y^2=x^3+24108x+2030560$	2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.?	$[(84, 2156)]$
310464.z2	310464z1	310464.z	310464z	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{12} \cdot 3^{8} \cdot 7^{7} \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$616$	$12$	$0$	$1$	$1$		$1$	$1966080$	$1.645237$	$4410944/7623$	$0.81189$	$3.36639$	$[0, 0, 0, 24108, -2030560]$	$y^2=x^3+24108x-2030560$	2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.?	$[ ]$
369600.dc2	369600dc1	369600.dc	369600dc	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{12} \cdot 3^{2} \cdot 5^{6} \cdot 7 \cdot 11^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$616$	$12$	$0$	$1.655426473$	$1$		$7$	$409600$	$0.927695$	$4410944/7623$	$0.81189$	$2.64897$	$[0, -1, 0, 1367, -27863]$	$y^2=x^3-x^2+1367x-27863$	2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.?	$[(61, 528)]$
369600.xl2	369600xl1	369600.xl	369600xl	$2$	$2$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{12} \cdot 3^{2} \cdot 5^{6} \cdot 7 \cdot 11^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$616$	$12$	$0$	$1$	$1$		$1$	$409600$	$0.927695$	$4410944/7623$	$0.81189$	$2.64897$	$[0, 1, 0, 1367, 27863]$	$y^2=x^3+x^2+1367x+27863$	2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.?	$[ ]$
487872.qr2	487872qr1	487872.qr	487872qr	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{12} \cdot 3^{8} \cdot 7 \cdot 11^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$616$	$12$	$0$	$8.877268490$	$1$		$1$	$4915200$	$1.871231$	$4410944/7623$	$0.81189$	$3.45727$	$[0, 0, 0, 59532, -7879520]$	$y^2=x^3+59532x-7879520$	2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.?	$[(57506/5, 13863096/5)]$
487872.qz2	487872qz1	487872.qz	487872qz	$2$	$2$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 11^{2} $	$ - 2^{12} \cdot 3^{8} \cdot 7 \cdot 11^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$616$	$12$	$0$	$1$	$4$	$2$	$1$	$4915200$	$1.871231$	$4410944/7623$	$0.81189$	$3.45727$	$[0, 0, 0, 59532, 7879520]$	$y^2=x^3+59532x+7879520$	2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.?	$[ ]$

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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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