LMFDB - Elliptic curves over $\Q$ of conductor 240

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 (26 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	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
240.a1	240c4	240.a	240c	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5 $	$ 2^{11} \cdot 3^{4} \cdot 5 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.8	2B	$120$	$48$	$0$	$0.222905284$	$1$		$11$	$64$	$0.069403$	$546718898/405$	$0.99169$	$5.06220$	$[0, -1, 0, -216, 1296]$	$y^2=x^3-x^2-216x+1296$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 20.12.0-4.c.1.2, 24.24.0-24.y.1.16, $\ldots$	$[(8, 4)]$
240.a2	240c3	240.a	240c	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5 $	$ 2^{11} \cdot 3 \cdot 5^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.7	2B	$120$	$48$	$0$	$0.891621139$	$1$		$7$	$64$	$0.069403$	$136835858/1875$	$0.97925$	$4.80946$	$[0, -1, 0, -136, -560]$	$y^2=x^3-x^2-136x-560$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 12.12.0-4.c.1.2, 24.24.0-24.s.1.3, $\ldots$	$[(-6, 2)]$
240.a3	240c2	240.a	240c	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5 $	$ 2^{10} \cdot 3^{2} \cdot 5^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$120$	$48$	$0$	$0.445810569$	$1$		$17$	$32$	$-0.277171$	$470596/225$	$1.13245$	$3.64797$	$[0, -1, 0, -16, 16]$	$y^2=x^3-x^2-16x+16$	2.6.0.a.1, 8.12.0-2.a.1.1, 12.12.0-2.a.1.1, 20.12.0-2.a.1.1, 24.24.0-24.b.1.3, $\ldots$	$[(0, 4)]$
240.a4	240c1	240.a	240c	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5 $	$ - 2^{8} \cdot 3 \cdot 5 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.12	2B	$120$	$48$	$0$	$0.891621139$	$1$		$5$	$16$	$-0.623744$	$21296/15$	$0.85611$	$2.83023$	$[0, -1, 0, 4, 0]$	$y^2=x^3-x^2+4x$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 12.12.0-4.c.1.1, 20.12.0-4.c.1.1, $\ldots$	$[(1, 2)]$
240.b1	240b8	240.b	240b	$8$	$12$	$ 2^{4} \cdot 3 \cdot 5 $	$ 2^{15} \cdot 3^{4} \cdot 5^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.12.0.8, 3.4.0.1	2B, 3B	$120$	$384$	$5$	$1$	$1$		$1$	$576$	$1.257313$	$16778985534208729/81000$	$1.08181$	$8.33419$	$[0, -1, 0, -85336, 9623536]$	$y^2=x^3-x^2-85336x+9623536$	2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 8.12.0-4.c.1.4, $\ldots$	$[]$
240.b2	240b7	240.b	240b	$8$	$12$	$ 2^{4} \cdot 3 \cdot 5 $	$ 2^{15} \cdot 3 \cdot 5^{12} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.12.0.7, 3.4.0.1	2B, 3B	$120$	$384$	$5$	$1$	$1$		$1$	$576$	$1.257313$	$10316097499609/5859375000$	$1.13600$	$6.98504$	$[0, -1, 0, -7256, 34800]$	$y^2=x^3-x^2-7256x+34800$	2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 8.12.0-4.c.1.3, $\ldots$	$[]$
240.b3	240b6	240.b	240b	$8$	$12$	$ 2^{4} \cdot 3 \cdot 5 $	$ 2^{18} \cdot 3^{2} \cdot 5^{6} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.12.0.1, 3.4.0.1	2Cs, 3B	$120$	$384$	$5$	$1$	$1$		$3$	$288$	$0.910740$	$4102915888729/9000000$	$1.05221$	$6.81681$	$[0, -1, 0, -5336, 151536]$	$y^2=x^3-x^2-5336x+151536$	2.6.0.a.1, 3.4.0.a.1, 6.24.0.a.1, 8.12.0-2.a.1.1, 12.96.0-12.a.1.3, $\ldots$	$[]$
240.b4	240b4	240.b	240b	$8$	$12$	$ 2^{4} \cdot 3 \cdot 5 $	$ 2^{13} \cdot 3^{3} \cdot 5^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.12.0.7, 3.4.0.1	2B, 3B	$120$	$384$	$5$	$1$	$1$		$1$	$192$	$0.708007$	$2656166199049/33750$	$1.05017$	$6.73748$	$[0, -1, 0, -4616, -119184]$	$y^2=x^3-x^2-4616x-119184$	2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 8.12.0-4.c.1.3, $\ldots$	$[]$
240.b5	240b5	240.b	240b	$8$	$12$	$ 2^{4} \cdot 3 \cdot 5 $	$ 2^{13} \cdot 3^{12} \cdot 5 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.12.0.8, 3.4.0.1	2B, 3B	$120$	$384$	$5$	$1$	$1$		$1$	$192$	$0.708007$	$35578826569/5314410$	$1.03393$	$5.95054$	$[0, -1, 0, -1096, 12400]$	$y^2=x^3-x^2-1096x+12400$	2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 8.12.0-4.c.1.4, $\ldots$	$[]$
240.b6	240b2	240.b	240b	$8$	$12$	$ 2^{4} \cdot 3 \cdot 5 $	$ 2^{14} \cdot 3^{6} \cdot 5^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.12.0.1, 3.4.0.1	2Cs, 3B	$120$	$384$	$5$	$1$	$1$		$3$	$96$	$0.361434$	$702595369/72900$	$1.00457$	$5.23444$	$[0, -1, 0, -296, -1680]$	$y^2=x^3-x^2-296x-1680$	2.6.0.a.1, 3.4.0.a.1, 6.24.0.a.1, 8.12.0-2.a.1.1, 12.96.0-12.a.2.7, $\ldots$	$[]$
240.b7	240b3	240.b	240b	$8$	$12$	$ 2^{4} \cdot 3 \cdot 5 $	$ - 2^{24} \cdot 3 \cdot 5^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.12.0.12, 3.4.0.1	2B, 3B	$120$	$384$	$5$	$1$	$1$		$1$	$144$	$0.564166$	$-273359449/1536000$	$1.04920$	$5.49483$	$[0, -1, 0, -216, 4080]$	$y^2=x^3-x^2-216x+4080$	2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 8.12.0-4.c.1.2, $\ldots$	$[]$
240.b8	240b1	240.b	240b	$8$	$12$	$ 2^{4} \cdot 3 \cdot 5 $	$ - 2^{16} \cdot 3^{3} \cdot 5 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.12.0.12, 3.4.0.1	2B, 3B	$120$	$384$	$5$	$1$	$1$		$1$	$48$	$0.014860$	$357911/2160$	$0.99689$	$4.26037$	$[0, -1, 0, 24, -144]$	$y^2=x^3-x^2+24x-144$	2.3.0.a.1, 3.4.0.a.1, 4.6.0.c.1, 6.12.0.a.1, 8.12.0-4.c.1.2, $\ldots$	$[]$
240.c1	240a5	240.c	240a	$6$	$8$	$ 2^{4} \cdot 3 \cdot 5 $	$ 2^{11} \cdot 3 \cdot 5^{2} $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.31	2B	$240$	$192$	$1$	$1$	$1$		$3$	$128$	$0.479999$	$1770025017602/75$	$1.12837$	$6.53694$	$[0, -1, 0, -3200, 70752]$	$y^2=x^3-x^2-3200x+70752$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 16.48.0-16.f.1.4, 24.48.0-24.bj.1.5, $\ldots$	$[]$
240.c2	240a3	240.c	240a	$6$	$8$	$ 2^{4} \cdot 3 \cdot 5 $	$ 2^{10} \cdot 3^{2} \cdot 5^{4} $	$0$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.27	2Cs	$120$	$192$	$1$	$1$	$1$		$7$	$64$	$0.133425$	$868327204/5625$	$1.10029$	$5.02014$	$[0, -1, 0, -200, 1152]$	$y^2=x^3-x^2-200x+1152$	2.6.0.a.1, 4.24.0-4.b.1.3, 8.48.0-8.d.1.10, 24.96.0-24.k.1.2, 40.96.0-40.v.1.7, $\ldots$	$[]$
240.c3	240a6	240.c	240a	$6$	$8$	$ 2^{4} \cdot 3 \cdot 5 $	$ - 2^{11} \cdot 3 \cdot 5^{8} $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.162	2B	$240$	$192$	$1$	$1$	$1$		$3$	$128$	$0.479999$	$-27995042/1171875$	$1.07729$	$5.30361$	$[0, -1, 0, -80, 2400]$	$y^2=x^3-x^2-80x+2400$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.ba.1.2, 24.96.0-24.bo.1.4, 80.96.0.?, $\ldots$	$[]$
240.c4	240a2	240.c	240a	$6$	$8$	$ 2^{4} \cdot 3 \cdot 5 $	$ 2^{8} \cdot 3^{4} \cdot 5^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.33	2Cs	$120$	$192$	$1$	$1$	$1$		$3$	$32$	$-0.213148$	$3631696/2025$	$1.02576$	$3.76788$	$[0, -1, 0, -20, 0]$	$y^2=x^3-x^2-20x$	2.6.0.a.1, 4.24.0-4.b.1.1, 8.48.0-8.d.2.2, 20.48.0-20.c.1.2, 24.96.0-24.p.2.4, $\ldots$	$[]$
240.c5	240a1	240.c	240a	$6$	$8$	$ 2^{4} \cdot 3 \cdot 5 $	$ 2^{4} \cdot 3^{2} \cdot 5 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.47	2B	$240$	$192$	$1$	$1$	$1$		$1$	$16$	$-0.559722$	$24918016/45$	$0.99237$	$3.61339$	$[0, -1, 0, -15, -18]$	$y^2=x^3-x^2-15x-18$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 10.6.0.a.1, 16.48.0-16.f.2.11, $\ldots$	$[]$
240.c6	240a4	240.c	240a	$6$	$8$	$ 2^{4} \cdot 3 \cdot 5 $	$ - 2^{10} \cdot 3^{8} \cdot 5 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.178	2B	$240$	$192$	$1$	$1$	$1$		$1$	$64$	$0.133425$	$54607676/32805$	$1.06524$	$4.51538$	$[0, -1, 0, 80, -80]$	$y^2=x^3-x^2+80x-80$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.ba.2.6, 20.24.0-20.h.1.1, 40.96.0-40.bm.2.4, $\ldots$	$[]$
240.d1	240d7	240.d	240d	$8$	$16$	$ 2^{4} \cdot 3 \cdot 5 $	$ 2^{12} \cdot 3^{4} \cdot 5 $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.96.0.104	2B	$480$	$768$	$13$	$1$	$1$		$3$	$256$	$0.984016$	$1114544804970241/405$	$1.07354$	$7.83941$	$[0, 1, 0, -34560, 2461428]$	$y^2=x^3+x^2-34560x+2461428$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.bb.2.4, 10.6.0.a.1, 16.96.0-16.x.2.3, $\ldots$	$[]$
240.d2	240d5	240.d	240d	$8$	$16$	$ 2^{4} \cdot 3 \cdot 5 $	$ 2^{12} \cdot 3^{8} \cdot 5^{2} $	$0$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.96.0.41	2Cs	$240$	$768$	$13$	$1$	$1$		$7$	$128$	$0.637444$	$272223782641/164025$	$1.03897$	$6.32183$	$[0, 1, 0, -2160, 37908]$	$y^2=x^3+x^2-2160x+37908$	2.6.0.a.1, 4.24.0-4.b.1.3, 8.96.0-8.k.1.2, 20.48.0-20.c.1.1, 40.192.1-40.cc.2.1, $\ldots$	$[]$
240.d3	240d8	240.d	240d	$8$	$16$	$ 2^{4} \cdot 3 \cdot 5 $	$ - 2^{12} \cdot 3^{16} \cdot 5 $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.96.0.101	2B	$480$	$768$	$13$	$1$	$1$		$3$	$256$	$0.984016$	$-147281603041/215233605$	$1.05949$	$6.43964$	$[0, 1, 0, -1760, 52788]$	$y^2=x^3+x^2-1760x+52788$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.ba.2.2, 16.96.0-16.u.2.4, 20.24.0-20.h.1.2, $\ldots$	$[]$
240.d4	240d3	240.d	240d	$8$	$16$	$ 2^{4} \cdot 3 \cdot 5 $	$ 2^{12} \cdot 3 \cdot 5 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	32.96.0.13	2B	$480$	$768$	$13$	$1$	$4$	$2$	$1$	$64$	$0.290870$	$56667352321/15$	$1.03019$	$6.03547$	$[0, 1, 0, -1280, -18060]$	$y^2=x^3+x^2-1280x-18060$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 16.48.0-16.g.1.6, 24.48.0-24.by.2.11, $\ldots$	$[]$
240.d5	240d4	240.d	240d	$8$	$16$	$ 2^{4} \cdot 3 \cdot 5 $	$ 2^{12} \cdot 3^{4} \cdot 5^{4} $	$0$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.96.0.1	2Cs	$240$	$768$	$13$	$1$	$1$		$7$	$64$	$0.290870$	$111284641/50625$	$1.02534$	$4.89822$	$[0, 1, 0, -160, 308]$	$y^2=x^3+x^2-160x+308$	2.6.0.a.1, 4.48.0-4.b.1.1, 8.96.0-8.b.2.2, 24.192.1-24.n.1.6, 40.192.1-40.s.1.2, $\ldots$	$[]$
240.d6	240d2	240.d	240d	$8$	$16$	$ 2^{4} \cdot 3 \cdot 5 $	$ 2^{12} \cdot 3^{2} \cdot 5^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.96.0.9	2Cs	$240$	$768$	$13$	$1$	$1$		$3$	$32$	$-0.055704$	$13997521/225$	$0.96230$	$4.51994$	$[0, 1, 0, -80, -300]$	$y^2=x^3+x^2-80x-300$	2.6.0.a.1, 4.24.0-4.b.1.1, 8.48.0-8.i.1.2, 16.96.0-16.d.2.2, 24.96.0-24.bb.2.1, $\ldots$	$[]$
240.d7	240d1	240.d	240d	$8$	$16$	$ 2^{4} \cdot 3 \cdot 5 $	$ - 2^{12} \cdot 3 \cdot 5 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	32.96.0.13	2B	$480$	$768$	$13$	$1$	$1$		$1$	$16$	$-0.402277$	$-1/15$	$1.19808$	$3.37197$	$[0, 1, 0, 0, -12]$	$y^2=x^3+x^2-12$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 16.48.0-16.g.1.6, 24.48.0-24.bz.1.11, $\ldots$	$[]$
240.d8	240d6	240.d	240d	$8$	$16$	$ 2^{4} \cdot 3 \cdot 5 $	$ - 2^{12} \cdot 3^{2} \cdot 5^{8} $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.96.0.101	2B	$480$	$768$	$13$	$1$	$1$		$3$	$128$	$0.637444$	$4733169839/3515625$	$1.05585$	$5.58249$	$[0, 1, 0, 560, 2900]$	$y^2=x^3+x^2+560x+2900$	2.3.0.a.1, 4.24.0-4.d.1.1, 8.96.0-8.n.2.2, 24.192.1-24.cv.2.5, 80.192.1.?, $\ldots$	$[]$

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 (26 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 (26 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