LMFDB - Elliptic curves over $\Q$ of conductor 390

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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 (26 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	Semistable	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
390.a1	390a3	390.a	390a	$4$	$4$	$ 2 \cdot 3 \cdot 5 \cdot 13 $	$ 2 \cdot 3^{2} \cdot 5 \cdot 13^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	8.12.0.7	2B	$520$	$48$	$0$	$1.175373745$	$1$		$6$	$128$	$0.227033$	$12501706118329/2570490$	$0.96978$	$5.05467$	$[1, 1, 0, -483, -4293]$	$y^2+xy=x^3+x^2-483x-4293$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 20.12.0-4.c.1.1, 40.24.0-40.v.1.4, $\ldots$	$[(-13, 7)]$
390.a2	390a2	390.a	390a	$4$	$4$	$ 2 \cdot 3 \cdot 5 \cdot 13 $	$ 2^{2} \cdot 3^{4} \cdot 5^{2} \cdot 13^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	8.12.0.1	2Cs	$520$	$48$	$0$	$0.587686872$	$1$		$16$	$64$	$-0.119541$	$4165509529/1368900$	$0.92273$	$3.71263$	$[1, 1, 0, -33, -63]$	$y^2+xy=x^3+x^2-33x-63$	2.6.0.a.1, 8.12.0-2.a.1.1, 20.12.0-2.a.1.1, 40.24.0-40.a.1.3, 52.12.0-2.a.1.1, $\ldots$	$[(-4, 7)]$
390.a3	390a1	390.a	390a	$4$	$4$	$ 2 \cdot 3 \cdot 5 \cdot 13 $	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	8.12.0.12	2B	$520$	$48$	$0$	$0.293843436$	$1$		$9$	$32$	$-0.466115$	$273359449/9360$	$0.87806$	$3.25609$	$[1, 1, 0, -13, 13]$	$y^2+xy=x^3+x^2-13x+13$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 20.12.0-4.c.1.2, 40.24.0-40.bb.1.9, $\ldots$	$[(1, 1)]$
390.a4	390a4	390.a	390a	$4$	$4$	$ 2 \cdot 3 \cdot 5 \cdot 13 $	$ - 2 \cdot 3^{8} \cdot 5^{4} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	8.12.0.8	2B	$520$	$48$	$0$	$1.175373745$	$1$		$4$	$128$	$0.227033$	$99317171591/106616250$	$1.03579$	$4.24421$	$[1, 1, 0, 97, -297]$	$y^2+xy=x^3+x^2+97x-297$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 40.24.0-40.bb.1.14, 52.12.0-4.c.1.1, $\ldots$	$[(9, 33)]$
390.b1	390f2	390.b	390f	$2$	$2$	$ 2 \cdot 3 \cdot 5 \cdot 13 $	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$		$0$	$160$	$0.251836$	$68523370149961/243360$	$0.97981$	$5.33983$	$[1, 1, 0, -852, -9936]$	$y^2+xy=x^3+x^2-852x-9936$	2.3.0.a.1, 40.6.0.b.1, 156.6.0.?, 1560.12.0.?	$[]$
390.b2	390f1	390.b	390f	$2$	$2$	$ 2 \cdot 3 \cdot 5 \cdot 13 $	$ - 2^{10} \cdot 3 \cdot 5^{2} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$		$1$	$80$	$-0.094738$	$-16022066761/998400$	$0.92192$	$3.95557$	$[1, 1, 0, -52, -176]$	$y^2+xy=x^3+x^2-52x-176$	2.3.0.a.1, 40.6.0.c.1, 78.6.0.?, 1560.12.0.?	$[]$
390.c1	390g4	390.c	390g	$4$	$4$	$ 2 \cdot 3 \cdot 5 \cdot 13 $	$ 2^{5} \cdot 3 \cdot 5^{4} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	8.12.0.8	2B	$120$	$48$	$0$	$1$	$1$		$0$	$1280$	$1.197264$	$71647584155243142409/10140000$	$1.03753$	$7.66295$	$[1, 0, 1, -86529, 9789652]$	$y^2+xy+y=x^3-86529x+9789652$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 12.12.0-4.c.1.1, 24.24.0-24.s.1.4, $\ldots$	$[]$
390.c2	390g3	390.c	390g	$4$	$4$	$ 2 \cdot 3 \cdot 5 \cdot 13 $	$ 2^{5} \cdot 3^{4} \cdot 5 \cdot 13^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	8.12.0.7	2B	$120$	$48$	$0$	$1$	$1$		$0$	$1280$	$1.197264$	$26465989780414729/10571870144160$	$1.02500$	$6.33820$	$[1, 0, 1, -6209, 104276]$	$y^2+xy+y=x^3-6209x+104276$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 20.12.0-4.c.1.1, 24.24.0-24.y.1.8, $\ldots$	$[]$
390.c3	390g2	390.c	390g	$4$	$4$	$ 2 \cdot 3 \cdot 5 \cdot 13 $	$ 2^{10} \cdot 3^{2} \cdot 5^{2} \cdot 13^{4} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	8.12.0.1	2Cs	$120$	$48$	$0$	$1$	$1$		$2$	$640$	$0.850690$	$17496824387403529/6580454400$	$1.00721$	$6.26884$	$[1, 0, 1, -5409, 152596]$	$y^2+xy+y=x^3-5409x+152596$	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.1.2, $\ldots$	$[]$
390.c4	390g1	390.c	390g	$4$	$4$	$ 2 \cdot 3 \cdot 5 \cdot 13 $	$ - 2^{20} \cdot 3 \cdot 5 \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	8.12.0.12	2B	$120$	$48$	$0$	$1$	$1$		$1$	$320$	$0.504116$	$-2656166199049/2658140160$	$0.97703$	$4.96333$	$[1, 0, 1, -289, 3092]$	$y^2+xy+y=x^3-289x+3092$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 12.12.0-4.c.1.2, 20.12.0-4.c.1.2, $\ldots$	$[]$
390.d1	390d4	390.d	390d	$4$	$6$	$ 2 \cdot 3 \cdot 5 \cdot 13 $	$ 2^{15} \cdot 3^{6} \cdot 5 \cdot 13^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$1560$	$96$	$1$	$1$	$1$		$0$	$4320$	$2.005386$	$73474353581350183614361/576510977802240$	$1.05636$	$8.82500$	$[1, 0, 1, -872578, -313799212]$	$y^2+xy+y=x^3-872578x-313799212$	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 40.6.0.b.1, 120.48.0.?, $\ldots$	$[]$
390.d2	390d3	390.d	390d	$4$	$6$	$ 2 \cdot 3 \cdot 5 \cdot 13 $	$ - 2^{30} \cdot 3^{3} \cdot 5^{2} \cdot 13^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$1560$	$96$	$1$	$1$	$1$		$1$	$2160$	$1.658812$	$-16818951115904497561/1592332281446400$	$1.03465$	$7.44543$	$[1, 0, 1, -53378, -5124652]$	$y^2+xy+y=x^3-53378x-5124652$	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 40.6.0.c.1, 78.48.0.?, $\ldots$	$[]$
390.d3	390d2	390.d	390d	$4$	$6$	$ 2 \cdot 3 \cdot 5 \cdot 13 $	$ 2^{5} \cdot 3^{18} \cdot 5^{3} \cdot 13^{2} $	$0$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$1560$	$96$	$1$	$1$	$1$		$4$	$1440$	$1.456079$	$453198971846635561/261896250564000$	$1.11183$	$6.81430$	$[1, 0, 1, -16003, 27998]$	$y^2+xy+y=x^3-16003x+27998$	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 40.6.0.b.1, 120.48.0.?, $\ldots$	$[]$
390.d4	390d1	390.d	390d	$4$	$6$	$ 2 \cdot 3 \cdot 5 \cdot 13 $	$ - 2^{10} \cdot 3^{9} \cdot 5^{6} \cdot 13 $	$0$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$1560$	$96$	$1$	$1$	$1$		$5$	$720$	$1.109507$	$7064514799444439/4094064000000$	$1.10261$	$6.11682$	$[1, 0, 1, 3997, 3998]$	$y^2+xy+y=x^3+3997x+3998$	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 40.6.0.c.1, 78.48.0.?, $\ldots$	$[]$
390.e1	390e2	390.e	390e	$2$	$2$	$ 2 \cdot 3 \cdot 5 \cdot 13 $	$ 2 \cdot 3^{6} \cdot 5 \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$		$0$	$96$	$-0.099044$	$10779215329/1232010$	$1.08676$	$3.87199$	$[1, 1, 1, -46, -127]$	$y^2+xy+y=x^3+x^2-46x-127$	2.3.0.a.1, 40.6.0.b.1, 156.6.0.?, 1560.12.0.?	$[]$
390.e2	390e1	390.e	390e	$2$	$2$	$ 2 \cdot 3 \cdot 5 \cdot 13 $	$ - 2^{2} \cdot 3^{3} \cdot 5^{2} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$1560$	$12$	$0$	$1$	$1$		$1$	$48$	$-0.445617$	$6967871/35100$	$0.89079$	$2.98327$	$[1, 1, 1, 4, -7]$	$y^2+xy+y=x^3+x^2+4x-7$	2.3.0.a.1, 40.6.0.c.1, 78.6.0.?, 1560.12.0.?	$[]$
390.f1	390b5	390.f	390b	$6$	$8$	$ 2 \cdot 3 \cdot 5 \cdot 13 $	$ 2 \cdot 3^{8} \cdot 5 \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	8.24.0.55	2B	$3120$	$192$	$1$	$1$	$4$	$2$	$0$	$512$	$0.764073$	$81025909800741361/11088090$	$1.01361$	$6.52574$	$[1, 1, 1, -9015, -333213]$	$y^2+xy+y=x^3+x^2-9015x-333213$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 40.48.0-40.bp.1.7, 48.48.0-48.f.2.7, $\ldots$	$[]$
390.f2	390b4	390.f	390b	$6$	$8$	$ 2 \cdot 3 \cdot 5 \cdot 13 $	$ 2^{2} \cdot 3 \cdot 5^{8} \cdot 13 $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	8.24.0.45	2B	$3120$	$192$	$1$	$1$	$1$		$2$	$256$	$0.417500$	$66730743078481/60937500$	$0.97968$	$5.33538$	$[1, 1, 1, -845, 9095]$	$y^2+xy+y=x^3+x^2-845x+9095$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 24.48.0-24.by.1.3, 80.48.0.?, $\ldots$	$[]$
390.f3	390b3	390.f	390b	$6$	$8$	$ 2 \cdot 3 \cdot 5 \cdot 13 $	$ 2^{2} \cdot 3^{4} \cdot 5^{2} \cdot 13^{4} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	4.24.0.6	2Cs	$1560$	$192$	$1$	$1$	$1$		$2$	$256$	$0.417500$	$19948814692561/231344100$	$0.97293$	$5.13299$	$[1, 1, 1, -565, -5353]$	$y^2+xy+y=x^3+x^2-565x-5353$	2.6.0.a.1, 4.24.0-4.b.1.1, 24.48.0-24.h.2.5, 40.48.0-40.e.1.10, 104.48.0.?, $\ldots$	$[]$
390.f4	390b6	390.f	390b	$6$	$8$	$ 2 \cdot 3 \cdot 5 \cdot 13 $	$ - 2 \cdot 3^{2} \cdot 5 \cdot 13^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	8.24.0.55	2B	$3120$	$192$	$1$	$1$	$1$		$0$	$512$	$0.764073$	$-168288035761/73415764890$	$1.05371$	$5.44329$	$[1, 1, 1, -115, -13093]$	$y^2+xy+y=x^3+x^2-115x-13093$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 24.48.0-24.by.2.11, 40.48.0-40.bl.1.7, $\ldots$	$[]$
390.f5	390b2	390.f	390b	$6$	$8$	$ 2 \cdot 3 \cdot 5 \cdot 13 $	$ 2^{4} \cdot 3^{2} \cdot 5^{4} \cdot 13^{2} $	$0$	$\Z/2\Z\oplus\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	4.24.0.5	2Cs	$1560$	$192$	$1$	$1$	$1$		$6$	$128$	$0.070926$	$30400540561/15210000$	$0.96238$	$4.04578$	$[1, 1, 1, -65, 47]$	$y^2+xy+y=x^3+x^2-65x+47$	2.6.0.a.1, 4.24.0-4.b.1.3, 24.48.0-24.h.1.5, 40.48.0-40.l.1.10, 104.48.0.?, $\ldots$	$[]$
390.f6	390b1	390.f	390b	$6$	$8$	$ 2 \cdot 3 \cdot 5 \cdot 13 $	$ - 2^{8} \cdot 3 \cdot 5^{2} \cdot 13 $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	8.24.0.45	2B	$3120$	$192$	$1$	$1$	$1$		$3$	$64$	$-0.275648$	$371694959/249600$	$0.92494$	$3.30759$	$[1, 1, 1, 15, 15]$	$y^2+xy+y=x^3+x^2+15x+15$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 48.48.0-48.f.1.7, 78.6.0.?, $\ldots$	$[]$
390.g1	390c4	390.g	390c	$4$	$6$	$ 2 \cdot 3 \cdot 5 \cdot 13 $	$ 2 \cdot 3^{2} \cdot 5^{3} \cdot 13^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$1560$	$96$	$1$	$1$	$1$		$0$	$288$	$0.679823$	$189208196468929/10860320250$	$0.98694$	$5.51007$	$[1, 0, 0, -1196, -15210]$	$y^2+xy=x^3-1196x-15210$	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 40.6.0.b.1, 120.48.0.?, $\ldots$	$[]$
390.g2	390c2	390.g	390c	$4$	$6$	$ 2 \cdot 3 \cdot 5 \cdot 13 $	$ 2^{3} \cdot 3^{6} \cdot 5 \cdot 13^{2} $	$0$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$1560$	$96$	$1$	$1$	$1$		$4$	$96$	$0.130517$	$967068262369/4928040$	$0.95296$	$4.62569$	$[1, 0, 0, -206, 1116]$	$y^2+xy=x^3-206x+1116$	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 40.6.0.b.1, 120.48.0.?, $\ldots$	$[]$
390.g3	390c1	390.g	390c	$4$	$6$	$ 2 \cdot 3 \cdot 5 \cdot 13 $	$ - 2^{6} \cdot 3^{3} \cdot 5^{2} \cdot 13 $	$0$	$\Z/6\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.1	2B, 3B.1.1	$1560$	$96$	$1$	$1$	$1$		$5$	$48$	$-0.216057$	$-24137569/561600$	$1.08140$	$3.47257$	$[1, 0, 0, -6, 36]$	$y^2+xy=x^3-6x+36$	2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 40.6.0.c.1, 78.48.0.?, $\ldots$	$[]$
390.g4	390c3	390.g	390c	$4$	$6$	$ 2 \cdot 3 \cdot 5 \cdot 13 $	$ - 2^{2} \cdot 3 \cdot 5^{6} \cdot 13^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.3.0.1, 3.8.0.2	2B, 3B.1.2	$1560$	$96$	$1$	$1$	$1$		$1$	$144$	$0.333250$	$17394111071/411937500$	$1.08898$	$4.57018$	$[1, 0, 0, 54, -960]$	$y^2+xy=x^3+54x-960$	2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 40.6.0.c.1, 78.48.0.?, $\ldots$	$[]$

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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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