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The results below are complete, since the LMFDB contains all elliptic curves with conductor at most 500000

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Results (1-50 of 61 matches)

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Label Class Conductor Rank Torsion CM Regulator Weierstrass coefficients Weierstrass equation mod-$m$ images MW-generators
6370.a1 6370.a \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $2$ $\Z/3\Z$ $0.520529683$ $[1, 0, 1, -369, 3476]$ \(y^2+xy+y=x^3-369x+3476\) 3.8.0-3.a.1.2, 52.2.0.a.1, 156.16.0.? $[(-17, 78), (11, 22)]$
6370.a2 6370.a \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $2$ $\mathsf{trivial}$ $0.520529683$ $[1, 0, 1, 2816, -36018]$ \(y^2+xy+y=x^3+2816x-36018\) 3.8.0-3.a.1.1, 52.2.0.a.1, 156.16.0.? $[(46, 414), (25, 211)]$
6370.b1 6370.b \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $0$ $\mathsf{trivial}$ $1$ $[1, 1, 0, -2474656678, 50249707696532]$ \(y^2+xy=x^3+x^2-2474656678x+50249707696532\) 3.4.0.a.1, 9.12.0.a.1, 21.8.0-3.a.1.2, 63.24.0-9.a.1.2, 117.36.0.?, $\ldots$ $[ ]$
6370.b2 6370.b \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $0$ $\mathsf{trivial}$ $1$ $[1, 1, 0, -28343928, -62991234368]$ \(y^2+xy=x^3+x^2-28343928x-62991234368\) 3.4.0.a.1, 9.12.0.a.1, 21.8.0-3.a.1.1, 63.24.0-9.a.1.1, 117.36.0.?, $\ldots$ $[ ]$
6370.b3 6370.b \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $0$ $\mathsf{trivial}$ $1$ $[1, 1, 0, 174546697, 57840468757]$ \(y^2+xy=x^3+x^2+174546697x+57840468757\) 3.12.0.a.1, 21.24.0-3.a.1.1, 117.36.0.?, 312.24.0.?, 728.2.0.?, $\ldots$ $[ ]$
6370.c1 6370.c \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $1$ $\mathsf{trivial}$ $0.194372334$ $[1, 1, 0, -2867, 392869]$ \(y^2+xy=x^3+x^2-2867x+392869\) 3.4.0.a.1, 21.8.0-3.a.1.2, 312.8.0.?, 728.2.0.?, 2184.16.0.? $[(83, 816)]$
6370.c2 6370.c \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $1$ $\mathsf{trivial}$ $0.583117002$ $[1, 1, 0, 318, -14174]$ \(y^2+xy=x^3+x^2+318x-14174\) 3.4.0.a.1, 21.8.0-3.a.1.1, 312.8.0.?, 728.2.0.?, 2184.16.0.? $[(27, 109)]$
6370.d1 6370.d \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $1$ $\Z/2\Z$ $1.156562637$ $[1, -1, 0, -1430, 18976]$ \(y^2+xy=x^3-x^2-1430x+18976\) 2.3.0.a.1, 56.6.0.c.1, 130.6.0.?, 3640.12.0.? $[(30, 34)]$
6370.d2 6370.d \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $1$ $\Z/2\Z$ $2.313125274$ $[1, -1, 0, 2000, 93750]$ \(y^2+xy=x^3-x^2+2000x+93750\) 2.3.0.a.1, 56.6.0.b.1, 260.6.0.?, 3640.12.0.? $[(-19, 230)]$
6370.e1 6370.e \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $1$ $\Z/2\Z$ $0.765022911$ $[1, -1, 0, -65, -169]$ \(y^2+xy=x^3-x^2-65x-169\) 2.3.0.a.1, 56.6.0.a.1, 520.6.0.?, 1820.6.0.?, 3640.12.0.? $[(-5, 6)]$
6370.e2 6370.e \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $1$ $\Z/2\Z$ $1.530045822$ $[1, -1, 0, 5, -15]$ \(y^2+xy=x^3-x^2+5x-15\) 2.3.0.a.1, 56.6.0.d.1, 520.6.0.?, 910.6.0.?, 3640.12.0.? $[(3, 3)]$
6370.f1 6370.f \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $1$ $\Z/2\Z$ $1.631984749$ $[1, -1, 0, -3194, 64350]$ \(y^2+xy=x^3-x^2-3194x+64350\) 2.3.0.a.1, 56.6.0.a.1, 520.6.0.?, 1820.6.0.?, 3640.12.0.? $[(41, 12)]$
6370.f2 6370.f \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $1$ $\Z/2\Z$ $3.263969499$ $[1, -1, 0, 236, 4668]$ \(y^2+xy=x^3-x^2+236x+4668\) 2.3.0.a.1, 56.6.0.d.1, 520.6.0.?, 910.6.0.?, 3640.12.0.? $[(-11, 31)]$
6370.g1 6370.g \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $0$ $\Z/2\Z$ $1$ $[1, -1, 0, -5342969, 4754787533]$ \(y^2+xy=x^3-x^2-5342969x+4754787533\) 2.3.0.a.1, 4.6.0.c.1, 40.12.0.y.1, 56.12.0-4.c.1.2, 104.12.0.?, $\ldots$ $[ ]$
6370.g2 6370.g \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[1, -1, 0, -348889, 67344045]$ \(y^2+xy=x^3-x^2-348889x+67344045\) 2.6.0.a.1, 40.12.0.b.1, 56.12.0-2.a.1.1, 104.12.0.?, 140.12.0.?, $\ldots$ $[ ]$
6370.g3 6370.g \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $0$ $\Z/2\Z$ $1$ $[1, -1, 0, -98009, -10779987]$ \(y^2+xy=x^3-x^2-98009x-10779987\) 2.3.0.a.1, 4.6.0.c.1, 40.12.0.y.1, 56.12.0-4.c.1.4, 104.12.0.?, $\ldots$ $[ ]$
6370.g4 6370.g \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $0$ $\Z/2\Z$ $1$ $[1, -1, 0, 631111, 376828045]$ \(y^2+xy=x^3-x^2+631111x+376828045\) 2.3.0.a.1, 4.6.0.c.1, 40.12.0.s.1, 56.12.0-4.c.1.1, 104.12.0.?, $\ldots$ $[ ]$
6370.h1 6370.h \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, -10168, 374592]$ \(y^2+xy=x^3+x^2-10168x+374592\) 2.3.0.a.1, 3.4.0.a.1, 4.6.0.b.1, 6.12.0.a.1, 12.24.0.f.1, $\ldots$ $[ ]$
6370.h2 6370.h \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, -1593, -25003]$ \(y^2+xy=x^3+x^2-1593x-25003\) 2.3.0.a.1, 3.4.0.a.1, 4.6.0.b.1, 6.12.0.a.1, 12.24.0.f.1, $\ldots$ $[ ]$
6370.h3 6370.h \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, -613, -54207]$ \(y^2+xy=x^3+x^2-613x-54207\) 2.3.0.a.1, 3.4.0.a.1, 4.6.0.a.1, 6.12.0.a.1, 12.48.0.b.1, $\ldots$ $[ ]$
6370.h4 6370.h \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, 5512, 1443968]$ \(y^2+xy=x^3+x^2+5512x+1443968\) 2.3.0.a.1, 3.4.0.a.1, 4.6.0.a.1, 6.12.0.a.1, 12.48.0.b.2, $\ldots$ $[ ]$
6370.i1 6370.i \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $1$ $\mathsf{trivial}$ $5.375752057$ $[1, 1, 0, -18057, -1210411]$ \(y^2+xy=x^3+x^2-18057x-1210411\) 3.4.0.a.1, 21.8.0-3.a.1.1, 52.2.0.a.1, 156.8.0.?, 1092.16.0.? $[(350, 5783)]$
6370.i2 6370.i \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $1$ $\mathsf{trivial}$ $1.791917352$ $[1, 1, 0, 138008, 12492096]$ \(y^2+xy=x^3+x^2+138008x+12492096\) 3.4.0.a.1, 21.8.0-3.a.1.2, 52.2.0.a.1, 156.8.0.?, 1092.16.0.? $[(-48, 2424)]$
6370.j1 6370.j \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $1$ $\Z/2\Z$ $0.789900001$ $[1, 1, 0, -718757, 234238901]$ \(y^2+xy=x^3+x^2-718757x+234238901\) 2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 21.8.0-3.a.1.2, 24.24.0-6.a.1.4, $\ldots$ $[(97, 12814)]$
6370.j2 6370.j \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $1$ $\Z/2\Z$ $1.579800003$ $[1, 1, 0, -46477, 3377949]$ \(y^2+xy=x^3+x^2-46477x+3377949\) 2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 21.8.0-3.a.1.2, 24.24.0-6.a.1.15, $\ldots$ $[(258, 2811)]$
6370.j3 6370.j \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $1$ $\Z/2\Z$ $2.369700005$ $[1, 1, 0, -14872, -171366]$ \(y^2+xy=x^3+x^2-14872x-171366\) 2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 21.8.0-3.a.1.1, 24.24.0-6.a.1.12, $\ldots$ $[(-15, 228)]$
6370.j4 6370.j \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $1$ $\Z/2\Z$ $4.739400011$ $[1, 1, 0, -11442, -475264]$ \(y^2+xy=x^3+x^2-11442x-475264\) 2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 21.8.0-3.a.1.1, 24.24.0-6.a.1.7, $\ldots$ $[(1070, 34304)]$
6370.k1 6370.k \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $1$ $\Z/3\Z$ $0.361827814$ $[1, 0, 0, -7352941, 7674505425]$ \(y^2+xy=x^3-7352941x+7674505425\) 3.8.0-3.a.1.2, 52.2.0.a.1, 156.16.0.? $[(1538, 1311)]$
6370.k2 6370.k \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $1$ $\mathsf{trivial}$ $0.120609271$ $[1, 0, 0, 988819, 23788766161]$ \(y^2+xy=x^3+988819x+23788766161\) 3.8.0-3.a.1.1, 52.2.0.a.1, 156.16.0.? $[(886, 158807)]$
6370.l1 6370.l \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $1$ $\Z/2\Z$ $0.132362345$ $[1, 0, 0, -41210, 3216100]$ \(y^2+xy=x^3-41210x+3216100\) 2.3.0.a.1, 4.6.0.b.1, 56.12.0-4.b.1.2, 130.6.0.?, 260.24.0.?, $\ldots$ $[(60, 950)]$
6370.l2 6370.l \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $1$ $\Z/2\Z$ $0.264724691$ $[1, 0, 0, -37290, 3853492]$ \(y^2+xy=x^3-37290x+3853492\) 2.3.0.a.1, 4.6.0.a.1, 56.12.0-4.a.1.1, 260.12.0.?, 520.24.0.?, $\ldots$ $[(74, 1188)]$
6370.m1 6370.m \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $0$ $\Z/2\Z$ $1$ $[1, 0, 0, -3725, -87725]$ \(y^2+xy=x^3-3725x-87725\) 2.3.0.a.1, 56.6.0.a.1, 260.6.0.?, 3640.12.0.? $[ ]$
6370.m2 6370.m \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $0$ $\Z/2\Z$ $1$ $[1, 0, 0, -295, -603]$ \(y^2+xy=x^3-295x-603\) 2.3.0.a.1, 56.6.0.d.1, 130.6.0.?, 3640.12.0.? $[ ]$
6370.n1 6370.n \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $0$ $\mathsf{trivial}$ $1$ $[1, 1, 1, -14456, -681591]$ \(y^2+xy+y=x^3+x^2-14456x-681591\) 20.2.0.a.1 $[ ]$
6370.o1 6370.o \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $1$ $\mathsf{trivial}$ $0.431039570$ $[1, 1, 1, -770701, 260100483]$ \(y^2+xy+y=x^3+x^2-770701x+260100483\) 3.4.0.a.1, 20.2.0.a.1, 21.8.0-3.a.1.2, 60.8.0.a.1, 420.16.0.? $[(449, 1972)]$
6370.o2 6370.o \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $1$ $\mathsf{trivial}$ $0.143679856$ $[1, 1, 1, -9101, 385923]$ \(y^2+xy+y=x^3+x^2-9101x+385923\) 3.4.0.a.1, 20.2.0.a.1, 21.8.0-3.a.1.1, 60.8.0.a.1, 420.16.0.? $[(-41, 852)]$
6370.p1 6370.p \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $0$ $\mathsf{trivial}$ $1$ $[1, 1, 1, -215111, 38323683]$ \(y^2+xy+y=x^3+x^2-215111x+38323683\) 728.2.0.? $[ ]$
6370.q1 6370.q \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $1$ $\mathsf{trivial}$ $0.022943576$ $[1, 1, 1, -4075, 109017]$ \(y^2+xy+y=x^3+x^2-4075x+109017\) 728.2.0.? $[(-43, 476)]$
6370.r1 6370.r \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $1$ $\Z/2\Z$ $2.077762263$ $[1, -1, 1, -67948, 6834251]$ \(y^2+xy+y=x^3-x^2-67948x+6834251\) 2.3.0.a.1, 4.6.0.c.1, 8.12.0.o.1, 16.24.0.i.1, 28.12.0-4.c.1.1, $\ldots$ $[(153, -29)]$
6370.r2 6370.r \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $1.038881131$ $[1, -1, 1, -4248, 107531]$ \(y^2+xy+y=x^3-x^2-4248x+107531\) 2.6.0.a.1, 4.12.0.a.1, 8.24.0.g.1, 28.24.0-4.a.1.1, 56.48.0-8.g.1.1, $\ldots$ $[(23, 135)]$
6370.r3 6370.r \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $1$ $\Z/2\Z$ $2.077762263$ $[1, -1, 1, -3268, 157707]$ \(y^2+xy+y=x^3-x^2-3268x+157707\) 2.3.0.a.1, 4.24.0.c.1, 28.48.0-4.c.1.1, 520.48.1.?, 1040.96.3.?, $\ldots$ $[(37, 275)]$
6370.r4 6370.r \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $1$ $\Z/2\Z$ $0.519440565$ $[1, -1, 1, -328, 907]$ \(y^2+xy+y=x^3-x^2-328x+907\) 2.3.0.a.1, 4.6.0.c.1, 8.12.0.o.1, 16.24.0.i.1, 28.12.0-4.c.1.2, $\ldots$ $[(-5, 51)]$
6370.s1 6370.s \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $0$ $\Z/2\Z$ $1$ $[1, -1, 1, -1660987, -757855829]$ \(y^2+xy+y=x^3-x^2-1660987x-757855829\) 2.3.0.a.1, 56.6.0.c.1, 130.6.0.?, 3640.12.0.? $[ ]$
6370.s2 6370.s \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $0$ $\Z/2\Z$ $1$ $[1, -1, 1, 1851333, -3538208341]$ \(y^2+xy+y=x^3-x^2+1851333x-3538208341\) 2.3.0.a.1, 56.6.0.b.1, 260.6.0.?, 3640.12.0.? $[ ]$
6370.t1 6370.t \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $1$ $\mathsf{trivial}$ $1.295568449$ $[1, 0, 0, -199676, -37991920]$ \(y^2+xy=x^3-199676x-37991920\) 728.2.0.? $[(788, 16756)]$
6370.u1 6370.u \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $1$ $\mathsf{trivial}$ $0.251166809$ $[1, 0, 0, -9605, -2028223]$ \(y^2+xy=x^3-9605x-2028223\) 728.2.0.? $[(914, 26983)]$
6370.v1 6370.v \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $1$ $\mathsf{trivial}$ $0.413314181$ $[1, 0, 0, -295, 1945]$ \(y^2+xy=x^3-295x+1945\) 20.2.0.a.1 $[(12, 7)]$
6370.w1 6370.w \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $0$ $\mathsf{trivial}$ $1$ $[1, 0, 0, -37764350, -89327758780]$ \(y^2+xy=x^3-37764350x-89327758780\) 3.8.0-3.a.1.1, 20.2.0.a.1, 60.16.0-60.a.1.5 $[ ]$
6370.w2 6370.w \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $0$ $\Z/3\Z$ $1$ $[1, 0, 0, -445950, -133709500]$ \(y^2+xy=x^3-445950x-133709500\) 3.8.0-3.a.1.2, 20.2.0.a.1, 60.16.0-60.a.1.8 $[ ]$
6370.x1 6370.x \( 2 \cdot 5 \cdot 7^{2} \cdot 13 \) $0$ $\mathsf{trivial}$ $1$ $[1, 0, 0, -4390, -112358]$ \(y^2+xy=x^3-4390x-112358\) 728.2.0.? $[ ]$
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