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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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Label Class Conductor Rank Torsion CM Regulator Weierstrass coefficients Weierstrass equation mod-$m$ images MW-generators
417600.a1 417600.a \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $1$ $\mathsf{trivial}$ $2.997719184$ $[0, 0, 0, -27300, -1753000]$ \(y^2=x^3-27300x-1753000\) 174.2.0.? $[(205, 1125)]$
417600.b1 417600.b \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $1$ $\mathsf{trivial}$ $1.327236908$ $[0, 0, 0, 18900, 13122000]$ \(y^2=x^3+18900x+13122000\) 696.2.0.? $[(-54, 3456)]$
417600.c1 417600.c \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $0$ $\mathsf{trivial}$ $1$ $[0, 0, 0, 2100, -486000]$ \(y^2=x^3+2100x-486000\) 696.2.0.? $[ ]$
417600.d1 417600.d \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $0$ $\mathsf{trivial}$ $1$ $[0, 0, 0, 10500, 137000]$ \(y^2=x^3+10500x+137000\) 174.2.0.? $[ ]$
417600.e1 417600.e \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $0$ $\mathsf{trivial}$ $1$ $[0, 0, 0, -110945100, -2120488058000]$ \(y^2=x^3-110945100x-2120488058000\) 3.4.0.a.1, 120.8.0.?, 696.8.0.?, 870.8.0.?, 3480.16.0.? $[ ]$
417600.e2 417600.e \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $0$ $\mathsf{trivial}$ $1$ $[0, 0, 0, 991302900, 54978162838000]$ \(y^2=x^3+991302900x+54978162838000\) 3.4.0.a.1, 120.8.0.?, 696.8.0.?, 870.8.0.?, 3480.16.0.? $[ ]$
417600.f1 417600.f \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $2$ $\Z/2\Z$ $6.986980004$ $[0, 0, 0, -8400, -295000]$ \(y^2=x^3-8400x-295000\) 2.3.0.a.1, 4.6.0.b.1, 58.6.0.a.1, 116.24.0.?, 120.12.0.?, $\ldots$ $[(-55, 25), (1570, 62100)]$
417600.f2 417600.f \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $2$ $\Z/2\Z$ $6.986980004$ $[0, 0, 0, -3900, -610000]$ \(y^2=x^3-3900x-610000\) 2.3.0.a.1, 4.6.0.a.1, 60.12.0-4.a.1.1, 116.12.0.?, 232.24.0.?, $\ldots$ $[(280, 4500), (820, 23400)]$
417600.g1 417600.g \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $1$ $\Z/2\Z$ $1.634275376$ $[0, 0, 0, -11820, -117200]$ \(y^2=x^3-11820x-117200\) 2.3.0.a.1, 20.6.0.b.1, 116.6.0.?, 290.6.0.?, 580.12.0.? $[(-40, 540)]$
417600.g2 417600.g \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $1$ $\Z/2\Z$ $3.268550753$ $[0, 0, 0, 45780, -923600]$ \(y^2=x^3+45780x-923600\) 2.3.0.a.1, 20.6.0.a.1, 116.6.0.?, 580.12.0.? $[(344, 7452)]$
417600.h1 417600.h \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $1$ $\Z/2\Z$ $7.250999801$ $[0, 0, 0, -7704300, 8214842000]$ \(y^2=x^3-7704300x+8214842000\) 2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 24.12.0.y.1, 120.24.0.?, $\ldots$ $[(8716, 776664)]$
417600.h2 417600.h \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $1$ $\Z/2\Z$ $1.812749950$ $[0, 0, 0, -6732300, -6692722000]$ \(y^2=x^3-6732300x-6692722000\) 2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 24.12.0.s.1, 120.24.0.?, $\ldots$ $[(-1435, 3625)]$
417600.h3 417600.h \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $3.625499900$ $[0, 0, 0, -657300, 26228000]$ \(y^2=x^3-657300x+26228000\) 2.6.0.a.1, 20.12.0-2.a.1.1, 24.12.0.b.1, 116.12.0.?, 120.24.0.?, $\ldots$ $[(-680, 12600)]$
417600.h4 417600.h \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $1$ $\Z/2\Z$ $7.250999801$ $[0, 0, 0, 162825, 3264500]$ \(y^2=x^3+162825x+3264500\) 2.3.0.a.1, 4.6.0.c.1, 24.12.0.y.1, 40.12.0-4.c.1.5, 116.12.0.?, $\ldots$ $[(905/4, 227675/4)]$
417600.i1 417600.i \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $2$ $\Z/2\Z$ $7.710506140$ $[0, 0, 0, -3348300, -2358182000]$ \(y^2=x^3-3348300x-2358182000\) 2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 24.12.0-4.c.1.6, 120.24.0.?, $\ldots$ $[(-1054, 144), (2114, 3312)]$
417600.i2 417600.i \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $2$ $\Z/2\Z\oplus\Z/2\Z$ $7.710506140$ $[0, 0, 0, -216300, -34238000]$ \(y^2=x^3-216300x-34238000\) 2.6.0.a.1, 20.12.0-2.a.1.1, 24.12.0-2.a.1.1, 116.12.0.?, 120.24.0.?, $\ldots$ $[(-195, 725), (-315, 1625)]$
417600.i3 417600.i \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $2$ $\Z/2\Z$ $1.927626535$ $[0, 0, 0, -54300, 4318000]$ \(y^2=x^3-54300x+4318000\) 2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.1, 40.12.0-4.c.1.5, 120.24.0.?, $\ldots$ $[(290, 3600), (90, 400)]$
417600.i4 417600.i \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $2$ $\Z/2\Z$ $7.710506140$ $[0, 0, 0, 323700, -177878000]$ \(y^2=x^3+323700x-177878000\) 2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 24.12.0-4.c.1.2, 120.24.0.?, $\ldots$ $[(960, 31900), (5740/3, 458200/3)]$
417600.j1 417600.j \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $0$ $\Z/2\Z$ $1$ $[0, 0, 0, -941700, 317176000]$ \(y^2=x^3-941700x+317176000\) 2.3.0.a.1, 24.6.0.c.1, 290.6.0.?, 3480.12.0.? $[ ]$
417600.j2 417600.j \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $0$ $\Z/2\Z$ $1$ $[0, 0, 0, 1245300, 1572514000]$ \(y^2=x^3+1245300x+1572514000\) 2.3.0.a.1, 24.6.0.b.1, 580.6.0.?, 3480.12.0.? $[ ]$
417600.k1 417600.k \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $1$ $\Z/2\Z$ $2.443681323$ $[0, 0, 0, -3708300, 2708278000]$ \(y^2=x^3-3708300x+2708278000\) 2.3.0.a.1, 4.6.0.c.1, 10.6.0.a.1, 20.12.0.g.1, 24.12.0-4.c.1.1, $\ldots$ $[(1365, 13775)]$
417600.k2 417600.k \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $4.887362646$ $[0, 0, 0, -468300, -58682000]$ \(y^2=x^3-468300x-58682000\) 2.6.0.a.1, 20.12.0.b.1, 24.12.0-2.a.1.1, 116.12.0.?, 120.24.0.?, $\ldots$ $[(2036, 86184)]$
417600.k3 417600.k \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $1$ $\Z/2\Z$ $2.443681323$ $[0, 0, 0, -396300, -95978000]$ \(y^2=x^3-396300x-95978000\) 2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.2, 40.12.0.z.1, 120.24.0.?, $\ldots$ $[(-364, 216)]$
417600.k4 417600.k \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $1$ $\Z/2\Z$ $9.774725292$ $[0, 0, 0, 1619700, -438698000]$ \(y^2=x^3+1619700x-438698000\) 2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.6, 40.12.0.z.1, 116.12.0.?, $\ldots$ $[(276585/14, 187256875/14)]$
417600.l1 417600.l \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $1$ $\mathsf{trivial}$ $11.74339932$ $[0, 0, 0, -6127500, -5844490000]$ \(y^2=x^3-6127500x-5844490000\) 3.4.0.a.1, 8.2.0.a.1, 12.8.0-3.a.1.4, 24.16.0-24.a.1.4 $[(4423925/31, 7507309025/31)]$
417600.l2 417600.l \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $1$ $\mathsf{trivial}$ $35.23019796$ $[0, 0, 0, 8272500, -27173770000]$ \(y^2=x^3+8272500x-27173770000\) 3.4.0.a.1, 8.2.0.a.1, 12.8.0-3.a.1.3, 24.16.0-24.a.1.2 $[(199251523201474709/6975217, 93181027692030168731474927/6975217)]$
417600.m1 417600.m \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $0$ $\mathsf{trivial}$ $1$ $[0, 0, 0, -1537050, 733495750]$ \(y^2=x^3-1537050x+733495750\) 870.2.0.? $[ ]$
417600.n1 417600.n \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $1$ $\mathsf{trivial}$ $3.780531957$ $[0, 0, 0, -3900, 146000]$ \(y^2=x^3-3900x+146000\) 3.4.0.a.1, 116.2.0.?, 120.8.0.?, 348.8.0.?, 3480.16.0.? $[(-16, 452)]$
417600.n2 417600.n \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $1$ $\mathsf{trivial}$ $11.34159587$ $[0, 0, 0, 32100, -2374000]$ \(y^2=x^3+32100x-2374000\) 3.4.0.a.1, 116.2.0.?, 120.8.0.?, 348.8.0.?, 3480.16.0.? $[(152096/13, 60385844/13)]$
417600.o1 417600.o \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $1$ $\Z/2\Z$ $3.068885051$ $[0, 0, 0, -1268220, -549718000]$ \(y^2=x^3-1268220x-549718000\) 2.3.0.a.1, 20.6.0.b.1, 116.6.0.?, 290.6.0.?, 580.12.0.? $[(2350, 97200)]$
417600.o2 417600.o \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $1$ $\Z/2\Z$ $6.137770102$ $[0, 0, 0, -1264620, -552994000]$ \(y^2=x^3-1264620x-552994000\) 2.3.0.a.1, 20.6.0.a.1, 116.6.0.?, 580.12.0.? $[(4925, 335675)]$
417600.p1 417600.p \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $1$ $\mathsf{trivial}$ $21.18886030$ $[0, 0, 0, -39758700, -394822558640]$ \(y^2=x^3-39758700x-394822558640\) 232.2.0.? $[(169274444634/3721, 50121353717768192/3721)]$
417600.q1 417600.q \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $0$ $\mathsf{trivial}$ $1$ $[0, 0, 0, -79500, 29770000]$ \(y^2=x^3-79500x+29770000\) 232.2.0.? $[ ]$
417600.r1 417600.r \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $1$ $\mathsf{trivial}$ $3.272398698$ $[0, 0, 0, -56167500, 162042950000]$ \(y^2=x^3-56167500x+162042950000\) 232.2.0.? $[(4366, 6336)]$
417600.s1 417600.s \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $2$ $\Z/2\Z$ $2.337913083$ $[0, 0, 0, -24780, -1478000]$ \(y^2=x^3-24780x-1478000\) 2.3.0.a.1, 120.6.0.?, 580.6.0.?, 696.6.0.?, 3480.12.0.? $[(-94, 144), (194, 1008)]$
417600.s2 417600.s \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $2$ $\Z/2\Z$ $2.337913083$ $[0, 0, 0, -3180, 34000]$ \(y^2=x^3-3180x+34000\) 2.3.0.a.1, 120.6.0.?, 290.6.0.?, 696.6.0.?, 3480.12.0.? $[(5, 135), (-4, 216)]$
417600.t1 417600.t \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $2$ $\Z/2\Z$ $8.002359742$ $[0, 0, 0, -27300, 1028000]$ \(y^2=x^3-27300x+1028000\) 2.3.0.a.1, 4.6.0.b.1, 24.12.0-4.b.1.1, 58.6.0.a.1, 116.12.0.?, $\ldots$ $[(20, 700), (445, 8775)]$
417600.t2 417600.t \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $2$ $\Z/2\Z$ $8.002359742$ $[0, 0, 0, 5325, 114500]$ \(y^2=x^3+5325x+114500\) 2.3.0.a.1, 4.6.0.a.1, 12.12.0-4.a.1.1, 116.12.0.?, 232.24.0.?, $\ldots$ $[(160, 2250), (2860, 153000)]$
417600.u1 417600.u \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $1$ $\Z/2\Z$ $2.315539597$ $[0, 0, 0, -160500, 24100000]$ \(y^2=x^3-160500x+24100000\) 2.3.0.a.1, 20.6.0.b.1, 116.6.0.?, 290.6.0.?, 580.12.0.? $[(146, 1944)]$
417600.u2 417600.u \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $1$ $\Z/2\Z$ $4.631079195$ $[0, 0, 0, 2625, 1262500]$ \(y^2=x^3+2625x+1262500\) 2.3.0.a.1, 20.6.0.a.1, 116.6.0.?, 580.12.0.? $[(224, 3618)]$
417600.v1 417600.v \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $1$ $\mathsf{trivial}$ $18.42451709$ $[0, 0, 0, -257587500, 2355860450000]$ \(y^2=x^3-257587500x+2355860450000\) 232.2.0.? $[(-442710214/151, 666594960784/151)]$
417600.w1 417600.w \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $0$ $\Z/2\Z$ $1$ $[0, 0, 0, -2395879500, -45103348550000]$ \(y^2=x^3-2395879500x-45103348550000\) 2.3.0.a.1, 120.6.0.?, 580.6.0.?, 696.6.0.?, 3480.12.0.? $[ ]$
417600.w2 417600.w \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $0$ $\Z/2\Z$ $1$ $[0, 0, 0, -184039500, -357825350000]$ \(y^2=x^3-184039500x-357825350000\) 2.3.0.a.1, 120.6.0.?, 290.6.0.?, 696.6.0.?, 3480.12.0.? $[ ]$
417600.x1 417600.x \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $2$ $\mathsf{trivial}$ $6.887351235$ $[0, 0, 0, -4347900, 3489534000]$ \(y^2=x^3-4347900x+3489534000\) 116.2.0.? $[(1204, 8), (10834/3, 152/3)]$
417600.y1 417600.y \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $1$ $\Z/2\Z$ $5.138628291$ $[0, 0, 0, -36468300, -84763078000]$ \(y^2=x^3-36468300x-84763078000\) 2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 24.24.0.cc.1, 60.24.0-6.a.1.8, $\ldots$ $[(9760, 699300)]$
417600.y2 417600.y \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $1$ $\Z/2\Z$ $10.27725658$ $[0, 0, 0, -34740300, -93157702000]$ \(y^2=x^3-34740300x-93157702000\) 2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 24.24.0.cb.1, 60.24.0-6.a.1.3, $\ldots$ $[(476960/7, 240333500/7)]$
417600.y3 417600.y \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $1$ $\Z/2\Z$ $1.712876097$ $[0, 0, 0, -828300, 105482000]$ \(y^2=x^3-828300x+105482000\) 2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 24.24.0.cc.1, 60.24.0-6.a.1.12, $\ldots$ $[(-190, 16000)]$
417600.y4 417600.y \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $1$ $\Z/2\Z$ $3.425752194$ $[0, 0, 0, 3059700, 813098000]$ \(y^2=x^3+3059700x+813098000\) 2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 24.24.0.cb.1, 60.24.0-6.a.1.1, $\ldots$ $[(1045, 71775)]$
417600.z1 417600.z \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $1$ $\Z/2\Z$ $7.275122136$ $[0, 0, 0, -608700, -182666000]$ \(y^2=x^3-608700x-182666000\) 2.3.0.a.1, 10.6.0.a.1, 116.6.0.?, 580.12.0.? $[(-3971/3, 2717/3)]$
417600.z2 417600.z \( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) $1$ $\Z/2\Z$ $3.637561068$ $[0, 0, 0, -46200, -1541000]$ \(y^2=x^3-46200x-1541000\) 2.3.0.a.1, 20.6.0.c.1, 58.6.0.a.1, 580.12.0.? $[(-94, 1404)]$
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