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Label Class Conductor Rank Torsion CM Regulator Weierstrass coefficients Weierstrass equation mod-$m$ images MW-generators
51376.a1 51376.a \( 2^{4} \cdot 13^{2} \cdot 19 \) $1$ $\mathsf{trivial}$ $0.612532812$ $[0, 0, 0, -165451, 25911418]$ \(y^2=x^3-165451x+25911418\) 104.2.0.? $[(247, 338)]$
51376.b1 51376.b \( 2^{4} \cdot 13^{2} \cdot 19 \) $2$ $\mathsf{trivial}$ $4.309516955$ $[0, 1, 0, 19210, 465739]$ \(y^2=x^3+x^2+19210x+465739\) 494.2.0.? $[(927, 28561), (511, 11999)]$
51376.c1 51376.c \( 2^{4} \cdot 13^{2} \cdot 19 \) $0$ $\mathsf{trivial}$ $1$ $[0, 1, 0, -132552, 19696756]$ \(y^2=x^3+x^2-132552x+19696756\) 4.2.0.a.1, 152.4.0.? $[ ]$
51376.d1 51376.d \( 2^{4} \cdot 13^{2} \cdot 19 \) $2$ $\mathsf{trivial}$ $1.294607216$ $[0, 1, 0, -1408, 20931]$ \(y^2=x^3+x^2-1408x+20931\) 494.2.0.? $[(-35, 169), (29/2, 845/2)]$
51376.e1 51376.e \( 2^{4} \cdot 13^{2} \cdot 19 \) $2$ $\mathsf{trivial}$ $1.497782910$ $[0, 1, 0, -3605, 82447]$ \(y^2=x^3+x^2-3605x+82447\) 38.2.0.a.1 $[(-9, 338), (133/2, 169/2)]$
51376.f1 51376.f \( 2^{4} \cdot 13^{2} \cdot 19 \) $1$ $\mathsf{trivial}$ $0.863728295$ $[0, 1, 0, -784, 8724]$ \(y^2=x^3+x^2-784x+8724\) 4.2.0.a.1, 1976.4.0.? $[(20, 38)]$
51376.g1 51376.g \( 2^{4} \cdot 13^{2} \cdot 19 \) $0$ $\mathsf{trivial}$ $1$ $[0, -1, 0, -273472, 511376384]$ \(y^2=x^3-x^2-273472x+511376384\) 104.2.0.? $[ ]$
51376.h1 51376.h \( 2^{4} \cdot 13^{2} \cdot 19 \) $1$ $\mathsf{trivial}$ $1.387112818$ $[0, -1, 0, -27096, 4602064]$ \(y^2=x^3-x^2-27096x+4602064\) 104.2.0.? $[(282, 4394)]$
51376.i1 51376.i \( 2^{4} \cdot 13^{2} \cdot 19 \) $1$ $\mathsf{trivial}$ $4.871435753$ $[0, -1, 0, -231248, 344373184]$ \(y^2=x^3-x^2-231248x+344373184\) 3.4.0.a.1, 9.12.0.a.1, 27.36.0.a.1, 152.2.0.?, 156.8.0.?, $\ldots$ $[(21816/7, 6225920/7)]$
51376.i2 51376.i \( 2^{4} \cdot 13^{2} \cdot 19 \) $1$ $\mathsf{trivial}$ $4.871435753$ $[0, -1, 0, -41968, -3296320]$ \(y^2=x^3-x^2-41968x-3296320\) 3.4.0.a.1, 9.12.0.a.1, 27.36.0.a.1, 152.2.0.?, 156.8.0.?, $\ldots$ $[(760, 20080)]$
51376.i3 51376.i \( 2^{4} \cdot 13^{2} \cdot 19 \) $1$ $\mathsf{trivial}$ $1.623811917$ $[0, -1, 0, 25632, -12587264]$ \(y^2=x^3-x^2+25632x-12587264\) 3.12.0.a.1, 9.36.0.b.1, 152.2.0.?, 156.24.0.?, 171.108.4.?, $\ldots$ $[(528, 12160)]$
51376.j1 51376.j \( 2^{4} \cdot 13^{2} \cdot 19 \) $0$ $\mathsf{trivial}$ $1$ $[0, -1, 0, -1408, 29600]$ \(y^2=x^3-x^2-1408x+29600\) 152.2.0.? $[ ]$
51376.k1 51376.k \( 2^{4} \cdot 13^{2} \cdot 19 \) $2$ $\mathsf{trivial}$ $0.389296807$ $[0, -1, 0, -160, 2144]$ \(y^2=x^3-x^2-160x+2144\) 104.2.0.? $[(-4, 52), (100, 988)]$
51376.l1 51376.l \( 2^{4} \cdot 13^{2} \cdot 19 \) $1$ $\mathsf{trivial}$ $9.771305557$ $[0, -1, 0, -46216824, 1123309048432]$ \(y^2=x^3-x^2-46216824x+1123309048432\) 104.2.0.? $[(-25814/3, 29972006/3)]$
51376.m1 51376.m \( 2^{4} \cdot 13^{2} \cdot 19 \) $1$ $\mathsf{trivial}$ $2.184691614$ $[0, 0, 0, -61220081, -362938057261]$ \(y^2=x^3-61220081x-362938057261\) 494.2.0.? $[(742105/2, 638703221/2)]$
51376.n1 51376.n \( 2^{4} \cdot 13^{2} \cdot 19 \) $1$ $\mathsf{trivial}$ $1.603746678$ $[0, 0, 0, 169, -6591]$ \(y^2=x^3+169x-6591\) 494.2.0.? $[(65/2, 169/2)]$
51376.o1 51376.o \( 2^{4} \cdot 13^{2} \cdot 19 \) $1$ $\Z/2\Z$ $18.51216825$ $[0, 0, 0, -557531, -160077814]$ \(y^2=x^3-557531x-160077814\) 2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 104.24.0.?, 152.24.0.?, $\ldots$ $[(-572081857/1139, 247116784530/1139)]$
51376.o2 51376.o \( 2^{4} \cdot 13^{2} \cdot 19 \) $1$ $\Z/4\Z$ $4.628042063$ $[0, 0, 0, -395291, 94844490]$ \(y^2=x^3-395291x+94844490\) 2.3.0.a.1, 4.12.0-4.c.1.1, 104.24.0.?, 152.24.0.?, 1976.48.0.? $[(101, 7480)]$
51376.o3 51376.o \( 2^{4} \cdot 13^{2} \cdot 19 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $9.256084127$ $[0, 0, 0, -43771, -1120470]$ \(y^2=x^3-43771x-1120470\) 2.6.0.a.1, 4.12.0-2.a.1.1, 104.24.0.?, 152.24.0.?, 988.24.0.?, $\ldots$ $[(-7955/17, 1238160/17)]$
51376.o4 51376.o \( 2^{4} \cdot 13^{2} \cdot 19 \) $1$ $\Z/2\Z$ $4.628042063$ $[0, 0, 0, 10309, -136214]$ \(y^2=x^3+10309x-136214\) 2.3.0.a.1, 4.12.0-4.c.1.2, 104.24.0.?, 152.24.0.?, 494.6.0.?, $\ldots$ $[(3471/5, 249106/5)]$
51376.p1 51376.p \( 2^{4} \cdot 13^{2} \cdot 19 \) $0$ $\mathsf{trivial}$ $1$ $[0, 0, 0, -18083, -940654]$ \(y^2=x^3-18083x-940654\) 4.16.0-4.b.1.1 $[ ]$
51376.q1 51376.q \( 2^{4} \cdot 13^{2} \cdot 19 \) $1$ $\mathsf{trivial}$ $18.21786285$ $[0, 0, 0, -3056027, -2066616838]$ \(y^2=x^3-3056027x-2066616838\) 4.8.0.b.1, 52.16.0-4.b.1.1 $[(2184778363/953, 58078175985842/953)]$
51376.r1 51376.r \( 2^{4} \cdot 13^{2} \cdot 19 \) $1$ $\mathsf{trivial}$ $5.110102674$ $[0, 0, 0, 2704, -79092]$ \(y^2=x^3+2704x-79092\) 38.2.0.a.1 $[(302, 5318)]$
51376.s1 51376.s \( 2^{4} \cdot 13^{2} \cdot 19 \) $2$ $\mathsf{trivial}$ $2.519148073$ $[0, 1, 0, 33744, -1075372]$ \(y^2=x^3+x^2+33744x-1075372\) 104.2.0.? $[(316, 6422), (31, 38)]$
51376.t1 51376.t \( 2^{4} \cdot 13^{2} \cdot 19 \) $2$ $\mathsf{trivial}$ $11.26778462$ $[0, 1, 0, -2706760, -1799597708]$ \(y^2=x^3+x^2-2706760x-1799597708\) 104.2.0.? $[(2526, 86528), (1932, 13642)]$
51376.u1 51376.u \( 2^{4} \cdot 13^{2} \cdot 19 \) $0$ $\mathsf{trivial}$ $1$ $[0, 1, 0, -189336, 35039252]$ \(y^2=x^3+x^2-189336x+35039252\) 5.12.0.a.2, 152.2.0.?, 260.24.0.?, 760.24.1.?, 9880.48.1.? $[ ]$
51376.u2 51376.u \( 2^{4} \cdot 13^{2} \cdot 19 \) $0$ $\mathsf{trivial}$ $1$ $[0, 1, 0, -56, -166828]$ \(y^2=x^3+x^2-56x-166828\) 5.12.0.a.1, 152.2.0.?, 260.24.0.?, 760.24.1.?, 9880.48.1.? $[ ]$
51376.v1 51376.v \( 2^{4} \cdot 13^{2} \cdot 19 \) $1$ $\mathsf{trivial}$ $5.451717244$ $[0, -1, 0, -160, -729]$ \(y^2=x^3-x^2-160x-729\) 494.2.0.? $[(729/4, 18603/4)]$
51376.w1 51376.w \( 2^{4} \cdot 13^{2} \cdot 19 \) $1$ $\mathsf{trivial}$ $5.796263560$ $[0, -1, 0, -2080277, 1155555101]$ \(y^2=x^3-x^2-2080277x+1155555101\) 3.4.0.a.1, 9.12.0.a.1, 27.36.0.a.1, 38.2.0.a.1, 114.8.0.?, $\ldots$ $[(163549/14, 189111/14)]$
51376.w2 51376.w \( 2^{4} \cdot 13^{2} \cdot 19 \) $1$ $\mathsf{trivial}$ $1.932087853$ $[0, -1, 0, -25237, 1650141]$ \(y^2=x^3-x^2-25237x+1650141\) 3.12.0.a.1, 9.36.0.b.1, 38.2.0.a.1, 114.24.1.?, 156.24.0.?, $\ldots$ $[(621/2, 9633/2)]$
51376.w3 51376.w \( 2^{4} \cdot 13^{2} \cdot 19 \) $1$ $\mathsf{trivial}$ $5.796263560$ $[0, -1, 0, 1803, 701]$ \(y^2=x^3-x^2+1803x+701\) 3.4.0.a.1, 9.12.0.a.1, 27.36.0.a.1, 38.2.0.a.1, 114.8.0.?, $\ldots$ $[(29/10, 34983/10)]$
51376.x1 51376.x \( 2^{4} \cdot 13^{2} \cdot 19 \) $0$ $\Z/2\Z$ $1$ $[0, -1, 0, -79824, 7589984]$ \(y^2=x^3-x^2-79824x+7589984\) 2.3.0.a.1, 104.6.0.?, 152.6.0.?, 988.6.0.?, 1976.12.0.? $[ ]$
51376.x2 51376.x \( 2^{4} \cdot 13^{2} \cdot 19 \) $0$ $\Z/2\Z$ $1$ $[0, -1, 0, 8056, 629888]$ \(y^2=x^3-x^2+8056x+629888\) 2.3.0.a.1, 104.6.0.?, 152.6.0.?, 494.6.0.?, 1976.12.0.? $[ ]$
51376.y1 51376.y \( 2^{4} \cdot 13^{2} \cdot 19 \) $0$ $\mathsf{trivial}$ $1$ $[0, -1, 0, 3662, 12531]$ \(y^2=x^3-x^2+3662x+12531\) 494.2.0.? $[ ]$
51376.z1 51376.z \( 2^{4} \cdot 13^{2} \cdot 19 \) $1$ $\mathsf{trivial}$ $7.076842275$ $[0, -1, 0, -324198, 71158151]$ \(y^2=x^3-x^2-324198x+71158151\) 3.4.0.a.1, 156.8.0.?, 228.8.0.?, 494.2.0.?, 1482.8.0.?, $\ldots$ $[(16097/7, 6495/7)]$
51376.z2 51376.z \( 2^{4} \cdot 13^{2} \cdot 19 \) $1$ $\mathsf{trivial}$ $2.358947425$ $[0, -1, 0, -3098, 143675]$ \(y^2=x^3-x^2-3098x+143675\) 3.4.0.a.1, 156.8.0.?, 228.8.0.?, 494.2.0.?, 1482.8.0.?, $\ldots$ $[(25, 285)]$
51376.ba1 51376.ba \( 2^{4} \cdot 13^{2} \cdot 19 \) $1$ $\mathsf{trivial}$ $3.035155501$ $[0, -1, 0, 22, -1]$ \(y^2=x^3-x^2+22x-1\) 494.2.0.? $[(1/4, 39/4)]$
51376.bb1 51376.bb \( 2^{4} \cdot 13^{2} \cdot 19 \) $1$ $\mathsf{trivial}$ $7.889457124$ $[0, -1, 0, -225, -7411]$ \(y^2=x^3-x^2-225x-7411\) 38.2.0.a.1 $[(23969/28, 2536521/28)]$
51376.bc1 51376.bc \( 2^{4} \cdot 13^{2} \cdot 19 \) $1$ $\Z/2\Z$ $1.895698311$ $[0, -1, 0, -472, 3600]$ \(y^2=x^3-x^2-472x+3600\) 2.3.0.a.1, 104.6.0.?, 152.6.0.?, 988.6.0.?, 1976.12.0.? $[(0, 60)]$
51376.bc2 51376.bc \( 2^{4} \cdot 13^{2} \cdot 19 \) $1$ $\Z/2\Z$ $3.791396622$ $[0, -1, 0, 48, 272]$ \(y^2=x^3-x^2+48x+272\) 2.3.0.a.1, 104.6.0.?, 152.6.0.?, 494.6.0.?, 1976.12.0.? $[(64/3, 820/3)]$
51376.bd1 51376.bd \( 2^{4} \cdot 13^{2} \cdot 19 \) $0$ $\mathsf{trivial}$ $1$ $[0, -1, 0, -27096, -1709917]$ \(y^2=x^3-x^2-27096x-1709917\) 494.2.0.? $[ ]$
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