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Label Class Conductor Rank Torsion CM Regulator Weierstrass coefficients Weierstrass equation mod-$m$ images
67830.a1 67830.a \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $2.741969115$ $[1, 1, 0, -175273, -28198667]$ \(y^2+xy=x^3+x^2-175273x-28198667\) 2.3.0.a.1, 170.6.0.?, 1596.6.0.?, 135660.12.0.?
67830.a2 67830.a \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $5.483938230$ $[1, 1, 0, -5273, -896667]$ \(y^2+xy=x^3+x^2-5273x-896667\) 2.3.0.a.1, 340.6.0.?, 798.6.0.?, 135660.12.0.?
67830.b1 67830.b \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $0$ $\mathsf{trivial}$ $1$ $[1, 1, 0, -6106725383, 183726343374837]$ \(y^2+xy=x^3+x^2-6106725383x+183726343374837\) 45220.2.0.?
67830.c1 67830.c \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $0$ $\mathsf{trivial}$ $1$ $[1, 1, 0, 6762, 228168]$ \(y^2+xy=x^3+x^2+6762x+228168\) 45220.2.0.?
67830.d1 67830.d \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, -2567593878, 50075850331332]$ \(y^2+xy=x^3+x^2-2567593878x+50075850331332\) 2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 28.12.0-4.c.1.1, 42.6.0.a.1, $\ldots$
67830.d2 67830.d \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, -162807158, 758465739108]$ \(y^2+xy=x^3+x^2-162807158x+758465739108\) 2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 28.12.0-4.c.1.2, 168.24.0.?, $\ldots$
67830.d3 67830.d \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[1, 1, 0, -160474758, 782383568148]$ \(y^2+xy=x^3+x^2-160474758x+782383568148\) 2.6.0.a.1, 12.12.0-2.a.1.1, 28.12.0-2.a.1.1, 84.24.0.?, 340.12.0.?, $\ldots$
67830.d4 67830.d \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, -9884038, 12593925652]$ \(y^2+xy=x^3+x^2-9884038x+12593925652\) 2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 56.12.0-4.c.1.5, 168.24.0.?, $\ldots$
67830.e1 67830.e \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $0$ $\mathsf{trivial}$ $1$ $[1, 1, 0, -3686063, -2727661083]$ \(y^2+xy=x^3+x^2-3686063x-2727661083\) 15960.2.0.?
67830.f1 67830.f \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $2$ $\Z/4\Z$ $6.515976518$ $[1, 1, 0, -114247, 14815801]$ \(y^2+xy=x^3+x^2-114247x+14815801\) 2.3.0.a.1, 4.12.0-4.c.1.1, 152.24.0.?, 2380.24.0.?, 90440.48.0.?
67830.f2 67830.f \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $2$ $\Z/2\Z\oplus\Z/2\Z$ $1.628994129$ $[1, 1, 0, -7147, 228781]$ \(y^2+xy=x^3+x^2-7147x+228781\) 2.6.0.a.1, 4.12.0-2.a.1.1, 76.24.0.?, 2380.24.0.?, 45220.48.0.?
67830.f3 67830.f \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $2$ $\Z/2\Z$ $0.407248532$ $[1, 1, 0, -3727, 452449]$ \(y^2+xy=x^3+x^2-3727x+452449\) 2.3.0.a.1, 4.12.0-4.c.1.2, 38.6.0.b.1, 76.24.0.?, 4760.24.0.?, $\ldots$
67830.f4 67830.f \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $2$ $\Z/2\Z$ $6.515976518$ $[1, 1, 0, -667, -611]$ \(y^2+xy=x^3+x^2-667x-611\) 2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 76.12.0.?, 152.24.0.?, $\ldots$
67830.g1 67830.g \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $3.440850747$ $[1, 1, 0, -7868745327, 267149873551041]$ \(y^2+xy=x^3+x^2-7868745327x+267149873551041\) 2.3.0.a.1, 4.12.0-4.c.1.2, 168.24.0.?, 170.6.0.?, 340.24.0.?, $\ldots$
67830.g2 67830.g \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $1.720425373$ $[1, 1, 0, -7856462827, 268029985914541]$ \(y^2+xy=x^3+x^2-7856462827x+268029985914541\) 2.6.0.a.1, 4.12.0-2.a.1.1, 84.24.0.?, 340.24.0.?, 7140.48.0.?
67830.g3 67830.g \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $3.440850747$ $[1, 1, 0, -7856462747, 268029991646109]$ \(y^2+xy=x^3+x^2-7856462747x+268029991646109\) 2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 84.12.0.?, 168.24.0.?, $\ldots$
67830.g4 67830.g \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $1$ $\Z/4\Z$ $3.440850747$ $[1, 1, 0, -7844181607, 268909731459289]$ \(y^2+xy=x^3+x^2-7844181607x+268909731459289\) 2.3.0.a.1, 4.12.0-4.c.1.1, 84.24.0.?, 680.24.0.?, 14280.48.0.?
67830.h1 67830.h \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $0$ $\mathsf{trivial}$ $1$ $[1, 1, 0, -1872622, 1430343604]$ \(y^2+xy=x^3+x^2-1872622x+1430343604\) 45220.2.0.?
67830.i1 67830.i \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, -7842592072, -94264625472416]$ \(y^2+xy=x^3+x^2-7842592072x-94264625472416\) 2.3.0.a.1, 4.6.0.c.1, 76.12.0.?, 136.12.0.?, 280.12.0.?, $\ldots$
67830.i2 67830.i \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[1, 1, 0, -6331417192, -193749196877504]$ \(y^2+xy=x^3+x^2-6331417192x-193749196877504\) 2.6.0.a.1, 76.12.0.?, 136.12.0.?, 140.12.0.?, 2584.24.0.?, $\ldots$
67830.i3 67830.i \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, -6329937512, -193844354210496]$ \(y^2+xy=x^3+x^2-6329937512x-193844354210496\) 2.3.0.a.1, 4.6.0.c.1, 76.12.0.?, 136.12.0.?, 140.12.0.?, $\ldots$
67830.i4 67830.i \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, -4843917192, -287143669377504]$ \(y^2+xy=x^3+x^2-4843917192x-287143669377504\) 2.3.0.a.1, 4.6.0.c.1, 136.12.0.?, 140.12.0.?, 152.12.0.?, $\ldots$
67830.j1 67830.j \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $1$ $\mathsf{trivial}$ $0.133841438$ $[1, 1, 0, 361583, 165761821]$ \(y^2+xy=x^3+x^2+361583x+165761821\) 18088.2.0.?
67830.k1 67830.k \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $1.552307783$ $[1, 1, 0, -1006502, -375717234]$ \(y^2+xy=x^3+x^2-1006502x-375717234\) 2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 24.12.0-4.c.1.2, 120.24.0.?, $\ldots$
67830.k2 67830.k \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.776153891$ $[1, 1, 0, -162752, 17301516]$ \(y^2+xy=x^3+x^2-162752x+17301516\) 2.6.0.a.1, 20.12.0-2.a.1.1, 24.12.0-2.a.1.1, 120.24.0.?, 9044.12.0.?, $\ldots$
67830.k3 67830.k \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $1.552307783$ $[1, 1, 0, -148172, 21888384]$ \(y^2+xy=x^3+x^2-148172x+21888384\) 2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 24.12.0-4.c.1.6, 120.24.0.?, $\ldots$
67830.k4 67830.k \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $1.552307783$ $[1, 1, 0, 447718, 117052314]$ \(y^2+xy=x^3+x^2+447718x+117052314\) 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.?, $\ldots$
67830.l1 67830.l \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $0$ $\mathsf{trivial}$ $1$ $[1, 1, 0, 365918, -252509324]$ \(y^2+xy=x^3+x^2+365918x-252509324\) 15960.2.0.?
67830.m1 67830.m \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $2$ $\Z/2\Z$ $0.339264077$ $[1, 0, 1, -15989, -555964]$ \(y^2+xy+y=x^3-15989x-555964\) 2.3.0.a.1, 76.6.0.?, 1020.6.0.?, 19380.12.0.?
67830.m2 67830.m \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $2$ $\Z/2\Z$ $1.357056311$ $[1, 0, 1, 2631, -56948]$ \(y^2+xy+y=x^3+2631x-56948\) 2.3.0.a.1, 76.6.0.?, 510.6.0.?, 19380.12.0.?
67830.n1 67830.n \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $0.385152294$ $[1, 0, 1, -28939, 1892342]$ \(y^2+xy+y=x^3-28939x+1892342\) 2.3.0.a.1, 170.6.0.?, 1596.6.0.?, 135660.12.0.?
67830.n2 67830.n \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $0.770304589$ $[1, 0, 1, -1739, 31862]$ \(y^2+xy+y=x^3-1739x+31862\) 2.3.0.a.1, 340.6.0.?, 798.6.0.?, 135660.12.0.?
67830.o1 67830.o \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $10.59474481$ $[1, 0, 1, -220119, -39767558]$ \(y^2+xy+y=x^3-220119x-39767558\) 2.3.0.a.1, 60.6.0.c.1, 2584.6.0.?, 38760.12.0.?
67830.o2 67830.o \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $5.297372405$ $[1, 0, 1, -13399, -656134]$ \(y^2+xy+y=x^3-13399x-656134\) 2.3.0.a.1, 30.6.0.a.1, 2584.6.0.?, 38760.12.0.?
67830.p1 67830.p \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $1$ $\mathsf{trivial}$ $0.293307733$ $[1, 0, 1, 86849626, 4484452919672]$ \(y^2+xy+y=x^3+86849626x+4484452919672\) 18088.2.0.?
67830.q1 67830.q \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $0.610032934$ $[1, 0, 1, -578294, 113832776]$ \(y^2+xy+y=x^3-578294x+113832776\) 2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 170.6.0.?, 510.48.0.?, $\ldots$
67830.q2 67830.q \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $1$ $\Z/6\Z$ $1.830098802$ $[1, 0, 1, -523979, 145944722]$ \(y^2+xy+y=x^3-523979x+145944722\) 2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 170.6.0.?, 510.48.0.?, $\ldots$
67830.q3 67830.q \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $1$ $\Z/6\Z$ $3.660197605$ $[1, 0, 1, -32679, 2288602]$ \(y^2+xy+y=x^3-32679x+2288602\) 2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 340.6.0.?, 798.48.0.?, $\ldots$
67830.q4 67830.q \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $1.220065868$ $[1, 0, 1, 101706, 12104776]$ \(y^2+xy+y=x^3+101706x+12104776\) 2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 340.6.0.?, 798.48.0.?, $\ldots$
67830.r1 67830.r \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $1.096989739$ $[1, 0, 1, -31034, 2101646]$ \(y^2+xy+y=x^3-31034x+2101646\) 2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 280.24.0.?, 1292.12.0.?, $\ldots$
67830.r2 67830.r \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.548494869$ $[1, 0, 1, -1964, 31862]$ \(y^2+xy+y=x^3-1964x+31862\) 2.6.0.a.1, 8.12.0-2.a.1.1, 140.12.0.?, 280.24.0.?, 1292.12.0.?, $\ldots$
67830.r3 67830.r \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $1.096989739$ $[1, 0, 1, -344, -1834]$ \(y^2+xy+y=x^3-344x-1834\) 2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 140.12.0.?, 280.24.0.?, $\ldots$
67830.r4 67830.r \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $1.096989739$ $[1, 0, 1, 1186, 125102]$ \(y^2+xy+y=x^3+1186x+125102\) 2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 140.12.0.?, 280.24.0.?, $\ldots$
67830.s1 67830.s \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $3.527156831$ $[1, 0, 1, -2903932529, 60196943047556]$ \(y^2+xy+y=x^3-2903932529x+60196943047556\) 2.3.0.a.1, 3.8.0-3.a.1.1, 4.6.0.c.1, 6.24.0-6.a.1.2, 8.12.0-4.c.1.4, $\ldots$
67830.s2 67830.s \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $1$ $\Z/6\Z$ $10.58147049$ $[1, 0, 1, -2903465114, 60217301097812]$ \(y^2+xy+y=x^3-2903465114x+60217301097812\) 2.3.0.a.1, 3.8.0-3.a.1.2, 4.6.0.c.1, 6.24.0-6.a.1.4, 8.12.0-4.c.1.4, $\ldots$
67830.s3 67830.s \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $1.763578415$ $[1, 0, 1, -217399409, 541937811332]$ \(y^2+xy+y=x^3-217399409x+541937811332\) 2.6.0.a.1, 3.8.0-3.a.1.1, 6.48.0-6.a.1.2, 8.12.0-2.a.1.1, 24.96.0-24.o.2.31, $\ldots$
67830.s4 67830.s \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z\oplus\Z/6\Z$ $5.290735247$ $[1, 0, 1, -181466594, 940883727476]$ \(y^2+xy+y=x^3-181466594x+940883727476\) 2.6.0.a.1, 3.8.0-3.a.1.2, 6.48.0-6.a.1.1, 8.12.0-2.a.1.1, 24.96.0-24.o.1.15, $\ldots$
67830.s5 67830.s \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $1$ $\Z/6\Z$ $10.58147049$ $[1, 0, 1, -180445994, 951990304916]$ \(y^2+xy+y=x^3-180445994x+951990304916\) 2.3.0.a.1, 3.8.0-3.a.1.2, 4.6.0.c.1, 6.24.0-6.a.1.4, 8.12.0-4.c.1.3, $\ldots$
67830.s6 67830.s \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $3.527156831$ $[1, 0, 1, -111231089, -445724835964]$ \(y^2+xy+y=x^3-111231089x-445724835964\) 2.3.0.a.1, 3.8.0-3.a.1.1, 4.6.0.c.1, 6.24.0-6.a.1.2, 8.12.0-4.c.1.2, $\ldots$
67830.s7 67830.s \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 19 \) $1$ $\Z/6\Z$ $10.58147049$ $[1, 0, 1, -11405474, 14526794612]$ \(y^2+xy+y=x^3-11405474x+14526794612\) 2.3.0.a.1, 3.8.0-3.a.1.2, 4.6.0.c.1, 6.24.0-6.a.1.4, 8.12.0-4.c.1.2, $\ldots$
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