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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 66 matches)

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Label Class Conductor Rank Torsion CM Regulator Weierstrass coefficients Weierstrass equation mod-$m$ images MW-generators
9690.a1 9690.a \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $1.066982663$ $[1, 1, 0, -34453, 2447137]$ \(y^2+xy=x^3+x^2-34453x+2447137\) 2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 24.12.0-4.c.1.3, 120.24.0.?, $\ldots$ $[(107, -49)]$
9690.a2 9690.a \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.533491331$ $[1, 1, 0, -2153, 37557]$ \(y^2+xy=x^3+x^2-2153x+37557\) 2.6.0.a.1, 12.12.0-2.a.1.1, 20.12.0-2.a.1.1, 60.24.0-60.b.1.2, 1292.12.0.?, $\ldots$ $[(14, 95)]$
9690.a3 9690.a \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $1.066982663$ $[1, 1, 0, -1853, 48777]$ \(y^2+xy=x^3+x^2-1853x+48777\) 2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 20.12.0-4.c.1.1, 30.6.0.a.1, $\ldots$ $[(19, 135)]$
9690.a4 9690.a \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $1.066982663$ $[1, 1, 0, -153, 357]$ \(y^2+xy=x^3+x^2-153x+357\) 2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 40.12.0-4.c.1.5, 120.24.0.?, $\ldots$ $[(2, 7)]$
9690.b1 9690.b \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, -116913, -15435207]$ \(y^2+xy=x^3+x^2-116913x-15435207\) 2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 1140.12.0.? $[ ]$
9690.b2 9690.b \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, -7093, -258083]$ \(y^2+xy=x^3+x^2-7093x-258083\) 2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.? $[ ]$
9690.c1 9690.c \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, -64828, -6378218]$ \(y^2+xy=x^3+x^2-64828x-6378218\) 2.3.0.a.1, 60.6.0.c.1, 136.6.0.?, 2040.12.0.? $[ ]$
9690.c2 9690.c \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, -3458, -130752]$ \(y^2+xy=x^3+x^2-3458x-130752\) 2.3.0.a.1, 30.6.0.a.1, 136.6.0.?, 2040.12.0.? $[ ]$
9690.d1 9690.d \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $21.94315446$ $[1, 1, 0, -1659413, -822735507]$ \(y^2+xy=x^3+x^2-1659413x-822735507\) 2.3.0.a.1, 8.6.0.d.1, 1938.6.0.?, 7752.12.0.? $[(62910572761/5408, 11630406759266131/5408)]$
9690.d2 9690.d \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $10.97157723$ $[1, 1, 0, -1259413, -1228895507]$ \(y^2+xy=x^3+x^2-1259413x-1228895507\) 2.3.0.a.1, 8.6.0.a.1, 3876.6.0.?, 7752.12.0.? $[(1999369/16, 2778297523/16)]$
9690.e1 9690.e \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $2$ $\Z/2\Z$ $0.298603216$ $[1, 1, 0, -2397, 19809]$ \(y^2+xy=x^3+x^2-2397x+19809\) 2.3.0.a.1, 68.6.0.c.1, 76.6.0.?, 1292.12.0.? $[(3, 111), (-22, 261)]$
9690.e2 9690.e \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $2$ $\Z/2\Z$ $0.298603216$ $[1, 1, 0, -2017, 34021]$ \(y^2+xy=x^3+x^2-2017x+34021\) 2.3.0.a.1, 34.6.0.a.1, 76.6.0.?, 1292.12.0.? $[(7, 139), (42, 139)]$
9690.f1 9690.f \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $1.239147463$ $[1, 1, 0, -5672, -153216]$ \(y^2+xy=x^3+x^2-5672x-153216\) 2.3.0.a.1, 60.6.0.c.1, 76.6.0.?, 1140.12.0.? $[(-40, 128)]$
9690.f2 9690.f \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $2.478294926$ $[1, 1, 0, 408, -10944]$ \(y^2+xy=x^3+x^2+408x-10944\) 2.3.0.a.1, 30.6.0.a.1, 76.6.0.?, 1140.12.0.? $[(35, 201)]$
9690.g1 9690.g \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, -142452, -20700684]$ \(y^2+xy=x^3+x^2-142452x-20700684\) 2.3.0.a.1, 76.6.0.?, 1020.6.0.?, 19380.12.0.? $[ ]$
9690.g2 9690.g \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, -5272, -590096]$ \(y^2+xy=x^3+x^2-5272x-590096\) 2.3.0.a.1, 76.6.0.?, 510.6.0.?, 19380.12.0.? $[ ]$
9690.h1 9690.h \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $1$ $\Z/4\Z$ $0.743885928$ $[1, 1, 0, -14742, 682596]$ \(y^2+xy=x^3+x^2-14742x+682596\) 2.3.0.a.1, 4.12.0-4.c.1.1, 76.24.0.?, 680.24.0.?, 12920.48.0.? $[(72, -6)]$
9690.h2 9690.h \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $2.975543712$ $[1, 1, 0, -7862, -266556]$ \(y^2+xy=x^3+x^2-7862x-266556\) 2.3.0.a.1, 4.12.0-4.c.1.2, 152.24.0.?, 170.6.0.?, 340.24.0.?, $\ldots$ $[(125, 788)]$
9690.h3 9690.h \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $1.487771856$ $[1, 1, 0, -1062, 6804]$ \(y^2+xy=x^3+x^2-1062x+6804\) 2.6.0.a.1, 4.12.0-2.a.1.1, 76.24.0.?, 340.24.0.?, 6460.48.0.? $[(45, 207)]$
9690.h4 9690.h \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $2.975543712$ $[1, 1, 0, 218, 916]$ \(y^2+xy=x^3+x^2+218x+916\) 2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 76.12.0.?, 152.24.0.?, $\ldots$ $[(5, 44)]$
9690.i1 9690.i \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $2$ $\Z/2\Z$ $0.253369464$ $[1, 0, 1, -1574, 23816]$ \(y^2+xy+y=x^3-1574x+23816\) 2.3.0.a.1, 76.6.0.?, 1020.6.0.?, 19380.12.0.? $[(9, 97), (21, 1)]$
9690.i2 9690.i \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $2$ $\Z/2\Z$ $1.013477858$ $[1, 0, 1, -54, 712]$ \(y^2+xy+y=x^3-54x+712\) 2.3.0.a.1, 76.6.0.?, 510.6.0.?, 19380.12.0.? $[(5, 21), (53, 357)]$
9690.j1 9690.j \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $0$ $\Z/2\Z$ $1$ $[1, 0, 1, -6557974, -6461024728]$ \(y^2+xy+y=x^3-6557974x-6461024728\) 2.3.0.a.1, 76.6.0.?, 1020.6.0.?, 19380.12.0.? $[ ]$
9690.j2 9690.j \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $0$ $\Z/2\Z$ $1$ $[1, 0, 1, -332054, -140470744]$ \(y^2+xy+y=x^3-332054x-140470744\) 2.3.0.a.1, 76.6.0.?, 510.6.0.?, 19380.12.0.? $[ ]$
9690.k1 9690.k \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $0$ $\Z/2\Z$ $1$ $[1, 0, 1, -392769, 94711576]$ \(y^2+xy+y=x^3-392769x+94711576\) 2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 40.12.0-4.c.1.5, 68.12.0-4.c.1.2, $\ldots$ $[ ]$
9690.k2 9690.k \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $0$ $\Z/2\Z$ $1$ $[1, 0, 1, -26249, 1261352]$ \(y^2+xy+y=x^3-26249x+1261352\) 2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 24.12.0-4.c.1.3, 68.12.0-4.c.1.1, $\ldots$ $[ ]$
9690.k3 9690.k \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[1, 0, 1, -24549, 1478272]$ \(y^2+xy+y=x^3-24549x+1478272\) 2.6.0.a.1, 12.12.0-2.a.1.1, 20.12.0-2.a.1.1, 60.24.0-60.b.1.3, 68.12.0-2.a.1.1, $\ldots$ $[ ]$
9690.k4 9690.k \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $0$ $\Z/2\Z$ $1$ $[1, 0, 1, -1429, 26336]$ \(y^2+xy+y=x^3-1429x+26336\) 2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 20.12.0-4.c.1.2, 30.6.0.a.1, $\ldots$ $[ ]$
9690.l1 9690.l \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $10.78016923$ $[1, 0, 1, -318403923, -2186860080722]$ \(y^2+xy+y=x^3-318403923x-2186860080722\) 2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 60.48.0-60.t.1.15, 2584.6.0.?, $\ldots$ $[(166727/2, 60209949/2)]$
9690.l2 9690.l \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $5.390084618$ $[1, 0, 1, -19900243, -34170942034]$ \(y^2+xy+y=x^3-19900243x-34170942034\) 2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 30.48.0-30.b.1.3, 2584.6.0.?, $\ldots$ $[(39967, 7918064)]$
9690.l3 9690.l \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $1$ $\Z/6\Z$ $3.593389745$ $[1, 0, 1, -3931548, -2999081822]$ \(y^2+xy+y=x^3-3931548x-2999081822\) 2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 60.48.0-60.t.1.16, 2584.6.0.?, $\ldots$ $[(-1126, 1290)]$
9690.l4 9690.l \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $1$ $\Z/6\Z$ $1.796694872$ $[1, 0, 1, -197668, -65745694]$ \(y^2+xy+y=x^3-197668x-65745694\) 2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 30.48.0-30.b.1.4, 2584.6.0.?, $\ldots$ $[(580, 3557)]$
9690.m1 9690.m \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $0.709324272$ $[1, 0, 1, -3443, 77456]$ \(y^2+xy+y=x^3-3443x+77456\) 2.3.0.a.1, 60.6.0.c.1, 2584.6.0.?, 38760.12.0.? $[(36, 4)]$
9690.m2 9690.m \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $0.354662136$ $[1, 0, 1, -213, 1228]$ \(y^2+xy+y=x^3-213x+1228\) 2.3.0.a.1, 30.6.0.a.1, 2584.6.0.?, 38760.12.0.? $[(2, 27)]$
9690.n1 9690.n \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $0$ $\Z/2\Z$ $1$ $[1, 0, 1, -250863021308, 48361646188879418]$ \(y^2+xy+y=x^3-250863021308x+48361646188879418\) 2.3.0.a.1, 8.6.0.d.1, 1938.6.0.?, 7752.12.0.? $[ ]$
9690.n2 9690.n \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $0$ $\Z/2\Z$ $1$ $[1, 0, 1, -246668717308, 50056836226178618]$ \(y^2+xy+y=x^3-246668717308x+50056836226178618\) 2.3.0.a.1, 8.6.0.a.1, 3876.6.0.?, 7752.12.0.? $[ ]$
9690.o1 9690.o \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $0.179474323$ $[1, 0, 1, -64578, 4238548]$ \(y^2+xy+y=x^3-64578x+4238548\) 2.3.0.a.1, 68.6.0.c.1, 76.6.0.?, 1292.12.0.? $[(-91, 3105)]$
9690.o2 9690.o \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $0.358948647$ $[1, 0, 1, -58498, 5439956]$ \(y^2+xy+y=x^3-58498x+5439956\) 2.3.0.a.1, 34.6.0.a.1, 76.6.0.?, 1292.12.0.? $[(160, 347)]$
9690.p1 9690.p \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $0$ $\Z/4\Z$ $1$ $[1, 0, 1, -14636923, 21552520406]$ \(y^2+xy+y=x^3-14636923x+21552520406\) 2.3.0.a.1, 4.12.0-4.c.1.1, 76.24.0.?, 408.24.0.?, 7752.48.0.? $[ ]$
9690.p2 9690.p \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[1, 0, 1, -918923, 333518006]$ \(y^2+xy+y=x^3-918923x+333518006\) 2.6.0.a.1, 4.12.0-2.a.1.1, 76.24.0.?, 204.24.0.?, 3876.48.0.? $[ ]$
9690.p3 9690.p \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $0$ $\Z/2\Z$ $1$ $[1, 0, 1, -118923, -7921994]$ \(y^2+xy+y=x^3-118923x-7921994\) 2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 76.12.0.?, 152.24.0.?, $\ldots$ $[ ]$
9690.p4 9690.p \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $0$ $\Z/2\Z$ $1$ $[1, 0, 1, -923, 969875606]$ \(y^2+xy+y=x^3-923x+969875606\) 2.3.0.a.1, 4.12.0-4.c.1.2, 102.6.0.?, 152.24.0.?, 204.24.0.?, $\ldots$ $[ ]$
9690.q1 9690.q \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $7.854894626$ $[1, 1, 1, -65266, -6444691]$ \(y^2+xy+y=x^3+x^2-65266x-6444691\) 2.3.0.a.1, 60.6.0.c.1, 136.6.0.?, 2040.12.0.? $[(10647/2, 1082951/2)]$
9690.q2 9690.q \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $3.927447313$ $[1, 1, 1, -3896, -111307]$ \(y^2+xy+y=x^3+x^2-3896x-111307\) 2.3.0.a.1, 30.6.0.a.1, 136.6.0.?, 2040.12.0.? $[(2657, 135623)]$
9690.r1 9690.r \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $0$ $\Z/2\Z$ $1$ $[1, 0, 0, -1706561, -530430615]$ \(y^2+xy=x^3-1706561x-530430615\) 2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.m.1.5, 68.12.0-4.c.1.1, 136.48.0.? $[ ]$
9690.r2 9690.r \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[1, 0, 0, -724641, 231342921]$ \(y^2+xy=x^3-724641x+231342921\) 2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.b.1.2, 68.24.0-68.b.1.1, 136.48.0.? $[ ]$
9690.r3 9690.r \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $0$ $\Z/4\Z$ $1$ $[1, 0, 0, -719521, 234856265]$ \(y^2+xy=x^3-719521x+234856265\) 2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.m.1.1, 34.6.0.a.1, 68.24.0-68.g.1.2, $\ldots$ $[ ]$
9690.r4 9690.r \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $0$ $\Z/2\Z$ $1$ $[1, 0, 0, 175359, 768282921]$ \(y^2+xy=x^3+175359x+768282921\) 2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.d.1.1, 136.48.0.? $[ ]$
9690.s1 9690.s \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $2.519802444$ $[1, 0, 0, -144790, -21209800]$ \(y^2+xy=x^3-144790x-21209800\) 2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 76.6.0.?, 228.48.0.?, $\ldots$ $[(-220, 20)]$
9690.s2 9690.s \( 2 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \) $1$ $\Z/2\Z$ $5.039604888$ $[1, 0, 0, -7610, -440748]$ \(y^2+xy=x^3-7610x-440748\) 2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 76.6.0.?, 228.48.0.?, $\ldots$ $[(252, 3570)]$
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