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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 74 matches)

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Label Class Conductor Rank Torsion CM Regulator Weierstrass coefficients Weierstrass equation mod-$m$ images MW-generators
6450.a1 6450.a \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $1$ $\mathsf{trivial}$ $0.842719286$ $[1, 1, 0, -200, -2250]$ \(y^2+xy=x^3+x^2-200x-2250\) 1720.2.0.? $[(35, 170)]$
6450.b1 6450.b \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $1$ $\Z/2\Z$ $7.117991280$ $[1, 1, 0, -857650, -133160000]$ \(y^2+xy=x^3+x^2-857650x-133160000\) 2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.d.1, 15.8.0-3.a.1.1, $\ldots$ $[(8250, 740450)]$
6450.b2 6450.b \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $1$ $\Z/2\Z$ $2.372663760$ $[1, 1, 0, -439150, 111824500]$ \(y^2+xy=x^3+x^2-439150x+111824500\) 2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.d.1, 15.8.0-3.a.1.2, $\ldots$ $[(255, 3935)]$
6450.b3 6450.b \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $1$ $\Z/2\Z$ $4.745327520$ $[1, 1, 0, -414150, 125149500]$ \(y^2+xy=x^3+x^2-414150x+125149500\) 2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.a.1, 15.8.0-3.a.1.2, $\ldots$ $[(295, 5215)]$
6450.b4 6450.b \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $1$ $\Z/2\Z$ $14.23598256$ $[1, 1, 0, 3048600, -1004253750]$ \(y^2+xy=x^3+x^2+3048600x-1004253750\) 2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.a.1, 15.8.0-3.a.1.1, $\ldots$ $[(6860125/29, 18260553800/29)]$
6450.c1 6450.c \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $0$ $\mathsf{trivial}$ $1$ $[1, 1, 0, -12735, -558495]$ \(y^2+xy=x^3+x^2-12735x-558495\) 86.2.0.? $[ ]$
6450.d1 6450.d \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $1$ $\Z/2\Z$ $0.701953798$ $[1, 1, 0, -2835, 46125]$ \(y^2+xy=x^3+x^2-2835x+46125\) 2.3.0.a.1, 24.6.0.j.1, 40.6.0.b.1, 60.6.0.c.1, 120.12.0.? $[(51, 168)]$
6450.d2 6450.d \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $1$ $\Z/2\Z$ $1.403907597$ $[1, 1, 0, 365, 4525]$ \(y^2+xy=x^3+x^2+365x+4525\) 2.3.0.a.1, 24.6.0.j.1, 30.6.0.a.1, 40.6.0.c.1, 120.12.0.? $[(-1, 65)]$
6450.e1 6450.e \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $1$ $\mathsf{trivial}$ $20.03918476$ $[1, 1, 0, -1497525, -706065375]$ \(y^2+xy=x^3+x^2-1497525x-706065375\) 7.24.0.a.2, 35.48.0-7.a.2.1, 516.2.0.?, 3612.48.2.?, 18060.96.2.? $[(641606156/319, 15818761274049/319)]$
6450.e2 6450.e \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $1$ $\mathsf{trivial}$ $2.862740681$ $[1, 1, 0, 3975, 217125]$ \(y^2+xy=x^3+x^2+3975x+217125\) 7.24.0.a.1, 35.48.0-7.a.1.1, 516.2.0.?, 3612.48.2.?, 18060.96.2.? $[(146, 1911)]$
6450.f1 6450.f \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, -3494890, 2513314900]$ \(y^2+xy=x^3+x^2-3494890x+2513314900\) 2.3.0.a.1, 40.6.0.b.1, 344.6.0.?, 860.6.0.?, 1720.12.0.? $[ ]$
6450.f2 6450.f \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, -218090, 39330900]$ \(y^2+xy=x^3+x^2-218090x+39330900\) 2.3.0.a.1, 40.6.0.c.1, 344.6.0.?, 430.6.0.?, 1720.12.0.? $[ ]$
6450.g1 6450.g \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $1$ $\Z/2\Z$ $0.625162682$ $[1, 1, 0, -50, 0]$ \(y^2+xy=x^3+x^2-50x\) 2.3.0.a.1, 8.6.0.d.1, 258.6.0.?, 1032.12.0.? $[(-5, 15)]$
6450.g2 6450.g \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $1$ $\Z/2\Z$ $1.250325364$ $[1, 1, 0, 200, 250]$ \(y^2+xy=x^3+x^2+200x+250\) 2.3.0.a.1, 8.6.0.a.1, 516.6.0.?, 1032.12.0.? $[(5, 35)]$
6450.h1 6450.h \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $0$ $\mathsf{trivial}$ $1$ $[1, 1, 0, 21425, -102875]$ \(y^2+xy=x^3+x^2+21425x-102875\) 1720.2.0.? $[ ]$
6450.i1 6450.i \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, -4775, 115125]$ \(y^2+xy=x^3+x^2-4775x+115125\) 2.3.0.a.1, 20.6.0.b.1, 258.6.0.?, 2580.12.0.? $[ ]$
6450.i2 6450.i \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, 5225, 545125]$ \(y^2+xy=x^3+x^2+5225x+545125\) 2.3.0.a.1, 20.6.0.a.1, 516.6.0.?, 2580.12.0.? $[ ]$
6450.j1 6450.j \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, -4325, -82875]$ \(y^2+xy=x^3+x^2-4325x-82875\) 2.3.0.a.1, 40.6.0.b.1, 344.6.0.?, 860.6.0.?, 1720.12.0.? $[ ]$
6450.j2 6450.j \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, 675, -7875]$ \(y^2+xy=x^3+x^2+675x-7875\) 2.3.0.a.1, 40.6.0.c.1, 344.6.0.?, 430.6.0.?, 1720.12.0.? $[ ]$
6450.k1 6450.k \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $1$ $\Z/2\Z$ $6.477355034$ $[1, 0, 1, -137601, -19657652]$ \(y^2+xy+y=x^3-137601x-19657652\) 2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 40.24.0-8.m.1.2, 1032.24.0.?, $\ldots$ $[(436, 1592)]$
6450.k2 6450.k \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $3.238677517$ $[1, 0, 1, -8601, -307652]$ \(y^2+xy+y=x^3-8601x-307652\) 2.6.0.a.1, 8.12.0.b.1, 20.12.0-2.a.1.1, 40.24.0-8.b.1.2, 516.12.0.?, $\ldots$ $[(236, 3171)]$
6450.k3 6450.k \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $1$ $\Z/2\Z$ $1.619338758$ $[1, 0, 1, -7601, -381652]$ \(y^2+xy+y=x^3-7601x-381652\) 2.3.0.a.1, 4.6.0.c.1, 8.12.0.d.1, 20.12.0-4.c.1.1, 40.24.0-8.d.1.1, $\ldots$ $[(138, 1027)]$
6450.k4 6450.k \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $1$ $\Z/2\Z$ $1.619338758$ $[1, 0, 1, -601, -3652]$ \(y^2+xy+y=x^3-601x-3652\) 2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 20.12.0-4.c.1.2, 40.24.0-8.m.1.1, $\ldots$ $[(-18, 46)]$
6450.l1 6450.l \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $1$ $\mathsf{trivial}$ $0.160730030$ $[1, 0, 1, -6451, 206798]$ \(y^2+xy+y=x^3-6451x+206798\) 86.2.0.? $[(127, 1136)]$
6450.m1 6450.m \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $1$ $\Z/2\Z$ $0.856778246$ $[1, 0, 1, -33401, 2346698]$ \(y^2+xy+y=x^3-33401x+2346698\) 2.3.0.a.1, 40.6.0.b.1, 516.6.0.?, 5160.12.0.? $[(72, 526)]$
6450.m2 6450.m \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $1$ $\Z/2\Z$ $1.713556493$ $[1, 0, 1, -2151, 34198]$ \(y^2+xy+y=x^3-2151x+34198\) 2.3.0.a.1, 40.6.0.c.1, 258.6.0.?, 5160.12.0.? $[(37, 56)]$
6450.n1 6450.n \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $0$ $\Z/3\Z$ $1$ $[1, 0, 1, -201, 1798]$ \(y^2+xy+y=x^3-201x+1798\) 3.8.0-3.a.1.2, 1032.16.0.? $[ ]$
6450.n2 6450.n \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $0$ $\mathsf{trivial}$ $1$ $[1, 0, 1, 1674, -31952]$ \(y^2+xy+y=x^3+1674x-31952\) 3.8.0-3.a.1.1, 1032.16.0.? $[ ]$
6450.o1 6450.o \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $0$ $\mathsf{trivial}$ $1$ $[1, 0, 1, -5201, 1920548]$ \(y^2+xy+y=x^3-5201x+1920548\) 1720.2.0.? $[ ]$
6450.p1 6450.p \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $1$ $\mathsf{trivial}$ $0.260402041$ $[1, 0, 1, -1126, 26648]$ \(y^2+xy+y=x^3-1126x+26648\) 1720.2.0.? $[(-8, 191)]$
6450.q1 6450.q \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $1$ $\mathsf{trivial}$ $0.232227966$ $[1, 0, 1, -1103101, 445850348]$ \(y^2+xy+y=x^3-1103101x+445850348\) 516.2.0.? $[(601, -58)]$
6450.r1 6450.r \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $0$ $\mathsf{trivial}$ $1$ $[1, 0, 1, 68524, 6697298]$ \(y^2+xy+y=x^3+68524x+6697298\) 1032.2.0.? $[ ]$
6450.s1 6450.s \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $1$ $\Z/2\Z$ $3.601503627$ $[1, 0, 1, -4144401, -3247777052]$ \(y^2+xy+y=x^3-4144401x-3247777052\) 2.3.0.a.1, 24.6.0.a.1, 860.6.0.?, 5160.12.0.? $[(6482, 488946)]$
6450.s2 6450.s \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $1$ $\Z/2\Z$ $1.800751813$ $[1, 0, 1, -256401, -51841052]$ \(y^2+xy+y=x^3-256401x-51841052\) 2.3.0.a.1, 24.6.0.d.1, 430.6.0.?, 5160.12.0.? $[(722, 11451)]$
6450.t1 6450.t \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $1$ $\Z/2\Z$ $1.558052398$ $[1, 1, 1, -20963, 1151531]$ \(y^2+xy+y=x^3+x^2-20963x+1151531\) 2.3.0.a.1, 4.6.0.c.1, 24.12.0.s.1, 40.12.0-4.c.1.2, 60.12.0-4.c.1.1, $\ldots$ $[(-505/2, 11251/2)]$
6450.t2 6450.t \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $3.116104796$ $[1, 1, 1, -2213, -10969]$ \(y^2+xy+y=x^3+x^2-2213x-10969\) 2.6.0.a.1, 24.12.0.b.1, 40.12.0-2.a.1.1, 60.12.0-2.a.1.1, 120.24.0.?, $\ldots$ $[(339, 6022)]$
6450.t3 6450.t \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $1$ $\Z/2\Z$ $1.558052398$ $[1, 1, 1, -1713, -27969]$ \(y^2+xy+y=x^3+x^2-1713x-27969\) 2.3.0.a.1, 4.6.0.c.1, 24.12.0.y.1, 40.12.0-4.c.1.4, 60.12.0-4.c.1.2, $\ldots$ $[(65, 342)]$
6450.t4 6450.t \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $1$ $\Z/2\Z$ $6.232209593$ $[1, 1, 1, 8537, -75469]$ \(y^2+xy+y=x^3+x^2+8537x-75469\) 2.3.0.a.1, 4.6.0.c.1, 24.12.0.y.1, 40.12.0-4.c.1.1, 120.24.0.?, $\ldots$ $[(1331/2, 49101/2)]$
6450.u1 6450.u \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 1, -688, -6469]$ \(y^2+xy+y=x^3+x^2-688x-6469\) 2.3.0.a.1, 24.6.0.a.1, 860.6.0.?, 5160.12.0.? $[ ]$
6450.u2 6450.u \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 1, 62, -469]$ \(y^2+xy+y=x^3+x^2+62x-469\) 2.3.0.a.1, 24.6.0.d.1, 430.6.0.?, 5160.12.0.? $[ ]$
6450.v1 6450.v \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 1, -129563, -15542719]$ \(y^2+xy+y=x^3+x^2-129563x-15542719\) 2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 15.8.0-3.a.1.1, 24.24.0-6.a.1.13, $\ldots$ $[ ]$
6450.v2 6450.v \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 1, -124563, -16972719]$ \(y^2+xy+y=x^3+x^2-124563x-16972719\) 2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 15.8.0-3.a.1.1, 24.24.0-6.a.1.2, $\ldots$ $[ ]$
6450.v3 6450.v \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 1, -33938, 2389781]$ \(y^2+xy+y=x^3+x^2-33938x+2389781\) 2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 15.8.0-3.a.1.2, 24.24.0-6.a.1.5, $\ldots$ $[ ]$
6450.v4 6450.v \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 1, -2688, 14781]$ \(y^2+xy+y=x^3+x^2-2688x+14781\) 2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 15.8.0-3.a.1.2, 24.24.0-6.a.1.10, $\ldots$ $[ ]$
6450.w1 6450.w \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $1$ $\mathsf{trivial}$ $0.260057323$ $[1, 1, 1, 126662, -597382969]$ \(y^2+xy+y=x^3+x^2+126662x-597382969\) 1720.2.0.? $[(3125, 172587)]$
6450.x1 6450.x \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $0$ $\mathsf{trivial}$ $1$ $[1, 1, 1, 1713112, 837162281]$ \(y^2+xy+y=x^3+x^2+1713112x+837162281\) 1032.2.0.? $[ ]$
6450.y1 6450.y \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 1, -1659338, 821959031]$ \(y^2+xy+y=x^3+x^2-1659338x+821959031\) 2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 40.24.0-40.bb.1.5, 344.24.0.?, $\ldots$ $[ ]$
6450.y2 6450.y \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 1, -611338, -175192969]$ \(y^2+xy+y=x^3+x^2-611338x-175192969\) 2.3.0.a.1, 4.12.0-4.c.1.2, 40.24.0-40.v.1.1, 344.24.0.?, 1720.48.0.? $[ ]$
6450.y3 6450.y \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[1, 1, 1, -111338, 10807031]$ \(y^2+xy+y=x^3+x^2-111338x+10807031\) 2.6.0.a.1, 4.12.0-2.a.1.1, 40.24.0-40.a.1.4, 344.24.0.?, 860.24.0.?, $\ldots$ $[ ]$
6450.y4 6450.y \( 2 \cdot 3 \cdot 5^{2} \cdot 43 \) $0$ $\Z/4\Z$ $1$ $[1, 1, 1, 16662, 1079031]$ \(y^2+xy+y=x^3+x^2+16662x+1079031\) 2.3.0.a.1, 4.12.0-4.c.1.1, 40.24.0-40.bb.1.2, 344.24.0.?, 430.6.0.?, $\ldots$ $[ ]$
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