The results below are complete, since the LMFDB contains all elliptic curves with conductor at most 500000

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Results (32 matches)

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Label Class Conductor Rank Torsion CM Regulator Weierstrass coefficients Weierstrass equation mod-$m$ images MW-generators
690.a1 690.a \( 2 \cdot 3 \cdot 5 \cdot 23 \) $1$ $\Z/2\Z$ $1.874726531$ $[1, 1, 0, -1748, -25392]$ \(y^2+xy=x^3+x^2-1748x-25392\) 2.3.0.a.1, 24.6.0.a.1, 92.6.0.?, 552.12.0.? $[(-23, 69)]$
690.a2 690.a \( 2 \cdot 3 \cdot 5 \cdot 23 \) $1$ $\Z/2\Z$ $0.937363265$ $[1, 1, 0, 172, -1968]$ \(y^2+xy=x^3+x^2+172x-1968\) 2.3.0.a.1, 24.6.0.d.1, 46.6.0.a.1, 552.12.0.? $[(11, 32)]$
690.b1 690.b \( 2 \cdot 3 \cdot 5 \cdot 23 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, -753, -3843]$ \(y^2+xy=x^3+x^2-753x-3843\) 2.3.0.a.1, 60.6.0.c.1, 184.6.0.?, 2760.12.0.? $[ ]$
690.b2 690.b \( 2 \cdot 3 \cdot 5 \cdot 23 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, 167, -347]$ \(y^2+xy=x^3+x^2+167x-347\) 2.3.0.a.1, 30.6.0.a.1, 184.6.0.?, 2760.12.0.? $[ ]$
690.c1 690.c \( 2 \cdot 3 \cdot 5 \cdot 23 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, -3172057, -2148591611]$ \(y^2+xy=x^3+x^2-3172057x-2148591611\) 2.3.0.a.1, 24.6.0.a.1, 92.6.0.?, 552.12.0.? $[ ]$
690.c2 690.c \( 2 \cdot 3 \cdot 5 \cdot 23 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, -22777, -90852059]$ \(y^2+xy=x^3+x^2-22777x-90852059\) 2.3.0.a.1, 24.6.0.d.1, 46.6.0.a.1, 552.12.0.? $[ ]$
690.d1 690.d \( 2 \cdot 3 \cdot 5 \cdot 23 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, -242, -1554]$ \(y^2+xy=x^3+x^2-242x-1554\) 2.3.0.a.1, 60.6.0.c.1, 184.6.0.?, 2760.12.0.? $[ ]$
690.d2 690.d \( 2 \cdot 3 \cdot 5 \cdot 23 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 0, -12, -36]$ \(y^2+xy=x^3+x^2-12x-36\) 2.3.0.a.1, 30.6.0.a.1, 184.6.0.?, 2760.12.0.? $[ ]$
690.e1 690.e \( 2 \cdot 3 \cdot 5 \cdot 23 \) $1$ $\Z/2\Z$ $0.187349857$ $[1, 0, 1, -10644, 420826]$ \(y^2+xy+y=x^3-10644x+420826\) 2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 12.12.0-4.c.1.1, 24.24.0-24.s.1.4, $\ldots$ $[(56, 6)]$
690.e2 690.e \( 2 \cdot 3 \cdot 5 \cdot 23 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.374699714$ $[1, 0, 1, -924, 922]$ \(y^2+xy+y=x^3-924x+922\) 2.6.0.a.1, 8.12.0-2.a.1.1, 12.12.0-2.a.1.1, 24.24.0-24.b.1.2, 460.12.0.?, $\ldots$ $[(-4, 69)]$
690.e3 690.e \( 2 \cdot 3 \cdot 5 \cdot 23 \) $1$ $\Z/2\Z$ $0.749399428$ $[1, 0, 1, -604, -5734]$ \(y^2+xy+y=x^3-604x-5734\) 2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 12.12.0-4.c.1.2, 24.24.0-24.y.1.2, $\ldots$ $[(-14, 2)]$
690.e4 690.e \( 2 \cdot 3 \cdot 5 \cdot 23 \) $1$ $\Z/2\Z$ $0.749399428$ $[1, 0, 1, 3676, 8282]$ \(y^2+xy+y=x^3+3676x+8282\) 2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 24.24.0-24.y.1.8, 460.12.0.?, $\ldots$ $[(18, 274)]$
690.f1 690.f \( 2 \cdot 3 \cdot 5 \cdot 23 \) $0$ $\Z/2\Z$ $1$ $[1, 0, 1, -1473, -21872]$ \(y^2+xy+y=x^3-1473x-21872\) 2.3.0.a.1, 4.12.0-4.c.1.2, 40.24.0-40.ba.1.12, 138.6.0.?, 276.24.0.?, $\ldots$ $[ ]$
690.f2 690.f \( 2 \cdot 3 \cdot 5 \cdot 23 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[1, 0, 1, -93, -344]$ \(y^2+xy+y=x^3-93x-344\) 2.6.0.a.1, 4.12.0-2.a.1.1, 20.24.0-20.a.1.1, 276.24.0.?, 1380.48.0.? $[ ]$
690.f3 690.f \( 2 \cdot 3 \cdot 5 \cdot 23 \) $0$ $\Z/2\Z$ $1$ $[1, 0, 1, -13, 8]$ \(y^2+xy+y=x^3-13x+8\) 2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 20.12.0-4.c.1.2, 40.24.0-40.ba.1.10, $\ldots$ $[ ]$
690.f4 690.f \( 2 \cdot 3 \cdot 5 \cdot 23 \) $0$ $\Z/4\Z$ $1$ $[1, 0, 1, 7, -1024]$ \(y^2+xy+y=x^3+7x-1024\) 2.3.0.a.1, 4.12.0-4.c.1.1, 20.24.0-20.h.1.2, 552.24.0.?, 2760.48.0.? $[ ]$
690.g1 690.g \( 2 \cdot 3 \cdot 5 \cdot 23 \) $1$ $\Z/2\Z$ $0.356357135$ $[1, 1, 1, -116, 413]$ \(y^2+xy+y=x^3+x^2-116x+413\) 2.3.0.a.1, 24.6.0.a.1, 92.6.0.?, 552.12.0.? $[(-1, 23)]$
690.g2 690.g \( 2 \cdot 3 \cdot 5 \cdot 23 \) $1$ $\Z/2\Z$ $0.178178567$ $[1, 1, 1, 4, 29]$ \(y^2+xy+y=x^3+x^2+4x+29\) 2.3.0.a.1, 24.6.0.d.1, 46.6.0.a.1, 552.12.0.? $[(-1, 5)]$
690.h1 690.h \( 2 \cdot 3 \cdot 5 \cdot 23 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 1, -1382411, -626186311]$ \(y^2+xy+y=x^3+x^2-1382411x-626186311\) 2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.k.1.1, 184.48.0.? $[ ]$
690.h2 690.h \( 2 \cdot 3 \cdot 5 \cdot 23 \) $0$ $\Z/2\Z$ $1$ $[1, 1, 1, -101131, -6258247]$ \(y^2+xy+y=x^3+x^2-101131x-6258247\) 2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.p.1.7, 92.12.0.?, 184.48.0.? $[ ]$
690.h3 690.h \( 2 \cdot 3 \cdot 5 \cdot 23 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[1, 1, 1, -86411, -9808711]$ \(y^2+xy+y=x^3+x^2-86411x-9808711\) 2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.a.1.2, 92.24.0.?, 184.48.0.? $[ ]$
690.h4 690.h \( 2 \cdot 3 \cdot 5 \cdot 23 \) $0$ $\Z/4\Z$ $1$ $[1, 1, 1, -4491, -207687]$ \(y^2+xy+y=x^3+x^2-4491x-207687\) 2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.p.1.1, 46.6.0.a.1, 92.24.0.?, $\ldots$ $[ ]$
690.i1 690.i \( 2 \cdot 3 \cdot 5 \cdot 23 \) $0$ $\Z/2\Z$ $1$ $[1, 0, 0, -786, -5940]$ \(y^2+xy=x^3-786x-5940\) 2.3.0.a.1, 60.6.0.c.1, 184.6.0.?, 2760.12.0.? $[ ]$
690.i2 690.i \( 2 \cdot 3 \cdot 5 \cdot 23 \) $0$ $\Z/2\Z$ $1$ $[1, 0, 0, 134, -604]$ \(y^2+xy=x^3+134x-604\) 2.3.0.a.1, 30.6.0.a.1, 184.6.0.?, 2760.12.0.? $[ ]$
690.j1 690.j \( 2 \cdot 3 \cdot 5 \cdot 23 \) $0$ $\Z/2\Z$ $1$ $[1, 0, 0, -3925, -94975]$ \(y^2+xy=x^3-3925x-94975\) 2.3.0.a.1, 60.6.0.c.1, 184.6.0.?, 2760.12.0.? $[ ]$
690.j2 690.j \( 2 \cdot 3 \cdot 5 \cdot 23 \) $0$ $\Z/2\Z$ $1$ $[1, 0, 0, -245, -1503]$ \(y^2+xy=x^3-245x-1503\) 2.3.0.a.1, 30.6.0.a.1, 184.6.0.?, 2760.12.0.? $[ ]$
690.k1 690.k \( 2 \cdot 3 \cdot 5 \cdot 23 \) $0$ $\Z/4\Z$ $1$ $[1, 0, 0, -110400, 14109732]$ \(y^2+xy=x^3-110400x+14109732\) 2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 16.48.0-16.e.1.2, 24.48.0-24.by.1.3, $\ldots$ $[ ]$
690.k2 690.k \( 2 \cdot 3 \cdot 5 \cdot 23 \) $0$ $\Z/2\Z$ $1$ $[1, 0, 0, -25830, -1370850]$ \(y^2+xy=x^3-25830x-1370850\) 2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.bb.2.3, 24.96.0-24.bl.2.7, 368.96.0.?, $\ldots$ $[ ]$
690.k3 690.k \( 2 \cdot 3 \cdot 5 \cdot 23 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $[1, 0, 0, -7080, 207900]$ \(y^2+xy=x^3-7080x+207900\) 2.6.0.a.1, 4.24.0-4.b.1.1, 8.48.0-8.e.1.1, 24.96.0-24.m.2.3, 184.96.0.?, $\ldots$ $[ ]$
690.k4 690.k \( 2 \cdot 3 \cdot 5 \cdot 23 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $[1, 0, 0, -6900, 220032]$ \(y^2+xy=x^3-6900x+220032\) 2.6.0.a.1, 4.24.0-4.b.1.3, 8.48.0-8.e.2.2, 24.96.0-24.r.2.5, 92.48.0.?, $\ldots$ $[ ]$
690.k5 690.k \( 2 \cdot 3 \cdot 5 \cdot 23 \) $0$ $\Z/8\Z$ $1$ $[1, 0, 0, -420, 3600]$ \(y^2+xy=x^3-420x+3600\) 2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.bb.1.1, 46.6.0.a.1, 48.96.0-48.bp.1.7, $\ldots$ $[ ]$
690.k6 690.k \( 2 \cdot 3 \cdot 5 \cdot 23 \) $0$ $\Z/2\Z$ $1$ $[1, 0, 0, 8790, 1010922]$ \(y^2+xy=x^3+8790x+1010922\) 2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 16.48.0-16.e.2.5, 24.48.0-24.bn.1.7, $\ldots$ $[ ]$
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