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## Results (36 matches)

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Label Class Base field Conductor norm Rank Torsion CM Weierstrass equation
512.1-a1 512.1-a $$\Q(\sqrt{17})$$ $$2^{9}$$ $0$ $\Z/4\Z$ ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(5a+4\right){x}+30a+48$
512.1-a2 512.1-a $$\Q(\sqrt{17})$$ $$2^{9}$$ $0$ $\Z/2\Z$ ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-a+3\right){x}-2a+5$
512.1-a3 512.1-a $$\Q(\sqrt{17})$$ $$2^{9}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-5a-6\right){x}+10a+16$
512.1-a4 512.1-a $$\Q(\sqrt{17})$$ $$2^{9}$$ $0$ $\Z/2\Z$ ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-75a-116\right){x}+546a+852$
512.1-b1 512.1-b $$\Q(\sqrt{17})$$ $$2^{9}$$ $1$ $\Z/2\Z$ ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+2a{x}-a$
512.1-b2 512.1-b $$\Q(\sqrt{17})$$ $$2^{9}$$ $1$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-9a-14\right){x}$
512.1-b3 512.1-b $$\Q(\sqrt{17})$$ $$2^{9}$$ $1$ $\Z/2\Z$ ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-79a-124\right){x}-648a-1012$
512.1-b4 512.1-b $$\Q(\sqrt{17})$$ $$2^{9}$$ $1$ $\Z/4\Z$ ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-134a-209\right){x}+1065a+1663$
512.1-c1 512.1-c $$\Q(\sqrt{17})$$ $$2^{9}$$ $0$ $\Z/2\Z$ ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-9a-14\right){x}-520a-812$
512.1-c2 512.1-c $$\Q(\sqrt{17})$$ $$2^{9}$$ $0$ $\Z/2\Z$ ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3a-5\right){x}-2a-3$
512.1-d1 512.1-d $$\Q(\sqrt{17})$$ $$2^{9}$$ $0$ $\Z/2\Z$ ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(a+4\right){x}-2a-4$
512.1-d2 512.1-d $$\Q(\sqrt{17})$$ $$2^{9}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2={x}^{3}+a{x}^{2}+\left(9a-21\right){x}+8a-20$
512.1-d3 512.1-d $$\Q(\sqrt{17})$$ $$2^{9}$$ $0$ $\Z/2\Z$ ${y}^2={x}^{3}+a{x}^{2}+\left(124a-316\right){x}+1012a-2592$
512.1-d4 512.1-d $$\Q(\sqrt{17})$$ $$2^{9}$$ $0$ $\Z/2\Z$ ${y}^2={x}^{3}+a{x}^{2}+\left(59a-151\right){x}-378a+966$
512.1-e1 512.1-e $$\Q(\sqrt{17})$$ $$2^{9}$$ $0$ $\Z/2\Z$ ${y}^2={x}^{3}+{x}^{2}+8a+12$
512.1-e2 512.1-e $$\Q(\sqrt{17})$$ $$2^{9}$$ $0$ $\Z/2\Z$ ${y}^2={x}^{3}-{x}^{2}+\left(-768a-1200\right){x}-7764a-12124$
512.1-e3 512.1-e $$\Q(\sqrt{17})$$ $$2^{9}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(71a-178\right){x}+444a-1136$
512.1-e4 512.1-e $$\Q(\sqrt{17})$$ $$2^{9}$$ $0$ $\Z/4\Z$ ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(106a-273\right){x}-87a+223$
512.1-f1 512.1-f $$\Q(\sqrt{17})$$ $$2^{9}$$ $1$ $\Z/2\Z$ ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(5a-12\right){x}-50a+128$
512.1-f2 512.1-f $$\Q(\sqrt{17})$$ $$2^{9}$$ $1$ $\Z/2\Z$ ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(5a-60\right){x}-90a+144$
512.1-f3 512.1-f $$\Q(\sqrt{17})$$ $$2^{9}$$ $1$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-5a-10\right){x}+6a+16$
512.1-f4 512.1-f $$\Q(\sqrt{17})$$ $$2^{9}$$ $1$ $\Z/2\Z$ ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-90a-145\right){x}+633a+993$
512.1-g1 512.1-g $$\Q(\sqrt{17})$$ $$2^{9}$$ $1$ $\Z/2\Z$ ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-3a+12\right){x}-4a+12$
512.1-g2 512.1-g $$\Q(\sqrt{17})$$ $$2^{9}$$ $1$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-2\right){x}$
512.1-g3 512.1-g $$\Q(\sqrt{17})$$ $$2^{9}$$ $1$ $\Z/4\Z$ ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6a-17\right){x}+27a+49$
512.1-g4 512.1-g $$\Q(\sqrt{17})$$ $$2^{9}$$ $1$ $\Z/2\Z$ ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-31a-52\right){x}-108a-172$
512.1-h1 512.1-h $$\Q(\sqrt{17})$$ $$2^{9}$$ $1$ $\Z/2\Z$ ${y}^2={x}^{3}-a{x}^{2}+\left(a-1\right){x}-4$
512.1-h2 512.1-h $$\Q(\sqrt{17})$$ $$2^{9}$$ $1$ $\Z/2\Z$ ${y}^2={x}^{3}+a{x}^{2}+\left(7a-16\right){x}+22a-56$
512.1-i1 512.1-i $$\Q(\sqrt{17})$$ $$2^{9}$$ $1$ $\Z/2\Z$ ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(14a+24\right){x}+15a+24$
512.1-i2 512.1-i $$\Q(\sqrt{17})$$ $$2^{9}$$ $1$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2={x}^{3}-a{x}^{2}+\left(a-1\right){x}$
512.1-i3 512.1-i $$\Q(\sqrt{17})$$ $$2^{9}$$ $1$ $\Z/2\Z$ ${y}^2={x}^{3}-a{x}^{2}+\left(11a-31\right){x}-26a+66$
512.1-i4 512.1-i $$\Q(\sqrt{17})$$ $$2^{9}$$ $1$ $\Z/4\Z$ ${y}^2={x}^{3}-a{x}^{2}+\left(-4a+4\right){x}+16$
512.1-j1 512.1-j $$\Q(\sqrt{17})$$ $$2^{9}$$ $0$ $\Z/2\Z$ ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(97a-244\right){x}+752a-1928$
512.1-j2 512.1-j $$\Q(\sqrt{17})$$ $$2^{9}$$ $0$ $\Z/2\Z$ ${y}^2={x}^{3}-{x}^{2}+\left(-6a-9\right){x}-7a-11$
512.1-j3 512.1-j $$\Q(\sqrt{17})$$ $$2^{9}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(7a-14\right){x}+12a-32$
512.1-j4 512.1-j $$\Q(\sqrt{17})$$ $$2^{9}$$ $0$ $\Z/4\Z$ ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(17a-44\right){x}-36a+100$
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*The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.