## Results (40 matches)

Label Class Base field Conductor norm Rank Torsion CM Weierstrass equation
256.1-a1 256.1-a $$\Q(\sqrt{57})$$ $$2^{8}$$ $0$ $\mathsf{trivial}$ ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-10282063a-33672998\right){x}+34886965210a+114251923320$
256.1-a2 256.1-a $$\Q(\sqrt{57})$$ $$2^{8}$$ $0$ $\mathsf{trivial}$ ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(10282065a-43955062\right){x}-34876683146a+149094933468$
256.1-a3 256.1-a $$\Q(\sqrt{57})$$ $$2^{8}$$ $0$ $\mathsf{trivial}$ ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3823a-12518\right){x}+369018a+1208504$
256.1-a4 256.1-a $$\Q(\sqrt{57})$$ $$2^{8}$$ $0$ $\mathsf{trivial}$ ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(3825a-16342\right){x}-365194a+1561180$
256.1-b1 256.1-b $$\Q(\sqrt{57})$$ $$2^{8}$$ $1$ $\Z/2\Z$ ${y}^2={x}^{3}+{x}^{2}+\left(44320a-189464\right){x}+9682784a-41393100$
256.1-b2 256.1-b $$\Q(\sqrt{57})$$ $$2^{8}$$ $1$ $\Z/2\Z$ ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a+10\right){x}+204a-884$
256.1-c1 256.1-c $$\Q(\sqrt{57})$$ $$2^{8}$$ $0$ $\Z/2\Z$ ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(1461a-6246\right){x}+57028a-243796$
256.1-c2 256.1-c $$\Q(\sqrt{57})$$ $$2^{8}$$ $0$ $\Z/2\Z$ ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(21a-86\right){x}+20a-84$
256.1-c3 256.1-c $$\Q(\sqrt{57})$$ $$2^{8}$$ $0$ $\Z/2\Z$ ${y}^2={x}^{3}-a{x}^{2}+\left(-21a-65\right){x}-20a-64$
256.1-c4 256.1-c $$\Q(\sqrt{57})$$ $$2^{8}$$ $0$ $\Z/2\Z$ ${y}^2={x}^{3}-a{x}^{2}+\left(-1461a-4785\right){x}-57028a-186768$
256.1-d1 256.1-d $$\Q(\sqrt{57})$$ $$2^{8}$$ $1$ $\mathsf{trivial}$ ${y}^2={x}^{3}+a{x}^{2}+\left(-21a-65\right){x}-140a-460$
256.1-e1 256.1-e $$\Q(\sqrt{57})$$ $$2^{8}$$ $1$ $\mathsf{trivial}$ ${y}^2={x}^{3}-a{x}^{2}+\left(2823a-12062\right){x}-158029a+675558$
256.1-f1 256.1-f $$\Q(\sqrt{57})$$ $$2^{8}$$ $1$ $\mathsf{trivial}$ ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(21a-86\right){x}+140a-600$
256.1-g1 256.1-g $$\Q(\sqrt{57})$$ $$2^{8}$$ $1$ $\mathsf{trivial}$ ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-2823a-9239\right){x}+158029a+517529$
256.1-h1 256.1-h $$\Q(\sqrt{57})$$ $$2^{8}$$ $0$ $\Z/2\Z$ $-3$ ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+5\right){x}+133a+436$
256.1-h2 256.1-h $$\Q(\sqrt{57})$$ $$2^{8}$$ $0$ $\Z/2\Z$ $-3$ ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+5\right){x}-133a+574$
256.1-h3 256.1-h $$\Q(\sqrt{57})$$ $$2^{8}$$ $0$ $\Z/2\Z$ $-12$ ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-199a-650\right){x}+3294a+10788$
256.1-h4 256.1-h $$\Q(\sqrt{57})$$ $$2^{8}$$ $0$ $\Z/2\Z$ $-12$ ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(201a-850\right){x}-3094a+13232$
256.1-i1 256.1-i $$\Q(\sqrt{57})$$ $$2^{8}$$ $0$ $\mathsf{trivial}$ $-3$ ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+5\right){x}+93a-403$
256.1-i2 256.1-i $$\Q(\sqrt{57})$$ $$2^{8}$$ $0$ $\mathsf{trivial}$ $-3$ ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+5\right){x}-12213a-39997$
256.1-j1 256.1-j $$\Q(\sqrt{57})$$ $$2^{8}$$ $1$ $\Z/2\Z$ ${y}^2={x}^{3}-a{x}^{2}+\left(3a+7\right){x}-204a-680$
256.1-j2 256.1-j $$\Q(\sqrt{57})$$ $$2^{8}$$ $1$ $\Z/2\Z$ ${y}^2={x}^{3}+{x}^{2}+\left(-44320a-145144\right){x}-9682784a-31710316$
256.1-k1 256.1-k $$\Q(\sqrt{57})$$ $$2^{8}$$ $1$ $\mathsf{trivial}$ ${y}^2={x}^{3}-a{x}^{2}+\left(2395a+7847\right){x}-24172a-79160$
256.1-l1 256.1-l $$\Q(\sqrt{57})$$ $$2^{8}$$ $0$ $\mathsf{trivial}$ $-3$ ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+5\right){x}+12213a-52215$
256.1-l2 256.1-l $$\Q(\sqrt{57})$$ $$2^{8}$$ $0$ $\mathsf{trivial}$ $-3$ ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+5\right){x}-93a-305$
256.1-m1 256.1-m $$\Q(\sqrt{57})$$ $$2^{8}$$ $1$ $\Z/2\Z$ ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(77309a-330486\right){x}-22623164a+96712152$
256.1-m2 256.1-m $$\Q(\sqrt{57})$$ $$2^{8}$$ $1$ $\Z/2\Z$ ${y}^2={x}^{3}+a{x}^{2}+\left(27a-113\right){x}-188a+804$
256.1-n1 256.1-n $$\Q(\sqrt{57})$$ $$2^{8}$$ $1$ $\mathsf{trivial}$ ${y}^2={x}^{3}-{x}^{2}+\left(4a-17\right){x}+40a-171$
256.1-o1 256.1-o $$\Q(\sqrt{57})$$ $$2^{8}$$ $1$ $\mathsf{trivial}$ ${y}^2={x}^{3}-{x}^{2}+\left(-4a-13\right){x}-40a-131$
256.1-p1 256.1-p $$\Q(\sqrt{57})$$ $$2^{8}$$ $1$ $\mathsf{trivial}$ ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-2395a+10242\right){x}+24172a-103332$
256.1-q1 256.1-q $$\Q(\sqrt{57})$$ $$2^{8}$$ $1$ $\Z/2\Z$ ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-27a-86\right){x}+188a+616$
256.1-q2 256.1-q $$\Q(\sqrt{57})$$ $$2^{8}$$ $1$ $\Z/2\Z$ ${y}^2={x}^{3}+a{x}^{2}+\left(-77309a-253177\right){x}+22623164a+74088988$
256.1-r1 256.1-r $$\Q(\sqrt{57})$$ $$2^{8}$$ $0$ $\mathsf{trivial}$ ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(1142337a-4884238\right){x}+1290582430a-5517144100$
256.1-r2 256.1-r $$\Q(\sqrt{57})$$ $$2^{8}$$ $0$ $\mathsf{trivial}$ ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1142335a-3741902\right){x}-1289440094a-4222819768$
256.1-r3 256.1-r $$\Q(\sqrt{57})$$ $$2^{8}$$ $0$ $\mathsf{trivial}$ ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-3423a+14642\right){x}-190018a+812316$
256.1-r4 256.1-r $$\Q(\sqrt{57})$$ $$2^{8}$$ $0$ $\mathsf{trivial}$ ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(3425a+11218\right){x}+186594a+611080$
256.1-s1 256.1-s $$\Q(\sqrt{57})$$ $$2^{8}$$ $0$ $\Z/2\Z$ ${y}^2={x}^{3}+a{x}^{2}+\left(-47365a-155113\right){x}+11028284a+36116716$
256.1-s2 256.1-s $$\Q(\sqrt{57})$$ $$2^{8}$$ $0$ $\Z/2\Z$ ${y}^2={x}^{3}+a{x}^{2}+\left(2395a+7847\right){x}+72492a+237404$
256.1-s3 256.1-s $$\Q(\sqrt{57})$$ $$2^{8}$$ $0$ $\Z/2\Z$ ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2395a+10242\right){x}-72492a+309896$
256.1-s4 256.1-s $$\Q(\sqrt{57})$$ $$2^{8}$$ $0$ $\Z/2\Z$ ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(47365a-202478\right){x}-11028284a+47145000$