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Results (14 matches)

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Label Class Base field Conductor norm Rank Torsion CM Sato-Tate Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
2401.1-a1 2401.1-a Q(5)\Q(\sqrt{5}) 74 7^{4} 0 trivial\mathsf{trivial} SU(2)\mathrm{SU}(2) 11 4.4449427304.444942730 1.987838820 162677523113838677 -162677523113838677 [ϕ+1 \bigl[\phi + 1 , ϕ1 -\phi - 1 , 1 1 , 41617ϕ41617 -41617 \phi - 41617 , 5859391ϕ+4394543] 5859391 \phi + 4394543\bigr] y2+(ϕ+1)xy+y=x3+(ϕ1)x2+(41617ϕ41617)x+5859391ϕ+4394543{y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-41617\phi-41617\right){x}+5859391\phi+4394543
2401.1-a2 2401.1-a Q(5)\Q(\sqrt{5}) 74 7^{4} 0 trivial\mathsf{trivial} SU(2)\mathrm{SU}(2) 11 4.4449427304.444942730 1.987838820 9317 -9317 [ϕ+1 \bigl[\phi + 1 , ϕ1 -\phi - 1 , 1 1 , 2ϕ2 -2 \phi - 2 , ϕ1] -\phi - 1\bigr] y2+(ϕ+1)xy+y=x3+(ϕ1)x2+(2ϕ2)xϕ1{y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-2\phi-2\right){x}-\phi-1
2401.1-b1 2401.1-b Q(5)\Q(\sqrt{5}) 74 7^{4} 0 trivial\mathsf{trivial} 35-35 N(U(1))N(\mathrm{U}(1)) 11 2.4377555092.437755509 2.180394812 52756480a32604160 -52756480 a - 32604160 [0 \bigl[0 , 1 -1 , 1 1 , 14ϕ+19 -14 \phi + 19 , 21ϕ36] 21 \phi - 36\bigr] y2+y=x3x2+(14ϕ+19)x+21ϕ36{y}^2+{y}={x}^{3}-{x}^{2}+\left(-14\phi+19\right){x}+21\phi-36
2401.1-b2 2401.1-b Q(5)\Q(\sqrt{5}) 74 7^{4} 0 trivial\mathsf{trivial} 35-35 N(U(1))N(\mathrm{U}(1)) 11 2.4377555092.437755509 2.180394812 52756480a32604160 -52756480 a - 32604160 [0 \bigl[0 , 1 1 , 1 1 , 686ϕ+915 -686 \phi + 915 , 5831ϕ+10420] -5831 \phi + 10420\bigr] y2+y=x3+x2+(686ϕ+915)x5831ϕ+10420{y}^2+{y}={x}^{3}+{x}^{2}+\left(-686\phi+915\right){x}-5831\phi+10420
2401.1-b3 2401.1-b Q(5)\Q(\sqrt{5}) 74 7^{4} 0 trivial\mathsf{trivial} 35-35 N(U(1))N(\mathrm{U}(1)) 11 2.4377555092.437755509 2.180394812 52756480a85360640 52756480 a - 85360640 [0 \bigl[0 , 1 -1 , 1 1 , 14ϕ+5 14 \phi + 5 , 21ϕ15] -21 \phi - 15\bigr] y2+y=x3x2+(14ϕ+5)x21ϕ15{y}^2+{y}={x}^{3}-{x}^{2}+\left(14\phi+5\right){x}-21\phi-15
2401.1-b4 2401.1-b Q(5)\Q(\sqrt{5}) 74 7^{4} 0 trivial\mathsf{trivial} 35-35 N(U(1))N(\mathrm{U}(1)) 11 2.4377555092.437755509 2.180394812 52756480a85360640 52756480 a - 85360640 [0 \bigl[0 , 1 1 , 1 1 , 686ϕ+229 686 \phi + 229 , 5831ϕ+4589] 5831 \phi + 4589\bigr] y2+y=x3+x2+(686ϕ+229)x+5831ϕ+4589{y}^2+{y}={x}^{3}+{x}^{2}+\left(686\phi+229\right){x}+5831\phi+4589
2401.1-c1 2401.1-c Q(5)\Q(\sqrt{5}) 74 7^{4} 0 trivial\mathsf{trivial} SU(2)\mathrm{SU}(2) 11 0.0039903200.003990320 2.443015397 162677523113838677 -162677523113838677 [ϕ+1 \bigl[\phi + 1 , ϕ \phi , ϕ \phi , 2039213ϕ2039213 -2039213 \phi - 2039213 , 2007731903ϕ1505289124] -2007731903 \phi - 1505289124\bigr] y2+(ϕ+1)xy+ϕy=x3+ϕx2+(2039213ϕ2039213)x2007731903ϕ1505289124{y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\phi{x}^{2}+\left(-2039213\phi-2039213\right){x}-2007731903\phi-1505289124
2401.1-c2 2401.1-c Q(5)\Q(\sqrt{5}) 74 7^{4} 0 trivial\mathsf{trivial} SU(2)\mathrm{SU}(2) 11 5.4627484975.462748497 2.443015397 9317 -9317 [ϕ \bigl[\phi , ϕ1 \phi - 1 , ϕ \phi , 78ϕ157 78 \phi - 157 , 575ϕ+986] -575 \phi + 986\bigr] y2+ϕxy+ϕy=x3+(ϕ1)x2+(78ϕ157)x575ϕ+986{y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(78\phi-157\right){x}-575\phi+986
2401.1-d1 2401.1-d Q(5)\Q(\sqrt{5}) 74 7^{4} 0 trivial\mathsf{trivial} SU(2)\mathrm{SU}(2) 11 2.2003254092.200325409 1.968030875 288755302416807 -\frac{2887553024}{16807} [0 \bigl[0 , ϕ1 \phi - 1 , 1 1 , 1454ϕ1453 -1454 \phi - 1453 , 37868ϕ+28764] 37868 \phi + 28764\bigr] y2+y=x3+(ϕ1)x2+(1454ϕ1453)x+37868ϕ+28764{y}^2+{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-1454\phi-1453\right){x}+37868\phi+28764
2401.1-d2 2401.1-d Q(5)\Q(\sqrt{5}) 74 7^{4} 0 trivial\mathsf{trivial} SU(2)\mathrm{SU}(2) 11 2.2003254092.200325409 1.968030875 40967 \frac{4096}{7} [0 \bigl[0 , ϕ -\phi , 1 1 , 16ϕ+33 -16 \phi + 33 , 58ϕ106] 58 \phi - 106\bigr] y2+y=x3ϕx2+(16ϕ+33)x+58ϕ106{y}^2+{y}={x}^{3}-\phi{x}^{2}+\left(-16\phi+33\right){x}+58\phi-106
2401.1-e1 2401.1-e Q(5)\Q(\sqrt{5}) 74 7^{4} 0 Z/2Z\Z/2\Z 7-7 N(U(1))N(\mathrm{U}(1)) 11 3.7376941513.737694151 0.835773820 3375 -3375 [1 \bigl[1 , 1 -1 , 0 0 , 2 -2 , 1] -1\bigr] y2+xy=x3x22x1{y}^2+{x}{y}={x}^{3}-{x}^{2}-2{x}-1
2401.1-e2 2401.1-e Q(5)\Q(\sqrt{5}) 74 7^{4} 0 Z/2Z\Z/2\Z 7-7 N(U(1))N(\mathrm{U}(1)) 11 3.7376941513.737694151 0.835773820 3375 -3375 [1 \bigl[1 , 1 -1 , 0 0 , 107 -107 , 552] 552\bigr] y2+xy=x3x2107x+552{y}^2+{x}{y}={x}^{3}-{x}^{2}-107{x}+552
2401.1-e3 2401.1-e Q(5)\Q(\sqrt{5}) 74 7^{4} 0 Z/2Z\Z/2\Z 28-28 N(U(1))N(\mathrm{U}(1)) 11 3.7376941513.737694151 0.835773820 16581375 16581375 [1 \bigl[1 , 1 -1 , 0 0 , 37 -37 , 78] -78\bigr] y2+xy=x3x237x78{y}^2+{x}{y}={x}^{3}-{x}^{2}-37{x}-78
2401.1-e4 2401.1-e Q(5)\Q(\sqrt{5}) 74 7^{4} 0 Z/2Z\Z/2\Z 28-28 N(U(1))N(\mathrm{U}(1)) 11 3.7376941513.737694151 0.835773820 16581375 16581375 [1 \bigl[1 , 1 -1 , 0 0 , 1822 -1822 , 30393] 30393\bigr] y2+xy=x3x21822x+30393{y}^2+{x}{y}={x}^{3}-{x}^{2}-1822{x}+30393
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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.