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Results (36 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
2592.3-a1 2592.3-a \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.240339345$ $0.781788099$ 2.742676397 \( -\frac{1056226562}{6561} a - \frac{605268760}{6561} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -45 a + 199\) , \( 747 a + 424\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-45a+199\right){x}+747a+424$
2592.3-a2 2592.3-a \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.240339345$ $0.781788099$ 2.742676397 \( \frac{1056226562}{6561} a - \frac{605268760}{6561} \) \( \bigl[a\) , \( -1\) , \( a\) , \( 45 a + 199\) , \( -747 a + 424\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(45a+199\right){x}-747a+424$
2592.3-a3 2592.3-a \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.620169672$ $1.563576199$ 2.742676397 \( \frac{97336}{81} \) \( \bigl[a\) , \( -1\) , \( a\) , \( 19\) , \( 10\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+19{x}+10$
2592.3-a4 2592.3-a \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.310084836$ $1.563576199$ 2.742676397 \( \frac{21952}{9} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -21\) , \( -20\bigr] \) ${y}^2={x}^{3}-21{x}-20$
2592.3-a5 2592.3-a \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.620169672$ $1.563576199$ 2.742676397 \( \frac{140608}{3} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -39\) , \( -92\bigr] \) ${y}^2={x}^{3}-39{x}-92$
2592.3-a6 2592.3-a \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.620169672$ $1.563576199$ 2.742676397 \( \frac{7301384}{3} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -72\) , \( 275\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}-72{x}+275$
2592.3-b1 2592.3-b \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.558915471$ 1.580851681 \( -\frac{15347957750}{81} a - \frac{35138997500}{81} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( 720 a - 288\) , \( 8374 a + 4948\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(720a-288\right){x}+8374a+4948$
2592.3-b2 2592.3-b \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.558915471$ 1.580851681 \( \frac{15347957750}{81} a - \frac{35138997500}{81} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -720 a - 287\) , \( 9094 a - 4659\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-720a-287\right){x}+9094a-4659$
2592.3-b3 2592.3-b \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.117830943$ 1.580851681 \( -\frac{8000}{81} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 15\) , \( -68 a\bigr] \) ${y}^2={x}^{3}+15{x}-68a$
2592.3-b4 2592.3-b \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.558915471$ 1.580851681 \( -\frac{56997401750}{43046721} a + \frac{87757407500}{43046721} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -90 a - 107\) , \( -356 a - 339\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-90a-107\right){x}-356a-339$
2592.3-b5 2592.3-b \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.558915471$ 1.580851681 \( \frac{56997401750}{43046721} a + \frac{87757407500}{43046721} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( 90 a - 108\) , \( -446 a + 448\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(90a-108\right){x}-446a+448$
2592.3-b6 2592.3-b \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.117830943$ 1.580851681 \( -\frac{100738000}{6561} a + \frac{45365000}{6561} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( 45 a - 18\) , \( 112 a + 88\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(45a-18\right){x}+112a+88$
2592.3-b7 2592.3-b \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.117830943$ 1.580851681 \( \frac{100738000}{6561} a + \frac{45365000}{6561} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -45 a - 17\) , \( 157 a - 69\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-45a-17\right){x}+157a-69$
2592.3-b8 2592.3-b \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.117830943$ 1.580851681 \( \frac{2744000}{9} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 105\) , \( 292 a\bigr] \) ${y}^2={x}^{3}+105{x}+292a$
2592.3-c1 2592.3-c \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) $1$ $\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $0.250591196$ $3.969390382$ 2.813420292 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -3\) , \( 0\bigr] \) ${y}^2={x}^{3}-3{x}$
2592.3-c2 2592.3-c \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) $1$ $\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $0.125295598$ $3.969390382$ 2.813420292 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 3\) , \( 0\bigr] \) ${y}^2={x}^{3}+3{x}$
2592.3-d1 2592.3-d \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) $1$ $\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $0.444312937$ $2.291728606$ 2.880030840 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 9\) , \( 0\bigr] \) ${y}^2={x}^{3}+9{x}$
2592.3-d2 2592.3-d \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $0.222156468$ $2.291728606$ 2.880030840 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -9\) , \( 0\bigr] \) ${y}^2={x}^{3}-9{x}$
2592.3-d3 2592.3-d \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) $1$ $\Z/2\Z$ $-16$ $N(\mathrm{U}(1))$ $0.444312937$ $2.291728606$ 2.880030840 \( 287496 \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -24\) , \( -35\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}-24{x}-35$
2592.3-d4 2592.3-d \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) $1$ $\Z/2\Z$ $-16$ $N(\mathrm{U}(1))$ $0.444312937$ $2.291728606$ 2.880030840 \( 287496 \) \( \bigl[a\) , \( -1\) , \( a\) , \( -23\) , \( 60\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-23{x}+60$
2592.3-e1 2592.3-e \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $1$ $1.323130127$ 1.871188571 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -27\) , \( 0\bigr] \) ${y}^2={x}^{3}-27{x}$
2592.3-e2 2592.3-e \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $1$ $1.323130127$ 1.871188571 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 27\) , \( 0\bigr] \) ${y}^2={x}^{3}+27{x}$
2592.3-f1 2592.3-f \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.558915471$ 1.580851681 \( -\frac{15347957750}{81} a - \frac{35138997500}{81} \) \( \bigl[a\) , \( -1\) , \( a\) , \( 720 a - 287\) , \( -9094 a - 4659\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(720a-287\right){x}-9094a-4659$
2592.3-f2 2592.3-f \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.558915471$ 1.580851681 \( \frac{15347957750}{81} a - \frac{35138997500}{81} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -720 a - 288\) , \( -8374 a + 4948\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-720a-288\right){x}-8374a+4948$
2592.3-f3 2592.3-f \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.117830943$ 1.580851681 \( -\frac{8000}{81} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 15\) , \( 68 a\bigr] \) ${y}^2={x}^{3}+15{x}+68a$
2592.3-f4 2592.3-f \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.558915471$ 1.580851681 \( -\frac{56997401750}{43046721} a + \frac{87757407500}{43046721} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -90 a - 108\) , \( 446 a + 448\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-90a-108\right){x}+446a+448$
2592.3-f5 2592.3-f \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.558915471$ 1.580851681 \( \frac{56997401750}{43046721} a + \frac{87757407500}{43046721} \) \( \bigl[a\) , \( -1\) , \( a\) , \( 90 a - 107\) , \( 356 a - 339\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(90a-107\right){x}+356a-339$
2592.3-f6 2592.3-f \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.117830943$ 1.580851681 \( -\frac{100738000}{6561} a + \frac{45365000}{6561} \) \( \bigl[a\) , \( -1\) , \( a\) , \( 45 a - 17\) , \( -157 a - 69\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(45a-17\right){x}-157a-69$
2592.3-f7 2592.3-f \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.117830943$ 1.580851681 \( \frac{100738000}{6561} a + \frac{45365000}{6561} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -45 a - 18\) , \( -112 a + 88\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-45a-18\right){x}-112a+88$
2592.3-f8 2592.3-f \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.117830943$ 1.580851681 \( \frac{2744000}{9} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 105\) , \( -292 a\bigr] \) ${y}^2={x}^{3}+105{x}-292a$
2592.3-g1 2592.3-g \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.781788099$ 2.211230666 \( -\frac{1056226562}{6561} a - \frac{605268760}{6561} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -45 a + 198\) , \( -702 a - 621\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-45a+198\right){x}-702a-621$
2592.3-g2 2592.3-g \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.781788099$ 2.211230666 \( \frac{1056226562}{6561} a - \frac{605268760}{6561} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( 45 a + 198\) , \( 702 a - 621\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(45a+198\right){x}+702a-621$
2592.3-g3 2592.3-g \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.563576199$ 2.211230666 \( \frac{97336}{81} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( 18\) , \( -27\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+18{x}-27$
2592.3-g4 2592.3-g \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.563576199$ 2.211230666 \( \frac{21952}{9} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -21\) , \( 20\bigr] \) ${y}^2={x}^{3}-21{x}+20$
2592.3-g5 2592.3-g \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.563576199$ 2.211230666 \( \frac{140608}{3} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -39\) , \( 92\bigr] \) ${y}^2={x}^{3}-39{x}+92$
2592.3-g6 2592.3-g \(\Q(\sqrt{-2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $1.563576199$ 2.211230666 \( \frac{7301384}{3} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -71\) , \( -202\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-71{x}-202$
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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.