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Results (28 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
2592.1-a1 2592.1-a \(\Q(\sqrt{2}) \) \( 2^{5} \cdot 3^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.620169672$ $2.672415791$ 2.343848582 \( \frac{97336}{81} \) \( \bigl[a\) , \( 1\) , \( a\) , \( 17\) , \( -10\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+17{x}-10$
2592.1-a2 2592.1-a \(\Q(\sqrt{2}) \) \( 2^{5} \cdot 3^{4} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.240339345$ $5.344831582$ 2.343848582 \( \frac{21952}{9} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -21\) , \( -20\bigr] \) ${y}^2={x}^{3}-21{x}-20$
2592.1-a3 2592.1-a \(\Q(\sqrt{2}) \) \( 2^{5} \cdot 3^{4} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.620169672$ $10.68966316$ 2.343848582 \( \frac{140608}{3} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -39\) , \( 92\bigr] \) ${y}^2={x}^{3}-39{x}+92$
2592.1-a4 2592.1-a \(\Q(\sqrt{2}) \) \( 2^{5} \cdot 3^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.620169672$ $2.672415791$ 2.343848582 \( \frac{7301384}{3} \) \( \bigl[a\) , \( 1\) , \( 0\) , \( -72\) , \( -275\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}-72{x}-275$
2592.1-b1 2592.1-b \(\Q(\sqrt{2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.235661887$ 1.580851681 \( -\frac{8000}{81} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -15\) , \( -68 a\bigr] \) ${y}^2={x}^{3}-15{x}-68a$
2592.1-b2 2592.1-b \(\Q(\sqrt{2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $8.942647551$ 1.580851681 \( -\frac{98115010000}{3} a + 46251861000 \) \( \bigl[a\) , \( 1\) , \( 0\) , \( -450 a - 648\) , \( -342 a - 473\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-450a-648\right){x}-342a-473$
2592.1-b3 2592.1-b \(\Q(\sqrt{2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.471323775$ 1.580851681 \( \frac{2744000}{9} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -105\) , \( -292 a\bigr] \) ${y}^2={x}^{3}-105{x}-292a$
2592.1-b4 2592.1-b \(\Q(\sqrt{2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.235661887$ 1.580851681 \( \frac{98115010000}{3} a + 46251861000 \) \( \bigl[a\) , \( 1\) , \( a\) , \( 450 a - 649\) , \( 108 a - 176\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(450a-649\right){x}+108a-176$
2592.1-c1 2592.1-c \(\Q(\sqrt{2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $1$ $5.292520510$ 1.871188571 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -27\) , \( 0\bigr] \) ${y}^2={x}^{3}-27{x}$
2592.1-c2 2592.1-c \(\Q(\sqrt{2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $1$ $2.646260255$ 1.871188571 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 27\) , \( 0\bigr] \) ${y}^2={x}^{3}+27{x}$
2592.1-d1 2592.1-d \(\Q(\sqrt{2}) \) \( 2^{5} \cdot 3^{4} \) $1$ $\Z/2\Z$ $-64$ $N(\mathrm{U}(1))$ $3.554503499$ $1.145864303$ 2.880030840 \( -29071392966 a + 41113158120 \) \( \bigl[a\) , \( 1\) , \( a\) , \( 135 a - 205\) , \( 1107 a - 1662\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(135a-205\right){x}+1107a-1662$
2592.1-d2 2592.1-d \(\Q(\sqrt{2}) \) \( 2^{5} \cdot 3^{4} \) $1$ $\Z/2\Z$ $-64$ $N(\mathrm{U}(1))$ $0.222156468$ $9.166914424$ 2.880030840 \( -29071392966 a + 41113158120 \) \( \bigl[a\) , \( 1\) , \( 0\) , \( 135 a - 204\) , \( -972 a + 1457\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(135a-204\right){x}-972a+1457$
2592.1-d3 2592.1-d \(\Q(\sqrt{2}) \) \( 2^{5} \cdot 3^{4} \) $1$ $\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $0.444312937$ $4.583457212$ 2.880030840 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 9\) , \( 0\bigr] \) ${y}^2={x}^{3}+9{x}$
2592.1-d4 2592.1-d \(\Q(\sqrt{2}) \) \( 2^{5} \cdot 3^{4} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $0.888625874$ $9.166914424$ 2.880030840 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -9\) , \( 0\bigr] \) ${y}^2={x}^{3}-9{x}$
2592.1-d5 2592.1-d \(\Q(\sqrt{2}) \) \( 2^{5} \cdot 3^{4} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $-16$ $N(\mathrm{U}(1))$ $0.444312937$ $18.33382884$ 2.880030840 \( 287496 \) \( \bigl[a\) , \( 1\) , \( 0\) , \( -24\) , \( 35\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}-24{x}+35$
2592.1-d6 2592.1-d \(\Q(\sqrt{2}) \) \( 2^{5} \cdot 3^{4} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $-16$ $N(\mathrm{U}(1))$ $1.777251749$ $4.583457212$ 2.880030840 \( 287496 \) \( \bigl[a\) , \( 1\) , \( a\) , \( -25\) , \( -60\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-25{x}-60$
2592.1-d7 2592.1-d \(\Q(\sqrt{2}) \) \( 2^{5} \cdot 3^{4} \) $1$ $\Z/2\Z$ $-64$ $N(\mathrm{U}(1))$ $3.554503499$ $1.145864303$ 2.880030840 \( 29071392966 a + 41113158120 \) \( \bigl[a\) , \( 1\) , \( a\) , \( -135 a - 205\) , \( -1107 a - 1662\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-135a-205\right){x}-1107a-1662$
2592.1-d8 2592.1-d \(\Q(\sqrt{2}) \) \( 2^{5} \cdot 3^{4} \) $1$ $\Z/2\Z$ $-64$ $N(\mathrm{U}(1))$ $0.222156468$ $9.166914424$ 2.880030840 \( 29071392966 a + 41113158120 \) \( \bigl[a\) , \( 1\) , \( 0\) , \( -135 a - 204\) , \( 972 a + 1457\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-135a-204\right){x}+972a+1457$
2592.1-e1 2592.1-e \(\Q(\sqrt{2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.659266702$ 2.587492299 \( \frac{97336}{81} \) \( \bigl[a\) , \( 1\) , \( 0\) , \( 18\) , \( 27\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}+18{x}+27$
2592.1-e2 2592.1-e \(\Q(\sqrt{2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.318533405$ 2.587492299 \( \frac{21952}{9} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -21\) , \( 20\bigr] \) ${y}^2={x}^{3}-21{x}+20$
2592.1-e3 2592.1-e \(\Q(\sqrt{2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.659266702$ 2.587492299 \( \frac{140608}{3} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -39\) , \( -92\bigr] \) ${y}^2={x}^{3}-39{x}-92$
2592.1-e4 2592.1-e \(\Q(\sqrt{2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $14.63706681$ 2.587492299 \( \frac{7301384}{3} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -73\) , \( 202\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-73{x}+202$
2592.1-f1 2592.1-f \(\Q(\sqrt{2}) \) \( 2^{5} \cdot 3^{4} \) $1$ $\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $0.250591196$ $15.87756153$ 2.813420292 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -3\) , \( 0\bigr] \) ${y}^2={x}^{3}-3{x}$
2592.1-f2 2592.1-f \(\Q(\sqrt{2}) \) \( 2^{5} \cdot 3^{4} \) $1$ $\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $0.501182392$ $7.938780765$ 2.813420292 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 3\) , \( 0\bigr] \) ${y}^2={x}^{3}+3{x}$
2592.1-g1 2592.1-g \(\Q(\sqrt{2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.235661887$ 1.580851681 \( -\frac{8000}{81} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -15\) , \( 68 a\bigr] \) ${y}^2={x}^{3}-15{x}+68a$
2592.1-g2 2592.1-g \(\Q(\sqrt{2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.235661887$ 1.580851681 \( -\frac{98115010000}{3} a + 46251861000 \) \( \bigl[a\) , \( 1\) , \( a\) , \( -450 a - 649\) , \( -108 a - 176\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-450a-649\right){x}-108a-176$
2592.1-g3 2592.1-g \(\Q(\sqrt{2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.471323775$ 1.580851681 \( \frac{2744000}{9} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -105\) , \( 292 a\bigr] \) ${y}^2={x}^{3}-105{x}+292a$
2592.1-g4 2592.1-g \(\Q(\sqrt{2}) \) \( 2^{5} \cdot 3^{4} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $8.942647551$ 1.580851681 \( \frac{98115010000}{3} a + 46251861000 \) \( \bigl[a\) , \( 1\) , \( 0\) , \( 450 a - 648\) , \( 342 a - 473\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(450a-648\right){x}+342a-473$
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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.