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Results (23 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
72.2-a1 72.2-a \(\Q(\sqrt{-2}) \) \( 2^{3} \cdot 3^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.817673508$ 0.642644632 \( \frac{207646}{6561} \) \( \bigl[a\) , \( 1\) , \( a\) , \( 5\) , \( 23\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+5{x}+23$
144.2-a1 144.2-a \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 3^{2} \) 0 $\Z/2\Z\oplus\Z/8\Z$ $\mathrm{SU}(2)$ $1$ $1.817673508$ 1.285289264 \( \frac{207646}{6561} \) \( \bigl[a\) , \( 0\) , \( a\) , \( 5\) , \( -22\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+5{x}-22$
648.3-a1 648.3-a \(\Q(\sqrt{-2}) \) \( 2^{3} \cdot 3^{4} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.079273864$ $0.605891169$ 1.849572148 \( \frac{207646}{6561} \) \( \bigl[a\) , \( -1\) , \( a\) , \( 37\) , \( -607\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+37{x}-607$
1296.3-b1 1296.3-b \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 3^{4} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.605891169$ 1.713719018 \( \frac{207646}{6561} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( 36\) , \( 572\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+36{x}+572$
6912.2-a1 6912.2-a \(\Q(\sqrt{-2}) \) \( 2^{8} \cdot 3^{3} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.859743848$ $0.524717144$ 2.760090861 \( \frac{207646}{6561} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 32 a - 16\) , \( 180 a - 900\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(32a-16\right){x}+180a-900$
6912.2-n1 6912.2-n \(\Q(\sqrt{-2}) \) \( 2^{8} \cdot 3^{3} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.524717144$ 2.968248410 \( \frac{207646}{6561} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 32 a - 16\) , \( -180 a + 900\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(32a-16\right){x}-180a+900$
6912.3-a1 6912.3-a \(\Q(\sqrt{-2}) \) \( 2^{8} \cdot 3^{3} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.859743848$ $0.524717144$ 2.760090861 \( \frac{207646}{6561} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -32 a - 16\) , \( -180 a - 900\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-32a-16\right){x}-180a-900$
6912.3-n1 6912.3-n \(\Q(\sqrt{-2}) \) \( 2^{8} \cdot 3^{3} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.524717144$ 2.968248410 \( \frac{207646}{6561} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -32 a - 16\) , \( 180 a + 900\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-32a-16\right){x}+180a+900$
9216.2-m1 9216.2-m \(\Q(\sqrt{-2}) \) \( 2^{10} \cdot 3^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.642644632$ 1.817673508 \( \frac{207646}{6561} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -32\) , \( -360 a\bigr] \) ${y}^2={x}^{3}+a{x}^{2}-32{x}-360a$
9216.2-o1 9216.2-o \(\Q(\sqrt{-2}) \) \( 2^{10} \cdot 3^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.642644632$ 1.817673508 \( \frac{207646}{6561} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -32\) , \( 360 a\bigr] \) ${y}^2={x}^{3}-a{x}^{2}-32{x}+360a$
20808.4-c1 20808.4-c \(\Q(\sqrt{-2}) \) \( 2^{3} \cdot 3^{2} \cdot 17^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.440850580$ 2.493827480 \( \frac{207646}{6561} \) \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -46 a + 4\) , \( -808 a - 1016\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-46a+4\right){x}-808a-1016$
20808.6-c1 20808.6-c \(\Q(\sqrt{-2}) \) \( 2^{3} \cdot 3^{2} \cdot 17^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.440850580$ 2.493827480 \( \frac{207646}{6561} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 46 a + 4\) , \( 808 a - 1016\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(46a+4\right){x}+808a-1016$
26136.4-d1 26136.4-d \(\Q(\sqrt{-2}) \) \( 2^{3} \cdot 3^{3} \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.766583000$ $0.316416343$ 5.488492471 \( \frac{207646}{6561} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 31 a - 121\) , \( -2488 a - 2074\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(31a-121\right){x}-2488a-2074$
26136.6-i1 26136.6-i \(\Q(\sqrt{-2}) \) \( 2^{3} \cdot 3^{3} \cdot 11^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.316416343$ 3.579842277 \( \frac{207646}{6561} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 78 a + 66\) , \( -2936 a - 46\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(78a+66\right){x}-2936a-46$
26136.7-i1 26136.7-i \(\Q(\sqrt{-2}) \) \( 2^{3} \cdot 3^{3} \cdot 11^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.316416343$ 3.579842277 \( \frac{207646}{6561} \) \( \bigl[a\) , \( a + 1\) , \( 0\) , \( -78 a + 66\) , \( 2936 a - 46\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-78a+66\right){x}+2936a-46$
26136.9-d1 26136.9-d \(\Q(\sqrt{-2}) \) \( 2^{3} \cdot 3^{3} \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.766583000$ $0.316416343$ 5.488492471 \( \frac{207646}{6561} \) \( \bigl[a\) , \( a + 1\) , \( a\) , \( -31 a - 121\) , \( 2488 a - 2074\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-31a-121\right){x}+2488a-2074$
27648.2-v1 27648.2-v \(\Q(\sqrt{-2}) \) \( 2^{10} \cdot 3^{3} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $4.030505696$ $0.371031051$ 4.229750882 \( \frac{207646}{6561} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -62 a + 31\) , \( 1737 a + 751\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-62a+31\right){x}+1737a+751$
27648.2-bb1 27648.2-bb \(\Q(\sqrt{-2}) \) \( 2^{10} \cdot 3^{3} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.371031051$ 2.098868579 \( \frac{207646}{6561} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -62 a + 31\) , \( -1737 a - 751\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-62a+31\right){x}-1737a-751$
27648.3-f1 27648.3-f \(\Q(\sqrt{-2}) \) \( 2^{10} \cdot 3^{3} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $4.030505696$ $0.371031051$ 4.229750882 \( \frac{207646}{6561} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 62 a + 31\) , \( -1737 a + 751\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(62a+31\right){x}-1737a+751$
27648.3-bp1 27648.3-bp \(\Q(\sqrt{-2}) \) \( 2^{10} \cdot 3^{3} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.371031051$ 2.098868579 \( \frac{207646}{6561} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 62 a + 31\) , \( 1737 a - 751\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(62a+31\right){x}+1737a-751$
41616.4-c1 41616.4-c \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 3^{2} \cdot 17^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.518025393$ $0.440850580$ 5.167463847 \( \frac{207646}{6561} \) \( \bigl[a\) , \( a - 1\) , \( a\) , \( -48 a + 5\) , \( 855 a + 1013\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-48a+5\right){x}+855a+1013$
41616.6-g1 41616.6-g \(\Q(\sqrt{-2}) \) \( 2^{4} \cdot 3^{2} \cdot 17^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.518025393$ $0.440850580$ 5.167463847 \( \frac{207646}{6561} \) \( \bigl[a\) , \( -a - 1\) , \( a\) , \( 48 a + 5\) , \( -855 a + 1013\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(48a+5\right){x}-855a+1013$
45000.2-i1 45000.2-i \(\Q(\sqrt{-2}) \) \( 2^{3} \cdot 3^{2} \cdot 5^{4} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.534270860$ $0.363534701$ 8.789665301 \( \frac{207646}{6561} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( 98\) , \( 2714\bigr] \) ${y}^2+a{x}{y}={x}^{3}+98{x}+2714$
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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.