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Results (24 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
28.2-a6 28.2-a \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7 \) 0 $\Z/2\Z\oplus\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $7.878754216$ 0.330876576 \( -\frac{15625}{28} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}$
896.2-b6 896.2-b \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 7 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.785560266$ 2.105685636 \( -\frac{15625}{28} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -3 a\) , \( 4 a - 1\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-3a{x}+4a-1$
896.7-b6 896.7-b \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 7 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.785560266$ 2.105685636 \( -\frac{15625}{28} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( a - 3\) , \( -5 a + 3\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(a-3\right){x}-5a+3$
1568.2-b6 1568.2-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.488944592$ 2.251072633 \( -\frac{15625}{28} \) \( \bigl[a\) , \( -a\) , \( a\) , \( -11 a + 8\) , \( -16 a + 39\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-11a+8\right){x}-16a+39$
1568.5-b6 1568.5-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.488944592$ 2.251072633 \( -\frac{15625}{28} \) \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 9 a - 3\) , \( 15 a + 23\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(9a-3\right){x}+15a+23$
1792.5-b6 1792.5-b \(\Q(\sqrt{-7}) \) \( 2^{8} \cdot 7 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.389689685$ $1.969688554$ 2.320905398 \( -\frac{15625}{28} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -8\) , \( -16\bigr] \) ${y}^2={x}^{3}-{x}^{2}-8{x}-16$
2268.2-b6 2268.2-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.626251405$ 3.970518914 \( -\frac{15625}{28} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -5\) , \( -7\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-5{x}-7$
6272.2-b6 6272.2-b \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.817158102$ $1.052842818$ 2.601420732 \( -\frac{15625}{28} \) \( \bigl[a\) , \( a - 1\) , \( a\) , \( 17 a + 8\) , \( -9 a + 109\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(17a+8\right){x}-9a+109$
6272.7-b6 6272.7-b \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.817158102$ $1.052842818$ 2.601420732 \( -\frac{15625}{28} \) \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -19 a + 24\) , \( 15 a + 136\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-19a+24\right){x}+15a+136$
7168.5-h6 7168.5-h \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 7 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.392780133$ 2.105685636 \( -\frac{15625}{28} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -8 a + 16\) , \( -16 a - 32\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-8a+16\right){x}-16a-32$
7168.7-h6 7168.7-h \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 7 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.392780133$ 2.105685636 \( -\frac{15625}{28} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 8 a + 8\) , \( 16 a - 48\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(8a+8\right){x}+16a-48$
17500.2-f6 17500.2-f \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.876248795$ $1.575750843$ 8.939617596 \( -\frac{15625}{28} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -13\) , \( 31\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-13{x}+31$
23548.4-c6 23548.4-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7 \cdot 29^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.463047928$ 2.211920557 \( -\frac{15625}{28} \) \( \bigl[1\) , \( -a\) , \( 1\) , \( -4 a + 15\) , \( 25 a + 8\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-4a+15\right){x}+25a+8$
23548.6-e6 23548.6-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7 \cdot 29^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.463047928$ 2.211920557 \( -\frac{15625}{28} \) \( \bigl[1\) , \( a - 1\) , \( 1\) , \( 4 a + 11\) , \( -25 a + 33\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(4a+11\right){x}-25a+33$
23716.4-g6 23716.4-g \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.897867372$ 2.714895745 \( -\frac{15625}{28} \) \( \bigl[1\) , \( a + 1\) , \( 1\) , \( -28 a + 3\) , \( 119 a - 121\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-28a+3\right){x}+119a-121$
23716.6-e6 23716.6-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.897867372$ 2.714895745 \( -\frac{15625}{28} \) \( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 30 a - 26\) , \( -148 a + 24\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(30a-26\right){x}-148a+24$
27104.13-c6 27104.13-c \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7 \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.462919745$ $1.187766888$ 3.325124285 \( -\frac{15625}{28} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 7 a - 24\) , \( -38 a + 100\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(7a-24\right){x}-38a+100$
27104.15-j6 27104.15-j \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7 \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.065481787$ $1.187766888$ 7.653290664 \( -\frac{15625}{28} \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 3 a + 20\) , \( 77 a - 49\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3a+20\right){x}+77a-49$
27104.4-j6 27104.4-j \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7 \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.065481787$ $1.187766888$ 7.653290664 \( -\frac{15625}{28} \) \( \bigl[a\) , \( a\) , \( a\) , \( -3 a + 24\) , \( -54 a + 11\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-3a+24\right){x}-54a+11$
27104.6-c6 27104.6-c \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7 \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.462919745$ $1.187766888$ 3.325124285 \( -\frac{15625}{28} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -7 a - 17\) , \( 38 a + 62\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-7a-17\right){x}+38a+62$
28672.7-e6 28672.7-e \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.403390075$ $0.984844277$ 4.179140127 \( -\frac{15625}{28} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -33\) , \( -161\bigr] \) ${y}^2={x}^{3}+{x}^{2}-33{x}-161$
28672.7-o6 28672.7-o \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.984844277$ 1.488944592 \( -\frac{15625}{28} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -33\) , \( 161\bigr] \) ${y}^2={x}^{3}-{x}^{2}-33{x}+161$
38332.4-c6 38332.4-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7 \cdot 37^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.295259214$ 1.958247865 \( -\frac{15625}{28} \) \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 12 a + 3\) , \( a - 57\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(12a+3\right){x}+a-57$
38332.6-c6 38332.6-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7 \cdot 37^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.295259214$ 1.958247865 \( -\frac{15625}{28} \) \( \bigl[1\) , \( a\) , \( 1\) , \( -12 a + 15\) , \( -a - 56\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-12a+15\right){x}-a-56$
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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.