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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-a12 28.2-a \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.437708567$ 0.330876576 \( \frac{2251439055699625}{25088} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-2731{x}-55146$
896.2-b12 896.2-b \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.154753348$ 2.105685636 \( \frac{2251439055699625}{25088} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -13653 a - 5460\) , \( -937478 a + 330875\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-13653a-5460\right){x}-937478a+330875$
896.7-b12 896.7-b \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.154753348$ 2.105685636 \( \frac{2251439055699625}{25088} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 13651 a - 19113\) , \( 937477 a - 606603\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(13651a-19113\right){x}+937477a-606603$
1568.2-b12 1568.2-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.082719144$ 2.251072633 \( \frac{2251439055699625}{25088} \) \( \bigl[a\) , \( -a\) , \( a\) , \( -57341 a + 38228\) , \( 3474182 a - 8492445\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-57341a+38228\right){x}+3474182a-8492445$
1568.5-b12 1568.5-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.082719144$ 2.251072633 \( \frac{2251439055699625}{25088} \) \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 57339 a - 19113\) , \( -3474183 a - 5018263\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(57339a-19113\right){x}-3474183a-5018263$
1792.5-b12 1792.5-b \(\Q(\sqrt{-7}) \) \( 2^{8} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $7.014414334$ $0.109427141$ 2.320905398 \( \frac{2251439055699625}{25088} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -43688\) , \( 3529328\bigr] \) ${y}^2={x}^{3}-{x}^{2}-43688{x}+3529328$
2268.2-b12 2268.2-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.145902855$ 3.970518914 \( \frac{2251439055699625}{25088} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -24575\) , \( 1488935\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-24575{x}+1488935$
6272.2-b12 6272.2-b \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $14.70884583$ $0.058491267$ 2.601420732 \( \frac{2251439055699625}{25088} \) \( \bigl[a\) , \( a - 1\) , \( a\) , \( 95567 a + 38228\) , \( 1930101 a - 23933255\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(95567a+38228\right){x}+1930101a-23933255$
6272.7-b12 6272.7-b \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $14.70884583$ $0.058491267$ 2.601420732 \( \frac{2251439055699625}{25088} \) \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -95569 a + 133794\) , \( -1891875 a - 21812018\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-95569a+133794\right){x}-1891875a-21812018$
7168.5-h12 7168.5-h \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 7 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $0.077376674$ 2.105685636 \( \frac{2251439055699625}{25088} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -43688 a + 87376\) , \( 3529328 a + 7058656\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-43688a+87376\right){x}+3529328a+7058656$
7168.7-h12 7168.7-h \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 7 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $0.077376674$ 2.105685636 \( \frac{2251439055699625}{25088} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 43688 a + 43688\) , \( -3529328 a + 10587984\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(43688a+43688\right){x}-3529328a+10587984$
17500.2-f12 17500.2-f \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.416944176$ $0.087541713$ 8.939617596 \( \frac{2251439055699625}{25088} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -68263\) , \( -6893219\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-68263{x}-6893219$
23548.4-c12 23548.4-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7 \cdot 29^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.081280440$ 2.211920557 \( \frac{2251439055699625}{25088} \) \( \bigl[1\) , \( -a\) , \( 1\) , \( -21844 a + 84645\) , \( -5514575 a - 1819810\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-21844a+84645\right){x}-5514575a-1819810$
23548.6-e12 23548.6-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7 \cdot 29^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.081280440$ 2.211920557 \( \frac{2251439055699625}{25088} \) \( \bigl[1\) , \( a - 1\) , \( 1\) , \( 21844 a + 62801\) , \( 5514575 a - 7334385\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(21844a+62801\right){x}+5514575a-7334385$
23716.4-g12 23716.4-g \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.049881520$ 2.714895745 \( \frac{2251439055699625}{25088} \) \( \bigl[1\) , \( a + 1\) , \( 1\) , \( -152908 a + 19113\) , \( -26249377 a + 26635397\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-152908a+19113\right){x}-26249377a+26635397$
23716.6-e12 23716.6-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.049881520$ 2.714895745 \( \frac{2251439055699625}{25088} \) \( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 152910 a - 133796\) , \( 26096468 a + 519816\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(152910a-133796\right){x}+26096468a+519816$
27104.13-c12 27104.13-c \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $8.332555422$ $0.065987049$ 3.325124285 \( \frac{2251439055699625}{25088} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 35497 a - 128334\) , \( 6857722 a - 16580828\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(35497a-128334\right){x}+6857722a-16580828$
27104.15-j12 27104.15-j \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.130963575$ $0.065987049$ 7.653290664 \( \frac{2251439055699625}{25088} \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 13653 a + 111950\) , \( -11730733 a + 9512909\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(13653a+111950\right){x}-11730733a+9512909$
27104.4-j12 27104.4-j \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.130963575$ $0.065987049$ 7.653290664 \( \frac{2251439055699625}{25088} \) \( \bigl[a\) , \( a\) , \( a\) , \( -13653 a + 125604\) , \( 11856336 a - 2316121\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-13653a+125604\right){x}+11856336a-2316121$
27104.6-c12 27104.6-c \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $8.332555422$ $0.065987049$ 3.325124285 \( \frac{2251439055699625}{25088} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -35497 a - 92837\) , \( -6857722 a - 9723106\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-35497a-92837\right){x}-6857722a-9723106$
28672.7-e12 28672.7-e \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $25.26102135$ $0.054713570$ 4.179140127 \( \frac{2251439055699625}{25088} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -174753\) , \( 28059871\bigr] \) ${y}^2={x}^{3}+{x}^{2}-174753{x}+28059871$
28672.7-o12 28672.7-o \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.054713570$ 1.488944592 \( \frac{2251439055699625}{25088} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -174753\) , \( -28059871\bigr] \) ${y}^2={x}^{3}-{x}^{2}-174753{x}-28059871$
38332.4-c12 38332.4-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7 \cdot 37^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.071958845$ 1.958247865 \( \frac{2251439055699625}{25088} \) \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 65532 a + 19113\) , \( -220583 a + 12518085\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(65532a+19113\right){x}-220583a+12518085$
38332.6-c12 38332.6-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7 \cdot 37^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.071958845$ 1.958247865 \( \frac{2251439055699625}{25088} \) \( \bigl[1\) , \( a\) , \( 1\) , \( -65532 a + 84645\) , \( 220583 a + 12297502\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-65532a+84645\right){x}+220583a+12297502$
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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.