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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-a7 28.2-a \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7 \) 0 $\Z/2\Z\oplus\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $2.626251405$ 0.330876576 \( \frac{9938375}{21952} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+4{x}-6$
896.2-b7 896.2-b \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 7 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.928520088$ 2.105685636 \( \frac{9938375}{21952} \) \( \bigl[a\) , \( 1\) , \( a\) , \( 22 a + 10\) , \( -98 a + 35\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(22a+10\right){x}-98a+35$
896.7-b7 896.7-b \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 7 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.928520088$ 2.105685636 \( \frac{9938375}{21952} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -24 a + 32\) , \( 97 a - 63\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-24a+32\right){x}+97a-63$
1568.2-b7 1568.2-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.496314864$ 2.251072633 \( \frac{9938375}{21952} \) \( \bigl[a\) , \( -a\) , \( a\) , \( 94 a - 62\) , \( 362 a - 885\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(94a-62\right){x}+362a-885$
1568.5-b7 1568.5-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.496314864$ 2.251072633 \( \frac{9938375}{21952} \) \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -96 a + 32\) , \( -363 a - 523\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-96a+32\right){x}-363a-523$
1792.5-b7 1792.5-b \(\Q(\sqrt{-7}) \) \( 2^{8} \cdot 7 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.169069055$ $0.656562851$ 2.320905398 \( \frac{9938375}{21952} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 72\) , \( 368\bigr] \) ${y}^2={x}^{3}-{x}^{2}+72{x}+368$
2268.2-b7 2268.2-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{4} \cdot 7 \) 0 $\Z/2\Z\oplus\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.875417135$ 3.970518914 \( \frac{9938375}{21952} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( 40\) , \( 155\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+40{x}+155$
6272.2-b7 6272.2-b \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $2.451474306$ $0.350947606$ 2.601420732 \( \frac{9938375}{21952} \) \( \bigl[a\) , \( a - 1\) , \( a\) , \( -158 a - 62\) , \( 201 a - 2495\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-158a-62\right){x}+201a-2495$
6272.7-b7 6272.7-b \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $2.451474306$ $0.350947606$ 2.601420732 \( \frac{9938375}{21952} \) \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 156 a - 221\) , \( -265 a - 2608\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(156a-221\right){x}-265a-2608$
7168.5-h7 7168.5-h \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 7 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.464260044$ 2.105685636 \( \frac{9938375}{21952} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 72 a - 144\) , \( 368 a + 736\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(72a-144\right){x}+368a+736$
7168.7-h7 7168.7-h \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 7 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.464260044$ 2.105685636 \( \frac{9938375}{21952} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -72 a - 72\) , \( -368 a + 1104\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-72a-72\right){x}-368a+1104$
17500.2-f7 17500.2-f \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.625416265$ $0.525250281$ 8.939617596 \( \frac{9938375}{21952} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 112\) , \( -719\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+112{x}-719$
23548.4-c7 23548.4-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7 \cdot 29^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.487682642$ 2.211920557 \( \frac{9938375}{21952} \) \( \bigl[1\) , \( -a\) , \( 1\) , \( 36 a - 140\) , \( -575 a - 190\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(36a-140\right){x}-575a-190$
23548.6-e7 23548.6-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7 \cdot 29^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.487682642$ 2.211920557 \( \frac{9938375}{21952} \) \( \bigl[1\) , \( a - 1\) , \( 1\) , \( -36 a - 104\) , \( 575 a - 765\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-36a-104\right){x}+575a-765$
23716.4-g7 23716.4-g \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.299289124$ 2.714895745 \( \frac{9938375}{21952} \) \( \bigl[1\) , \( a + 1\) , \( 1\) , \( 252 a - 32\) , \( -2737 a + 2777\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(252a-32\right){x}-2737a+2777$
23716.6-e7 23716.6-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.299289124$ 2.714895745 \( \frac{9938375}{21952} \) \( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -250 a + 219\) , \( 2988 a - 179\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-250a+219\right){x}+2988a-179$
27104.13-c7 27104.13-c \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7 \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.388759237$ $0.395922296$ 3.325124285 \( \frac{9938375}{21952} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -58 a + 211\) , \( 777 a - 1953\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-58a+211\right){x}+777a-1953$
27104.15-j7 27104.15-j \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7 \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.355160595$ $0.395922296$ 7.653290664 \( \frac{9938375}{21952} \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -22 a - 185\) , \( -1443 a + 1039\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-22a-185\right){x}-1443a+1039$
27104.4-j7 27104.4-j \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7 \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.355160595$ $0.395922296$ 7.653290664 \( \frac{9938375}{21952} \) \( \bigl[a\) , \( a\) , \( a\) , \( 22 a - 206\) , \( 1236 a - 241\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(22a-206\right){x}+1236a-241$
27104.6-c7 27104.6-c \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7 \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.388759237$ $0.395922296$ 3.325124285 \( \frac{9938375}{21952} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( 58 a + 153\) , \( -777 a - 1176\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(58a+153\right){x}-777a-1176$
28672.7-e7 28672.7-e \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $4.210170225$ $0.328281425$ 4.179140127 \( \frac{9938375}{21952} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 287\) , \( 3231\bigr] \) ${y}^2={x}^{3}+{x}^{2}+287{x}+3231$
28672.7-o7 28672.7-o \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.328281425$ 1.488944592 \( \frac{9938375}{21952} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 287\) , \( -3231\bigr] \) ${y}^2={x}^{3}-{x}^{2}+287{x}-3231$
38332.4-c7 38332.4-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7 \cdot 37^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.431753071$ 1.958247865 \( \frac{9938375}{21952} \) \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -108 a - 32\) , \( -23 a + 1305\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-108a-32\right){x}-23a+1305$
38332.6-c7 38332.6-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7 \cdot 37^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.431753071$ 1.958247865 \( \frac{9938375}{21952} \) \( \bigl[1\) , \( a\) , \( 1\) , \( 108 a - 140\) , \( 23 a + 1282\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(108a-140\right){x}+23a+1282$
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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.