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Results (18 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
12544.1-a1 12544.1-a \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 7^{2} \) $2$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.186222298$ $4.016295718$ 2.991695286 \( \frac{432}{7} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 2 i\bigr] \) ${y}^2={x}^{3}-{x}+2i$
12544.1-a2 12544.1-a \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 7^{2} \) $2$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.744889195$ $1.004073929$ 2.991695286 \( \frac{11090466}{2401} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 59\) , \( -138 i\bigr] \) ${y}^2={x}^{3}+59{x}-138i$
12544.1-a3 12544.1-a \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 7^{2} \) $2$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.744889195$ $2.008147859$ 2.991695286 \( \frac{740772}{49} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 19\) , \( 30 i\bigr] \) ${y}^2={x}^{3}+19{x}+30i$
12544.1-a4 12544.1-a \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 7^{2} \) $2$ $\Z/4\Z$ $\mathrm{SU}(2)$ $2.979556781$ $1.004073929$ 2.991695286 \( \frac{1443468546}{7} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 299\) , \( 1990 i\bigr] \) ${y}^2={x}^{3}+299{x}+1990i$
12544.1-b1 12544.1-b \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.321742177$ $4.250988810$ 2.735444791 \( \frac{19872}{7} a + \frac{15296}{7} \) \( \bigl[0\) , \( -i + 1\) , \( 0\) , \( -3\) , \( i + 1\bigr] \) ${y}^2={x}^{3}+\left(-i+1\right){x}^{2}-3{x}+i+1$
12544.1-b2 12544.1-b \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.643484354$ $2.125494405$ 2.735444791 \( -\frac{694948}{49} a + \frac{30148}{7} \) \( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 10 i - 13\) , \( 31 i - 13\bigr] \) ${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(10i-13\right){x}+31i-13$
12544.1-c1 12544.1-c \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.321742177$ $4.250988810$ 2.735444791 \( -\frac{19872}{7} a + \frac{15296}{7} \) \( \bigl[0\) , \( -i - 1\) , \( 0\) , \( -3\) , \( i - 1\bigr] \) ${y}^2={x}^{3}+\left(-i-1\right){x}^{2}-3{x}+i-1$
12544.1-c2 12544.1-c \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.643484354$ $2.125494405$ 2.735444791 \( \frac{694948}{49} a + \frac{30148}{7} \) \( \bigl[0\) , \( -i - 1\) , \( 0\) , \( -10 i - 13\) , \( 31 i + 13\bigr] \) ${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(-10i-13\right){x}+31i+13$
12544.1-d1 12544.1-d \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.612005445$ $4.990559254$ 3.054249441 \( \frac{8000}{7} \) \( \bigl[0\) , \( -i\) , \( 0\) , \( -2\) , \( 0\bigr] \) ${y}^2={x}^{3}-i{x}^{2}-2{x}$
12544.1-d2 12544.1-d \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.306002722$ $2.495279627$ 3.054249441 \( \frac{125000}{49} \) \( \bigl[0\) , \( -i\) , \( 0\) , \( 8\) , \( -8 i\bigr] \) ${y}^2={x}^{3}-i{x}^{2}+8{x}-8i$
12544.1-e1 12544.1-e \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.218854283$ 1.969688554 \( -\frac{548347731625}{1835008} \) \( \bigl[0\) , \( i\) , \( 0\) , \( 2728\) , \( 55920 i\bigr] \) ${y}^2={x}^{3}+i{x}^{2}+2728{x}+55920i$
12544.1-e2 12544.1-e \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.969688554$ 1.969688554 \( -\frac{15625}{28} \) \( \bigl[0\) , \( i\) , \( 0\) , \( 8\) , \( -16 i\bigr] \) ${y}^2={x}^{3}+i{x}^{2}+8{x}-16i$
12544.1-e3 12544.1-e \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.656562851$ 1.969688554 \( \frac{9938375}{21952} \) \( \bigl[0\) , \( i\) , \( 0\) , \( -72\) , \( 368 i\bigr] \) ${y}^2={x}^{3}+i{x}^{2}-72{x}+368i$
12544.1-e4 12544.1-e \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.328281425$ 1.969688554 \( \frac{4956477625}{941192} \) \( \bigl[0\) , \( i\) , \( 0\) , \( 568\) , \( 4464 i\bigr] \) ${y}^2={x}^{3}+i{x}^{2}+568{x}+4464i$
12544.1-e5 12544.1-e \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.984844277$ 1.969688554 \( \frac{128787625}{98} \) \( \bigl[0\) , \( i\) , \( 0\) , \( 168\) , \( -784 i\bigr] \) ${y}^2={x}^{3}+i{x}^{2}+168{x}-784i$
12544.1-e6 12544.1-e \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.109427141$ 1.969688554 \( \frac{2251439055699625}{25088} \) \( \bigl[0\) , \( i\) , \( 0\) , \( 43688\) , \( 3529328 i\bigr] \) ${y}^2={x}^{3}+i{x}^{2}+43688{x}+3529328i$
12544.1-f1 12544.1-f \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.197869643$ 3.197869643 \( -\frac{4}{7} \) \( \bigl[0\) , \( i\) , \( 0\) , \( 0\) , \( -4 i\bigr] \) ${y}^2={x}^{3}+i{x}^{2}-4i$
12544.1-f2 12544.1-f \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.598934821$ 3.197869643 \( \frac{3543122}{49} \) \( \bigl[0\) , \( i\) , \( 0\) , \( 40\) , \( -84 i\bigr] \) ${y}^2={x}^{3}+i{x}^{2}+40{x}-84i$
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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.