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Results (5 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
98.1-a10 98.1-a \(\Q(\sqrt{2}) \) \( 2 \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.436190660$ 0.693975091 \( \frac{2251439055699625}{25088} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-2731{x}-55146$
686.1-d10 686.1-d \(\Q(\sqrt{2}) \) \( 2 \cdot 7^{3} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.661753152$ 2.105685636 \( \frac{2251439055699625}{25088} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -10923 a - 24576\) , \( 1213206 a + 1378643\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-10923a-24576\right){x}+1213206a+1378643$
686.2-d10 686.2-d \(\Q(\sqrt{2}) \) \( 2 \cdot 7^{3} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.661753152$ 2.105685636 \( \frac{2251439055699625}{25088} \) \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 10921 a - 24576\) , \( -1213207 a + 1378643\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(10921a-24576\right){x}-1213207a+1378643$
784.1-a10 784.1-a \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.513854052$ 1.242335014 \( \frac{2251439055699625}{25088} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -10922\) , \( 441166\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}-10922{x}+441166$
4802.1-z10 4802.1-z \(\Q(\sqrt{2}) \) \( 2 \cdot 7^{4} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.003958300$ 0.709905722 \( \frac{2251439055699625}{25088} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -133795\) , \( 18781197\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}-133795{x}+18781197$
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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.