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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-a9 98.1-a \(\Q(\sqrt{2}) \) \( 2 \cdot 7^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $1.962857973$ 0.693975091 \( \frac{392127492092318125}{55365148804} a + \frac{138814532776321000}{13841287201} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -130 a - 356\) , \( -2000 a - 2038\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-130a-356\right){x}-2000a-2038$
686.1-d9 686.1-d \(\Q(\sqrt{2}) \) \( 2 \cdot 7^{3} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.985259457$ 2.105685636 \( \frac{392127492092318125}{55365148804} a + \frac{138814532776321000}{13841287201} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -2593 a - 4241\) , \( 94830 a + 138943\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2593a-4241\right){x}+94830a+138943$
686.2-d9 686.2-d \(\Q(\sqrt{2}) \) \( 2 \cdot 7^{3} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.496314864$ 2.105685636 \( \frac{392127492092318125}{55365148804} a + \frac{138814532776321000}{13841287201} \) \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 251 a - 2161\) , \( 5169 a - 37057\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(251a-2161\right){x}+5169a-37057$
784.1-a9 784.1-a \(\Q(\sqrt{2}) \) \( 2^{4} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.756927026$ 1.242335014 \( \frac{392127492092318125}{55365148804} a + \frac{138814532776321000}{13841287201} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -520 a - 1422\) , \( 16000 a + 16302\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-520a-1422\right){x}+16000a+16302$
4802.1-z9 4802.1-z \(\Q(\sqrt{2}) \) \( 2 \cdot 7^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.501979150$ 0.709905722 \( \frac{392127492092318125}{55365148804} a + \frac{138814532776321000}{13841287201} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -6370 a - 17420\) , \( 679630 a + 681528\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-6370a-17420\right){x}+679630a+681528$
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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.