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Results (6 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
49.3-a1 49.3-a \(\Q(\sqrt{53}) \) \( 7^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.599378634$ $7.481352100$ 2.463788418 \( \frac{1840001024}{823543} a + \frac{5775437824}{823543} \) \( \bigl[0\) , \( a + 1\) , \( a\) , \( -4\) , \( -18 a + 70\bigr] \) ${y}^2+a{y}={x}^{3}+\left(a+1\right){x}^{2}-4{x}-18a+70$
49.3-a2 49.3-a \(\Q(\sqrt{53}) \) \( 7^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $4.195650442$ $1.068764585$ 2.463788418 \( \frac{195338235078135808}{7} a - \frac{808691822475743232}{7} \) \( \bigl[0\) , \( a + 1\) , \( a\) , \( 7700 a - 37314\) , \( -834775 a + 3292065\bigr] \) ${y}^2+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(7700a-37314\right){x}-834775a+3292065$
49.3-b1 49.3-b \(\Q(\sqrt{53}) \) \( 7^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.214508932$ $18.74863282$ 2.209718956 \( 4096 a + 12288 \) \( \bigl[0\) , \( -1\) , \( a\) , \( 2 a - 8\) , \( 5 a - 25\bigr] \) ${y}^2+a{y}={x}^{3}-{x}^{2}+\left(2a-8\right){x}+5a-25$
49.3-b2 49.3-b \(\Q(\sqrt{53}) \) \( 7^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.501562525$ $2.678376117$ 2.209718956 \( 68910804992 a + 216383696896 \) \( \bigl[0\) , \( -1\) , \( a\) , \( 232 a - 978\) , \( -3994 a + 16508\bigr] \) ${y}^2+a{y}={x}^{3}-{x}^{2}+\left(232a-978\right){x}-3994a+16508$
49.3-c1 49.3-c \(\Q(\sqrt{53}) \) \( 7^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.233677833$ $15.92365378$ 2.044477338 \( 4096 a + 12288 \) \( \bigl[0\) , \( a - 1\) , \( a\) , \( -25 a - 73\) , \( 98 a + 303\bigr] \) ${y}^2+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-25a-73\right){x}+98a+303$
49.3-c2 49.3-c \(\Q(\sqrt{53}) \) \( 7^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.635744836$ $2.274807683$ 2.044477338 \( 68910804992 a + 216383696896 \) \( \bigl[0\) , \( -a + 1\) , \( a\) , \( 4 a - 27\) , \( 24 a - 110\bigr] \) ${y}^2+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(4a-27\right){x}+24a-110$
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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.