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Results (3 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
49.1-b2 49.1-b \(\Q(\sqrt{53}) \) \( 7^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $24.30385482$ 1.669195602 \( -\frac{1063343}{49} a + \frac{4416725}{49} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( a + 1\) , \( a + 2\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}+a+2$
343.1-d2 343.1-d \(\Q(\sqrt{53}) \) \( 7^{3} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $12.76327400$ 1.753170515 \( -\frac{1063343}{49} a + \frac{4416725}{49} \) \( \bigl[a\) , \( 1\) , \( 1\) , \( 20 a + 68\) , \( 236 a + 742\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(20a+68\right){x}+236a+742$
343.2-e2 343.2-e \(\Q(\sqrt{53}) \) \( 7^{3} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.822878717$ 0.662473340 \( -\frac{1063343}{49} a + \frac{4416725}{49} \) \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 3 a\) , \( -22\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+3a{x}-22$
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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.