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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
507.1-b4 507.1-b \(\Q(\sqrt{3}) \) \( 3 \cdot 13^{2} \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $10.93460483$ 1.578274261 \( \frac{822656953}{85683} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -19\) , \( 22\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}-19{x}+22$
507.1-e4 507.1-e \(\Q(\sqrt{3}) \) \( 3 \cdot 13^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.282583906$ $5.228487579$ 1.706054394 \( \frac{822656953}{85683} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -20\) , \( -42\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-20{x}-42$
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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.