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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
12675.2-b5 12675.2-b \(\Q(\sqrt{-3}) \) \( 3 \cdot 5^{2} \cdot 13^{2} \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $0.346553450$ $0.370634167$ 2.373039851 \( \frac{15551989015681}{1445900625} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -520 a + 520\) , \( -4225\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-520a+520\right){x}-4225$
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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.