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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
72.1-a3 72.1-a \(\Q(\sqrt{19}) \) \( 2^{3} \cdot 3^{2} \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $37.20447790$ 0.533455787 \( \frac{35152}{9} \) \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 14369 a - 62603\) , \( -1468403 a + 6400670\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(14369a-62603\right){x}-1468403a+6400670$
72.1-j3 72.1-j \(\Q(\sqrt{19}) \) \( 2^{3} \cdot 3^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.562595083$ $22.73403407$ 4.074892574 \( \frac{35152}{9} \) \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 14368 a - 62606\) , \( 1448893 a - 6315542\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(14368a-62606\right){x}+1448893a-6315542$
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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.