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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
19.1-a1 19.1-a 3.3.316.1 \( 19 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.141881150$ $147.0278174$ 0.880120090 \( -\frac{613}{19} a^{2} + \frac{19934}{19} a + \frac{42110}{19} \) \( \bigl[a\) , \( -1\) , \( 1\) , \( -2 a + 1\) , \( -a^{2} + 2 a - 1\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-2a+1\right){x}-a^{2}+2a-1$
19.1-a2 19.1-a 3.3.316.1 \( 19 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.070940575$ $147.0278174$ 0.880120090 \( -\frac{2773405}{361} a^{2} + \frac{775470}{361} a + \frac{13611342}{361} \) \( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 2 a - 1\) , \( a - 1\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a-1\right){x}+a-1$
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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.