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Results (4 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
15.1-a3 15.1-a \(\Q(\sqrt{30}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.961688882$ 2.865230004 \( \frac{4733169839}{3515625} \) \( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 1536 a + 8452\) , \( -38388 a - 210217\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(1536a+8452\right){x}-38388a-210217$
15.1-b3 15.1-b \(\Q(\sqrt{30}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.547989231$ 0.930394118 \( \frac{4733169839}{3515625} \) \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -2967357 a + 16252869\) , \( -3478975110 a + 19055131440\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2967357a+16252869\right){x}-3478975110a+19055131440$
15.1-c3 15.1-c \(\Q(\sqrt{30}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $4.297783744$ $2.547989231$ 3.998632720 \( \frac{4733169839}{3515625} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -6162 a + 33754\) , \( -356336 a + 1951734\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6162a+33754\right){x}-356336a+1951734$
15.1-d3 15.1-d \(\Q(\sqrt{30}) \) \( 3 \cdot 5 \) $1$ $\Z/8\Z$ $\mathrm{SU}(2)$ $10.07379811$ $1.961688882$ 1.803984289 \( \frac{4733169839}{3515625} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+35{x}-28$
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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.