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Results (3 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
40.1-a1 40.1-a 3.3.169.1 \( 2^{3} \cdot 5 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $14.96312317$ 1.151009474 \( -\frac{53626624272}{3125} a^{2} - \frac{177085593453}{6250} a - \frac{20228557469}{3125} \) \( \bigl[a + 1\) , \( -a^{2} + 2 a + 2\) , \( a^{2} - a - 2\) , \( -a^{2} - 3 a\) , \( -3 a^{2} - 6 a - 3\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{2}+2a+2\right){x}^{2}+\left(-a^{2}-3a\right){x}-3a^{2}-6a-3$
40.1-b1 40.1-b 3.3.169.1 \( 2^{3} \cdot 5 \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $48.74212197$ 1.249797999 \( \frac{4300451}{250} a^{2} - \frac{3024513}{250} a - \frac{11109599}{125} \) \( \bigl[1\) , \( a^{2} - 3\) , \( a^{2} - a - 3\) , \( 12 a^{2} - 14 a - 42\) , \( -42 a^{2} + 54 a + 154\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(12a^{2}-14a-42\right){x}-42a^{2}+54a+154$
40.1-b2 40.1-b 3.3.169.1 \( 2^{3} \cdot 5 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.805263776$ 1.249797999 \( -\frac{590283258329401}{40} a^{2} + \frac{1403221722682083}{40} a + \frac{428609886619833}{40} \) \( \bigl[1\) , \( a^{2} - 3\) , \( a^{2} - a - 3\) , \( -48 a^{2} + 56 a + 163\) , \( -133 a^{2} + 143 a + 446\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-48a^{2}+56a+163\right){x}-133a^{2}+143a+446$
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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.