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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
39.1-a3 39.1-a 5.5.36497.1 \( 3 \cdot 13 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $2915.153153$ 0.953702256 \( -\frac{1065196}{28431} a^{4} + \frac{5295800}{9477} a^{3} + \frac{4095677}{9477} a^{2} - \frac{51097538}{28431} a + \frac{11953519}{28431} \) \( \bigl[a^{2} - 2\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 5 a\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 1\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 5 a + 3\) , \( 4 a^{4} - 3 a^{3} - 15 a^{2} + 1\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+6a+1\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+5a\right){x}^{2}+\left(a^{4}-2a^{3}-4a^{2}+5a+3\right){x}+4a^{4}-3a^{3}-15a^{2}+1$
39.1-b3 39.1-b 5.5.36497.1 \( 3 \cdot 13 \) 0 $\Z/14\Z$ $\mathrm{SU}(2)$ $1$ $8019.861435$ 1.49927138 \( -\frac{1065196}{28431} a^{4} + \frac{5295800}{9477} a^{3} + \frac{4095677}{9477} a^{2} - \frac{51097538}{28431} a + \frac{11953519}{28431} \) \( \bigl[2 a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 1\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 2 a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 2\) , \( -4 a^{4} + 9 a^{3} + 12 a^{2} - 20 a - 3\) , \( 2 a^{4} - 9 a^{2} + 10\bigr] \) ${y}^2+\left(2a^{4}-3a^{3}-6a^{2}+7a+1\right){x}{y}+\left(2a^{4}-3a^{3}-6a^{2}+7a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(-4a^{4}+9a^{3}+12a^{2}-20a-3\right){x}+2a^{4}-9a^{2}+10$
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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.