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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
41.4-b1 41.4-b 6.6.703493.1 \( 41 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4678.254988$ 1.39442 \( \frac{132422900}{41} a^{5} - \frac{141704392}{41} a^{4} - \frac{798145247}{41} a^{3} + \frac{689842493}{41} a^{2} + \frac{906291495}{41} a - \frac{237335216}{41} \) \( \bigl[2 a^{5} - 2 a^{4} - 11 a^{3} + 10 a^{2} + 9 a - 4\) , \( -a^{5} + a^{4} + 5 a^{3} - 4 a^{2} - 3 a - 1\) , \( 3 a^{5} - 2 a^{4} - 17 a^{3} + 10 a^{2} + 17 a - 2\) , \( -6 a^{5} + 5 a^{4} + 34 a^{3} - 23 a^{2} - 33 a + 4\) , \( -6 a^{5} + 3 a^{4} + 36 a^{3} - 15 a^{2} - 43 a + 5\bigr] \) ${y}^2+\left(2a^{5}-2a^{4}-11a^{3}+10a^{2}+9a-4\right){x}{y}+\left(3a^{5}-2a^{4}-17a^{3}+10a^{2}+17a-2\right){y}={x}^{3}+\left(-a^{5}+a^{4}+5a^{3}-4a^{2}-3a-1\right){x}^{2}+\left(-6a^{5}+5a^{4}+34a^{3}-23a^{2}-33a+4\right){x}-6a^{5}+3a^{4}+36a^{3}-15a^{2}-43a+5$
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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.