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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
49.1-a1 49.1-a 6.6.300125.1 \( 7^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.142635068$ 1.30358 \( -\frac{2887553024}{16807} \) \( \bigl[0\) , \( 4 a^{5} - a^{4} - 29 a^{3} - 13 a^{2} + 19 a + 5\) , \( 1\) , \( 120 a^{5} - 30 a^{4} - 870 a^{3} - 390 a^{2} + 570 a + 91\) , \( 408 a^{5} - 102 a^{4} - 2958 a^{3} - 1326 a^{2} + 1938 a + 324\bigr] \) ${y}^2+{y}={x}^{3}+\left(4a^{5}-a^{4}-29a^{3}-13a^{2}+19a+5\right){x}^{2}+\left(120a^{5}-30a^{4}-870a^{3}-390a^{2}+570a+91\right){x}+408a^{5}-102a^{4}-2958a^{3}-1326a^{2}+1938a+324$
49.1-a2 49.1-a 6.6.300125.1 \( 7^{2} \) 0 $\Z/5\Z$ $\mathrm{SU}(2)$ $1$ $17853.67294$ 1.30358 \( \frac{4096}{7} \) \( \bigl[0\) , \( 4 a^{5} - a^{4} - 29 a^{3} - 13 a^{2} + 19 a + 5\) , \( 1\) , \( 1\) , \( 0\bigr] \) ${y}^2+{y}={x}^{3}+\left(4a^{5}-a^{4}-29a^{3}-13a^{2}+19a+5\right){x}^{2}+{x}$
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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.