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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-b1 49.1-b 6.6.434581.1 \( 7^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.001804752$ $47699.10907$ 2.35052 \( \frac{2333735}{7} a^{5} - \frac{1536755}{7} a^{4} - 1654035 a^{3} - \frac{3465769}{7} a^{2} + \frac{4986743}{7} a + \frac{1824569}{7} \) \( \bigl[2 a^{5} - 4 a^{4} - 6 a^{3} + 7 a^{2} + 2 a - 1\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 11 a^{2} + a - 3\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a + 2\) , \( -a^{5} + a^{4} + 7 a^{3} - 3 a^{2} - 11 a + 1\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 12 a^{2} - 4\bigr] \) ${y}^2+\left(2a^{5}-4a^{4}-6a^{3}+7a^{2}+2a-1\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+4a+2\right){y}={x}^{3}+\left(2a^{5}-5a^{4}-5a^{3}+11a^{2}+a-3\right){x}^{2}+\left(-a^{5}+a^{4}+7a^{3}-3a^{2}-11a+1\right){x}+2a^{5}-5a^{4}-5a^{3}+12a^{2}-4$
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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.