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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
49.2-a1 49.2-a 4.4.4205.1 \( 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $102.9191920$ 1.587133170 \( \frac{91176666325}{282475249} a^{3} - \frac{91176666325}{282475249} a^{2} - \frac{547059997950}{282475249} a + \frac{199910878122}{282475249} \) \( \bigl[a^{3} - a^{2} - 4 a - 1\) , \( 0\) , \( 0\) , \( -4 a^{3} + 4 a^{2} + 24 a - 8\) , \( -a^{3} + a^{2} + 6 a - 1\bigr] \) ${y}^2+\left(a^{3}-a^{2}-4a-1\right){x}{y}={x}^{3}+\left(-4a^{3}+4a^{2}+24a-8\right){x}-a^{3}+a^{2}+6a-1$
343.3-d4 343.3-d 4.4.4205.1 \( 7^{3} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $13.08439948$ 2.017765978 \( \frac{91176666325}{282475249} a^{3} - \frac{91176666325}{282475249} a^{2} - \frac{547059997950}{282475249} a + \frac{199910878122}{282475249} \) \( \bigl[a^{3} - a^{2} - 4 a\) , \( a^{3} - a^{2} - 5 a - 1\) , \( -a^{3} + 2 a^{2} + 3 a\) , \( -2 a^{3} - 5 a^{2} + a + 3\) , \( -4140 a^{3} - 7622 a^{2} - 946 a + 1456\bigr] \) ${y}^2+\left(a^{3}-a^{2}-4a\right){x}{y}+\left(-a^{3}+2a^{2}+3a\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a-1\right){x}^{2}+\left(-2a^{3}-5a^{2}+a+3\right){x}-4140a^{3}-7622a^{2}-946a+1456$
343.4-d1 343.4-d 4.4.4205.1 \( 7^{3} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $13.08439948$ 2.017765978 \( \frac{91176666325}{282475249} a^{3} - \frac{91176666325}{282475249} a^{2} - \frac{547059997950}{282475249} a + \frac{199910878122}{282475249} \) \( \bigl[a^{2} - a - 1\) , \( 2 a^{3} - 3 a^{2} - 9 a\) , \( a^{3} - a^{2} - 5 a\) , \( 3 a^{3} - 7 a^{2} - 7 a + 4\) , \( 44 a^{3} - 82 a^{2} - 339 a - 173\bigr] \) ${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{3}-a^{2}-5a\right){y}={x}^{3}+\left(2a^{3}-3a^{2}-9a\right){x}^{2}+\left(3a^{3}-7a^{2}-7a+4\right){x}+44a^{3}-82a^{2}-339a-173$
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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.