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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
59.2-a1 59.2-a 4.4.6125.1 \( 59 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $175.2162663$ 2.238831327 \( \frac{528977945391}{205379} a^{3} + \frac{623147922314}{205379} a^{2} - \frac{3406714985428}{205379} a - \frac{2669026432747}{205379} \) \( \bigl[a^{3} + a^{2} - 5 a - 3\) , \( -a^{3} - 2 a^{2} + 6 a + 8\) , \( 2 a^{3} + 3 a^{2} - 12 a - 12\) , \( -19 a^{3} + 25 a^{2} + 142 a - 229\) , \( -404 a^{3} + 705 a^{2} + 3109 a - 5954\bigr] \) ${y}^2+\left(a^{3}+a^{2}-5a-3\right){x}{y}+\left(2a^{3}+3a^{2}-12a-12\right){y}={x}^{3}+\left(-a^{3}-2a^{2}+6a+8\right){x}^{2}+\left(-19a^{3}+25a^{2}+142a-229\right){x}-404a^{3}+705a^{2}+3109a-5954$
59.2-b1 59.2-b 4.4.6125.1 \( 59 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.062194364$ $271.9299651$ 2.593201710 \( \frac{528977945391}{205379} a^{3} + \frac{623147922314}{205379} a^{2} - \frac{3406714985428}{205379} a - \frac{2669026432747}{205379} \) \( \bigl[a^{3} + 2 a^{2} - 5 a - 8\) , \( a^{2} + a - 3\) , \( a^{3} + 2 a^{2} - 5 a - 8\) , \( 8 a^{3} + 12 a^{2} - 45 a - 44\) , \( 15 a^{3} + 20 a^{2} - 88 a - 73\bigr] \) ${y}^2+\left(a^{3}+2a^{2}-5a-8\right){x}{y}+\left(a^{3}+2a^{2}-5a-8\right){y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(8a^{3}+12a^{2}-45a-44\right){x}+15a^{3}+20a^{2}-88a-73$
59.2-c1 59.2-c 4.4.6125.1 \( 59 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.065073306$ $330.0357331$ 3.293002336 \( -\frac{8193056918637954}{205379} a^{3} + \frac{14306032866590959}{205379} a^{2} + \frac{63063543446609149}{205379} a - \frac{120790269614565170}{205379} \) \( \bigl[a^{3} + a^{2} - 5 a - 3\) , \( a^{3} + 2 a^{2} - 5 a - 9\) , \( 2 a^{3} + 3 a^{2} - 12 a - 11\) , \( -2 a^{3} + 10 a^{2} + 20 a - 65\) , \( 33 a^{3} - 20 a^{2} - 234 a + 242\bigr] \) ${y}^2+\left(a^{3}+a^{2}-5a-3\right){x}{y}+\left(2a^{3}+3a^{2}-12a-11\right){y}={x}^{3}+\left(a^{3}+2a^{2}-5a-9\right){x}^{2}+\left(-2a^{3}+10a^{2}+20a-65\right){x}+33a^{3}-20a^{2}-234a+242$
59.2-d1 59.2-d 4.4.6125.1 \( 59 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $56.70901513$ 0.724601215 \( -\frac{8193056918637954}{205379} a^{3} + \frac{14306032866590959}{205379} a^{2} + \frac{63063543446609149}{205379} a - \frac{120790269614565170}{205379} \) \( \bigl[a^{3} + 2 a^{2} - 5 a - 7\) , \( a^{3} + 2 a^{2} - 6 a - 8\) , \( a\) , \( 14 a^{3} + 6 a^{2} - 59 a - 52\) , \( 29 a^{3} - 33 a^{2} - 59 a - 22\bigr] \) ${y}^2+\left(a^{3}+2a^{2}-5a-7\right){x}{y}+a{y}={x}^{3}+\left(a^{3}+2a^{2}-6a-8\right){x}^{2}+\left(14a^{3}+6a^{2}-59a-52\right){x}+29a^{3}-33a^{2}-59a-22$
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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.