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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
59.3-a1 59.3-a 4.4.6125.1 \( 59 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $175.2162663$ 2.238831327 \( \frac{13620701540}{205379} a^{3} - \frac{80549275383}{205379} a^{2} + \frac{151123103842}{205379} a - \frac{87084955041}{205379} \) \( \bigl[a\) , \( a^{3} + a^{2} - 6 a - 3\) , \( a^{3} + 2 a^{2} - 6 a - 8\) , \( -124 a^{3} - 169 a^{2} + 715 a + 576\) , \( -3046 a^{3} - 4155 a^{2} + 17591 a + 14171\bigr] \) ${y}^2+a{x}{y}+\left(a^{3}+2a^{2}-6a-8\right){y}={x}^{3}+\left(a^{3}+a^{2}-6a-3\right){x}^{2}+\left(-124a^{3}-169a^{2}+715a+576\right){x}-3046a^{3}-4155a^{2}+17591a+14171$
59.3-b1 59.3-b 4.4.6125.1 \( 59 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.062194364$ $271.9299651$ 2.593201710 \( \frac{13620701540}{205379} a^{3} - \frac{80549275383}{205379} a^{2} + \frac{151123103842}{205379} a - \frac{87084955041}{205379} \) \( \bigl[a^{3} + 2 a^{2} - 5 a - 7\) , \( a^{2} + a - 5\) , \( a^{3} + a^{2} - 6 a - 4\) , \( 13 a^{3} + 17 a^{2} - 74 a - 56\) , \( 19 a^{3} + 25 a^{2} - 110 a - 87\bigr] \) ${y}^2+\left(a^{3}+2a^{2}-5a-7\right){x}{y}+\left(a^{3}+a^{2}-6a-4\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(13a^{3}+17a^{2}-74a-56\right){x}+19a^{3}+25a^{2}-110a-87$
59.3-c1 59.3-c 4.4.6125.1 \( 59 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.065073306$ $330.0357331$ 3.293002336 \( -\frac{61785124339543268}{205379} a^{3} - \frac{84284214124772181}{205379} a^{2} + \frac{356805544102478183}{205379} a + \frac{287475920285668815}{205379} \) \( \bigl[a\) , \( a^{3} + 2 a^{2} - 7 a - 7\) , \( 2 a^{3} + 3 a^{2} - 11 a - 12\) , \( -34 a^{3} - 44 a^{2} + 193 a + 154\) , \( 83 a^{3} + 115 a^{2} - 481 a - 391\bigr] \) ${y}^2+a{x}{y}+\left(2a^{3}+3a^{2}-11a-12\right){y}={x}^{3}+\left(a^{3}+2a^{2}-7a-7\right){x}^{2}+\left(-34a^{3}-44a^{2}+193a+154\right){x}+83a^{3}+115a^{2}-481a-391$
59.3-d1 59.3-d 4.4.6125.1 \( 59 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $56.70901513$ 0.724601215 \( -\frac{61785124339543268}{205379} a^{3} - \frac{84284214124772181}{205379} a^{2} + \frac{356805544102478183}{205379} a + \frac{287475920285668815}{205379} \) \( \bigl[a^{3} + 2 a^{2} - 5 a - 8\) , \( a^{2} - a - 3\) , \( a\) , \( 65 a^{3} + 80 a^{2} - 416 a - 328\) , \( 271 a^{3} + 327 a^{2} - 1725 a - 1356\bigr] \) ${y}^2+\left(a^{3}+2a^{2}-5a-8\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(65a^{3}+80a^{2}-416a-328\right){x}+271a^{3}+327a^{2}-1725a-1356$
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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.