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Results (4 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
25.2-a1 25.2-a \(\Q(\sqrt{29}) \) \( 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.914540520$ 1.528433200 \( -1407628760845 a - 3086342051803 \) \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -16 a - 38\) , \( -64 a - 195\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-16a-38\right){x}-64a-195$
25.2-a2 25.2-a \(\Q(\sqrt{29}) \) \( 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $8.230864683$ 1.528433200 \( -3515 a - 7688 \) \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -a + 2\) , \( -a - 2\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a+2\right){x}-a-2$
25.2-a3 25.2-a \(\Q(\sqrt{29}) \) \( 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.914540520$ 1.528433200 \( 1407628760845 a - 4493970812648 \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -15 a - 40\) , \( -481 a - 1066\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-15a-40\right){x}-481a-1066$
25.2-a4 25.2-a \(\Q(\sqrt{29}) \) \( 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $8.230864683$ 1.528433200 \( 3515 a - 11203 \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 0\) , \( 17 a + 37\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+17a+37$
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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.