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Results (15 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
1.1-a1 1.1-a \(\Q(\sqrt{29}) \) \( 1 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $2.044974771$ 0.379742281 \( -1407628760845 a - 3086342051803 \) \( \bigl[a\) , \( a + 1\) , \( a\) , \( -23 a - 53\) , \( -169 a - 372\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-23a-53\right){x}-169a-372$
25.2-a1 25.2-a \(\Q(\sqrt{29}) \) \( 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.914540520$ 1.528433200 \( -1407628760845 a - 3086342051803 \) \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -16 a - 38\) , \( -64 a - 195\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-16a-38\right){x}-64a-195$
25.3-a1 25.3-a \(\Q(\sqrt{29}) \) \( 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.914540520$ 1.528433200 \( -1407628760845 a - 3086342051803 \) \( \bigl[a\) , \( -1\) , \( a\) , \( 13 a - 53\) , \( 480 a - 1546\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(13a-53\right){x}+480a-1546$
49.2-b1 49.2-b \(\Q(\sqrt{29}) \) \( 7^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.315073727$ $7.296424013$ 1.707588603 \( -1407628760845 a - 3086342051803 \) \( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( 107 a - 344\) , \( 9766 a - 31179\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(107a-344\right){x}+9766a-31179$
49.3-b1 49.3-b \(\Q(\sqrt{29}) \) \( 7^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.575368639$ $1.459284802$ 1.707588603 \( -1407628760845 a - 3086342051803 \) \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -122 a - 265\) , \( -1292 a - 2825\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-122a-265\right){x}-1292a-2825$
81.1-a1 81.1-a \(\Q(\sqrt{29}) \) \( 3^{4} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $12.14895586$ 2.256004467 \( -1407628760845 a - 3086342051803 \) \( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -229 a - 503\) , \( 3200 a + 7022\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-229a-503\right){x}+3200a+7022$
169.2-a1 169.2-a \(\Q(\sqrt{29}) \) \( 13^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $10.10854230$ 1.877109181 \( -1407628760845 a - 3086342051803 \) \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -82 a - 189\) , \( 561 a + 1325\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-82a-189\right){x}+561a+1325$
169.3-a1 169.3-a \(\Q(\sqrt{29}) \) \( 13^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $10.10854230$ 1.877109181 \( -1407628760845 a - 3086342051803 \) \( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 71 a - 238\) , \( -5335 a + 17040\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(71a-238\right){x}-5335a+17040$
256.1-d1 256.1-d \(\Q(\sqrt{29}) \) \( 2^{8} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.556634139$ $4.826130850$ 1.995399799 \( -1407628760845 a - 3086342051803 \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -2 a - 73\) , \( 495 a - 1241\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a-73\right){x}+495a-1241$
256.1-h1 256.1-h \(\Q(\sqrt{29}) \) \( 2^{8} \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.103947800$ $9.111716899$ 2.814080433 \( -1407628760845 a - 3086342051803 \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -404 a - 888\) , \( 6724 a + 14760\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-404a-888\right){x}+6724a+14760$
256.1-i1 256.1-i \(\Q(\sqrt{29}) \) \( 2^{8} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $2.783170698$ $0.965226170$ 1.995399799 \( -1407628760845 a - 3086342051803 \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -2 a - 73\) , \( -495 a + 1241\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a-73\right){x}-495a+1241$
529.2-a1 529.2-a \(\Q(\sqrt{29}) \) \( 23^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $5.642831631$ $0.805054277$ 3.374296536 \( -1407628760845 a - 3086342051803 \) \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -57 a - 157\) , \( -544 a - 454\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-57a-157\right){x}-544a-454$
529.3-a1 529.3-a \(\Q(\sqrt{29}) \) \( 23^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.128566326$ $4.025271385$ 3.374296536 \( -1407628760845 a - 3086342051803 \) \( \bigl[a\) , \( -a\) , \( 0\) , \( 48 a - 193\) , \( 3674 a - 11624\bigr] \) ${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(48a-193\right){x}+3674a-11624$
625.1-f1 625.1-f \(\Q(\sqrt{29}) \) \( 5^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.408994954$ 0.683536107 \( -1407628760845 a - 3086342051803 \) \( \bigl[a\) , \( 0\) , \( a\) , \( -633 a - 1394\) , \( -14777 a - 32434\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-633a-1394\right){x}-14777a-32434$
841.1-a1 841.1-a \(\Q(\sqrt{29}) \) \( 29^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $6.768013403$ 5.027154151 \( -1407628760845 a - 3086342051803 \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -131\) , \( -974 a + 3393\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}-131{x}-974a+3393$
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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.