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Results (11 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
648.4-a1 648.4-a \(\Q(\sqrt{17}) \) \( 2^{3} \cdot 3^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.208013344$ $1.131349575$ 5.303518302 \( -\frac{80896}{9} a - \frac{388096}{27} \) \( \bigl[0\) , \( 0\) , \( a\) , \( -261 a - 408\) , \( -3373 a - 5268\bigr] \) ${y}^2+a{y}={x}^{3}+\left(-261a-408\right){x}-3373a-5268$
648.4-b1 648.4-b \(\Q(\sqrt{17}) \) \( 2^{3} \cdot 3^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.161399858$ 1.494358965 \( -675 a + 1728 \) \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -2 a - 8\) , \( 141 a + 220\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a-8\right){x}+141a+220$
648.4-b2 648.4-b \(\Q(\sqrt{17}) \) \( 2^{3} \cdot 3^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.161399858$ 1.494358965 \( 18495 a + 29916 \) \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -83 a + 208\) , \( -507 a + 1300\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-83a+208\right){x}-507a+1300$
648.4-c1 648.4-c \(\Q(\sqrt{17}) \) \( 2^{3} \cdot 3^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.451066374$ $8.577228616$ 1.876691877 \( -675 a + 1728 \) \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 0\) , \( -5 a - 8\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}-5a-8$
648.4-c2 648.4-c \(\Q(\sqrt{17}) \) \( 2^{3} \cdot 3^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.225533187$ $8.577228616$ 1.876691877 \( 18495 a + 29916 \) \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -9 a + 24\) , \( 14 a - 36\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-9a+24\right){x}+14a-36$
648.4-d1 648.4-d \(\Q(\sqrt{17}) \) \( 2^{3} \cdot 3^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.680814550$ $5.667089073$ 1.871519699 \( -7659605 a + 19620476 \) \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 39 a - 99\) , \( 205 a - 524\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(39a-99\right){x}+205a-524$
648.4-d2 648.4-d \(\Q(\sqrt{17}) \) \( 2^{3} \cdot 3^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.361629101$ $5.667089073$ 1.871519699 \( 343 a + 686 \) \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -51 a + 132\) , \( -948 a + 2428\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-51a+132\right){x}-948a+2428$
648.4-d3 648.4-d \(\Q(\sqrt{17}) \) \( 2^{3} \cdot 3^{4} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.680814550$ $11.33417814$ 1.871519699 \( -1995 a + 7016 \) \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 3 a - 12\) , \( -4 a + 12\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(3a-12\right){x}-4a+12$
648.4-d4 648.4-d \(\Q(\sqrt{17}) \) \( 2^{3} \cdot 3^{4} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.340407275$ $11.33417814$ 1.871519699 \( 24225 a + 44228 \) \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -123 a - 192\) , \( 1140 a + 1780\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-123a-192\right){x}+1140a+1780$
648.4-d5 648.4-d \(\Q(\sqrt{17}) \) \( 2^{3} \cdot 3^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.361629101$ $5.667089073$ 1.871519699 \( -21069823 a + 54821634 \) \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 48 a - 192\) , \( -427 a + 912\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(48a-192\right){x}-427a+912$
648.4-d6 648.4-d \(\Q(\sqrt{17}) \) \( 2^{3} \cdot 3^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.680814550$ $5.667089073$ 1.871519699 \( 2701312025 a + 4218241728 \) \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -717 a + 1836\) , \( 30184 a - 77316\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-717a+1836\right){x}+30184a-77316$
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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.