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Results (36 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
9408.2-a1 9408.2-a \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $1.025954500$ $3.469791130$ 2.055279100 \( \frac{23709440}{147} a - \frac{43353088}{147} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -3 a - 9\) , \( -2 a - 14\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a-9\right){x}-2a-14$
9408.2-a2 9408.2-a \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.025954500$ $0.867447782$ 2.055279100 \( -\frac{929345780}{21609} a - \frac{1842166336}{21609} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -168 a + 56\) , \( 688 a - 724\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-168a+56\right){x}+688a-724$
9408.2-a3 9408.2-a \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $0.512977250$ $1.734895565$ 2.055279100 \( -\frac{1350800}{7203} a + \frac{1244528}{2401} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -8 a - 4\) , \( 8 a - 28\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-8a-4\right){x}+8a-28$
9408.2-a4 9408.2-a \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.051909001$ $0.433723891$ 2.055279100 \( \frac{153229073258}{466948881} a + \frac{84793822342}{155649627} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -208 a + 176\) , \( 1152 a + 12\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-208a+176\right){x}+1152a+12$
9408.2-a5 9408.2-a \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $1.025954500$ $0.867447782$ 2.055279100 \( \frac{26384818300}{17294403} a + \frac{75886721584}{17294403} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 72 a + 16\) , \( 48 a - 228\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(72a+16\right){x}+48a-228$
9408.2-a6 9408.2-a \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.051909001$ $0.433723891$ 2.055279100 \( \frac{1359217262594}{147} a + \frac{271701873406}{49} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -2688 a + 896\) , \( 44704 a - 44404\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2688a+896\right){x}+44704a-44404$
9408.2-b1 9408.2-b \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.007296960$ 1.163126343 \( -\frac{21006592}{194481} a + \frac{3498416}{64827} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -19 a + 1\) , \( -115 a - 30\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-19a+1\right){x}-115a-30$
9408.2-b2 9408.2-b \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.503648480$ 1.163126343 \( -\frac{17414119304}{321489} a + \frac{8736162620}{321489} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -299 a + 421\) , \( -1431 a - 1878\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-299a+421\right){x}-1431a-1878$
9408.2-b3 9408.2-b \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) 0 $\Z/8\Z$ $\mathrm{SU}(2)$ $1$ $1.007296960$ 1.163126343 \( -\frac{41536905952}{17294403} a + \frac{28824949424}{5764801} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 66 a - 29\) , \( 91 a + 91\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(66a-29\right){x}+91a+91$
9408.2-b4 9408.2-b \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $2.014593921$ 1.163126343 \( \frac{232112128}{21609} a + \frac{133105664}{21609} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 21 a - 14\) , \( -26 a + 4\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(21a-14\right){x}-26a+4$
9408.2-b5 9408.2-b \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.503648480$ 1.163126343 \( \frac{10592413151048}{51883209} a + \frac{2055145495540}{51883209} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -379 a - 179\) , \( -4255 a + 42\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-379a-179\right){x}-4255a+42$
9408.2-b6 9408.2-b \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $1.007296960$ 1.163126343 \( \frac{34063884256}{147} a - \frac{4235820272}{49} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 336 a - 224\) , \( -1916 a + 88\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(336a-224\right){x}-1916a+88$
9408.2-c1 9408.2-c \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $1.025954500$ $3.469791130$ 2.055279100 \( -\frac{23709440}{147} a - \frac{19643648}{147} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 3 a - 12\) , \( 2 a - 16\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(3a-12\right){x}+2a-16$
9408.2-c2 9408.2-c \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.025954500$ $0.867447782$ 2.055279100 \( \frac{929345780}{21609} a - \frac{923837372}{7203} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 168 a - 112\) , \( -688 a - 36\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(168a-112\right){x}-688a-36$
9408.2-c3 9408.2-c \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $0.512977250$ $1.734895565$ 2.055279100 \( \frac{1350800}{7203} a + \frac{2382784}{7203} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 8 a - 12\) , \( -8 a - 20\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(8a-12\right){x}-8a-20$
9408.2-c4 9408.2-c \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.051909001$ $0.433723891$ 2.055279100 \( -\frac{153229073258}{466948881} a + \frac{407610540284}{466948881} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 208 a - 32\) , \( -1152 a + 1164\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(208a-32\right){x}-1152a+1164$
9408.2-c5 9408.2-c \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $1.025954500$ $0.867447782$ 2.055279100 \( -\frac{26384818300}{17294403} a + \frac{102271539884}{17294403} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -72 a + 88\) , \( -48 a - 180\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-72a+88\right){x}-48a-180$
9408.2-c6 9408.2-c \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.051909001$ $0.433723891$ 2.055279100 \( -\frac{1359217262594}{147} a + \frac{2174322882812}{147} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 2688 a - 1792\) , \( -44704 a + 300\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(2688a-1792\right){x}-44704a+300$
9408.2-d1 9408.2-d \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.007296960$ 1.163126343 \( \frac{21006592}{194481} a - \frac{10511344}{194481} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 19 a - 18\) , \( 115 a - 145\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(19a-18\right){x}+115a-145$
9408.2-d2 9408.2-d \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.503648480$ 1.163126343 \( \frac{17414119304}{321489} a - \frac{2892652228}{107163} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 299 a + 122\) , \( 1431 a - 3309\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(299a+122\right){x}+1431a-3309$
9408.2-d3 9408.2-d \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) 0 $\Z/8\Z$ $\mathrm{SU}(2)$ $1$ $1.007296960$ 1.163126343 \( \frac{41536905952}{17294403} a + \frac{44937942320}{17294403} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -66 a + 37\) , \( -91 a + 182\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-66a+37\right){x}-91a+182$
9408.2-d4 9408.2-d \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $2.014593921$ 1.163126343 \( -\frac{232112128}{21609} a + \frac{121739264}{7203} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -21 a + 7\) , \( 26 a - 22\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-21a+7\right){x}+26a-22$
9408.2-d5 9408.2-d \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.503648480$ 1.163126343 \( -\frac{10592413151048}{51883209} a + \frac{4215852882196}{17294403} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 379 a - 558\) , \( 4255 a - 4213\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(379a-558\right){x}+4255a-4213$
9408.2-d6 9408.2-d \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $1.007296960$ 1.163126343 \( -\frac{34063884256}{147} a + \frac{21356423440}{147} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -336 a + 112\) , \( 1916 a - 1828\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-336a+112\right){x}+1916a-1828$
9408.2-e1 9408.2-e \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $1.390851865$ 1.606017398 \( -\frac{2725888}{64827} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -7\) , \( 52\bigr] \) ${y}^2={x}^{3}-{x}^{2}-7{x}+52$
9408.2-e2 9408.2-e \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.347712966$ 1.606017398 \( \frac{6522128932}{3720087} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -392\) , \( -228\bigr] \) ${y}^2={x}^{3}-{x}^{2}-392{x}-228$
9408.2-e3 9408.2-e \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $0.695425932$ 1.606017398 \( -\frac{1412375961568}{51883209} a + \frac{1537135652144}{51883209} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -195 a + 158\) , \( -243 a + 970\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(-195a+158\right){x}-243a+970$
9408.2-e4 9408.2-e \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $0.695425932$ 1.606017398 \( \frac{1412375961568}{51883209} a + \frac{124759690576}{51883209} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 195 a - 37\) , \( 243 a + 727\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(195a-37\right){x}+243a+727$
9408.2-e5 9408.2-e \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.695425932$ 1.606017398 \( \frac{6940769488}{35721} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -252\) , \( 1620\bigr] \) ${y}^2={x}^{3}-{x}^{2}-252{x}+1620$
9408.2-e6 9408.2-e \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.347712966$ 1.606017398 \( \frac{7080974546692}{189} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -4032\) , \( 99900\bigr] \) ${y}^2={x}^{3}-{x}^{2}-4032{x}+99900$
9408.2-f1 9408.2-f \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.149717591$ $0.986178417$ 2.618460543 \( \frac{11696828}{7203} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 48 a - 48\) , \( 48\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(48a-48\right){x}+48$
9408.2-f2 9408.2-f \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $0.574858795$ $1.972356834$ 2.618460543 \( \frac{810448}{441} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -12 a + 12\) , \( 0\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-12a+12\right){x}$
9408.2-f3 9408.2-f \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $1.149717591$ $3.944713669$ 2.618460543 \( \frac{2725888}{21} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -7 a + 7\) , \( -10\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-7a+7\right){x}-10$
9408.2-f4 9408.2-f \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.299435182$ $0.493089208$ 2.618460543 \( -\frac{4089054504964}{17294403} a + \frac{5337554856122}{17294403} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 568 a - 488\) , \( 5312 a - 1552\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(568a-488\right){x}+5312a-1552$
9408.2-f5 9408.2-f \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.299435182$ $0.493089208$ 2.618460543 \( \frac{4089054504964}{17294403} a + \frac{1248500351158}{17294403} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 488 a - 568\) , \( -5312 a + 3760\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(488a-568\right){x}-5312a+3760$
9408.2-f6 9408.2-f \(\Q(\sqrt{-3}) \) \( 2^{6} \cdot 3 \cdot 7^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $1.149717591$ $0.986178417$ 2.618460543 \( \frac{381775972}{567} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -152 a + 152\) , \( 672\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-152a+152\right){x}+672$
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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.