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Results (23 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
111132.3-a1 111132.3-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{3} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.749014438$ 0.864887375 \( \frac{43477641}{14} a - \frac{4669083}{7} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -278 a + 356\) , \( 716 a + 1746\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-278a+356\right){x}+716a+1746$
111132.3-a2 111132.3-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{3} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.749014438$ 0.864887375 \( \frac{1192725}{1372} a - \frac{2098143}{2744} \) \( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 23 a + 50\) , \( 225 a - 358\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(23a+50\right){x}+225a-358$
111132.3-a3 111132.3-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{3} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.749014438$ 0.864887375 \( -\frac{50481832659}{80707214} a + \frac{60742004649}{80707214} \) \( \bigl[a\) , \( a\) , \( 0\) , \( -27 a - 45\) , \( 79 a - 293\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-27a-45\right){x}+79a-293$
111132.3-a4 111132.3-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{3} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.749014438$ 0.864887375 \( \frac{457190997}{1792} a + \frac{610173645}{3584} \) \( \bigl[a\) , \( a\) , \( 0\) , \( 178 a - 275\) , \( -1485 a + 1396\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(178a-275\right){x}-1485a+1396$
111132.3-a5 111132.3-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{3} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.749014438$ 0.864887375 \( \frac{13989364197}{7} a + \frac{2196790845}{14} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -778 a + 353\) , \( -5643 a + 7157\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-778a+353\right){x}-5643a+7157$
111132.3-b1 111132.3-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{3} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.330370853$ 1.525917611 \( -\frac{11527859979}{28} \) \( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -2119 a + 3389\) , \( -39591 a - 32614\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2119a+3389\right){x}-39591a-32614$
111132.3-b2 111132.3-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{3} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.330370853$ 1.525917611 \( -\frac{5000211}{21952} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -161 a + 257\) , \( 2300 a + 2034\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-161a+257\right){x}+2300a+2034$
111132.3-b3 111132.3-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{3} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.330370853$ 1.525917611 \( \frac{381790581}{1835008} \) \( \bigl[a\) , \( a\) , \( 1\) , \( 157 a - 252\) , \( 2065 a + 1755\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(157a-252\right){x}+2065a+1755$
111132.3-b4 111132.3-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{3} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.330370853$ 1.525917611 \( \frac{253806246034731}{161414428} a + \frac{39085341615816}{40353607} \) \( \bigl[a\) , \( a\) , \( 1\) , \( 1662 a - 112\) , \( -2079 a - 24131\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(1662a-112\right){x}-2079a-24131$
111132.3-b5 111132.3-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{3} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.330370853$ 1.525917611 \( -\frac{253806246034731}{161414428} a + \frac{410147612497995}{161414428} \) \( \bigl[a\) , \( a\) , \( 1\) , \( -1198 a - 632\) , \( -25551 a + 645\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-1198a-632\right){x}-25551a+645$
111132.3-c1 111132.3-c \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{3} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.537766275$ 1.241918015 \( \frac{57770589}{10976} a + \frac{58432257}{21952} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -245 a + 196\) , \( 343 a - 1372\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-245a+196\right){x}+343a-1372$
111132.3-c2 111132.3-c \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{3} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.537766275$ 1.241918015 \( -\frac{54675}{14} a + \frac{522909}{28} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 267 a + 6\) , \( -9 a + 1604\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(267a+6\right){x}-9a+1604$
111132.3-d1 111132.3-d \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{3} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.444228306$ 1.025901328 \( -\frac{545407363875}{14} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -1062 a - 1770\) , \( 30200 a + 25670\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1062a-1770\right){x}+30200a+25670$
111132.3-d2 111132.3-d \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{3} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.444228306$ 1.025901328 \( \frac{29319464398125}{80707214} a - \frac{9795711286125}{80707214} \) \( \bigl[a\) , \( a\) , \( 0\) , \( -650 a - 38\) , \( 7450 a - 3100\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-650a-38\right){x}+7450a-3100$
111132.3-d3 111132.3-d \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{3} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.444228306$ 1.025901328 \( -\frac{7414875}{2744} \) \( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -184 a + 293\) , \( -1332 a - 1042\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-184a+293\right){x}-1332a-1042$
111132.3-d4 111132.3-d \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{3} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.444228306$ 1.025901328 \( \frac{4492125}{3584} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 154 a - 247\) , \( -409 a - 423\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(154a-247\right){x}-409a-423$
111132.3-d5 111132.3-d \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{3} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.444228306$ 1.025901328 \( -\frac{29319464398125}{80707214} a + \frac{9761876556000}{40353607} \) \( \bigl[a\) , \( a\) , \( 0\) , \( 560 a + 182\) , \( -2450 a + 7350\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(560a+182\right){x}-2450a+7350$
111132.3-e1 111132.3-e \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.102838884$ $2.112027078$ 4.012787769 \( -\frac{3}{28} \) \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 2 a - 1\) , \( 9 a + 7\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a-1\right){x}+9a+7$
111132.3-f1 111132.3-f \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.423628438$ $0.674460306$ 3.959060297 \( -\frac{1788153}{686} a + \frac{1363608}{343} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -29 a + 134\) , \( 395 a + 35\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-29a+134\right){x}+395a+35$
111132.3-g1 111132.3-g \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.305665840$ $0.209217470$ 4.135254572 \( \frac{38983348653}{26353376} \) \( \bigl[1\) , \( a\) , \( 1\) , \( -1175 a + 440\) , \( -3589 a - 2331\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-1175a+440\right){x}-3589a-2331$
111132.3-h1 111132.3-h \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.333648630$ $3.090765406$ 4.763045706 \( -\frac{1788153}{686} a + \frac{1363608}{343} \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -3 a + 6\) , \( -2 a + 1\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-3a+6\right){x}-2a+1$
111132.3-i1 111132.3-i \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{3} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $0.149149633$ $0.821451554$ 5.093027425 \( \frac{57770589}{10976} a + \frac{58432257}{21952} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 60 a - 111\) , \( 291 a - 384\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(60a-111\right){x}+291a-384$
111132.3-i2 111132.3-i \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{4} \cdot 7^{3} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $0.447448899$ $2.464354663$ 5.093027425 \( -\frac{54675}{14} a + \frac{522909}{28} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -15 a + 9\) , \( 9 a - 21\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-15a+9\right){x}+9a-21$
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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.