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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
23716.4-a1 23716.4-a \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.383868981$ 0.870533023 \( -\frac{14992796757}{32768} a - \frac{10971811273}{32768} \) \( \bigl[1\) , \( -a + 1\) , \( a\) , \( -239 a + 1106\) , \( 8296 a + 1708\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-239a+1106\right){x}+8296a+1708$
23716.4-a2 23716.4-a \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $1.151606943$ 0.870533023 \( -\frac{51957}{32} a - \frac{18265}{32} \) \( \bigl[1\) , \( -a + 1\) , \( a\) , \( -29 a + 21\) , \( 43 a - 119\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-29a+21\right){x}+43a-119$
23716.4-b1 23716.4-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.085177090$ $0.191554991$ 2.514172357 \( \frac{2775668240489}{85184} a - \frac{3929396676037}{42592} \) \( \bigl[1\) , \( a - 1\) , \( a\) , \( 2412 a + 5574\) , \( 151200 a - 230660\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2412a+5574\right){x}+151200a-230660$
23716.4-b2 23716.4-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $2.170354180$ $0.191554991$ 2.514172357 \( \frac{49453830610989}{7256313856} a - \frac{991801247255}{3628156928} \) \( \bigl[1\) , \( -a\) , \( a + 1\) , \( -1223 a + 1581\) , \( -2906 a - 29970\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-1223a+1581\right){x}-2906a-29970$
23716.4-b3 23716.4-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $4.340708360$ $0.095777495$ 2.514172357 \( -\frac{41728910180660407}{200859416110144} a - \frac{5044929390482523}{100429708055072} \) \( \bigl[1\) , \( -a\) , \( a + 1\) , \( 2067 a + 111\) , \( 29910 a - 161122\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(2067a+111\right){x}+29910a-161122$
23716.4-b4 23716.4-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.361725696$ $0.574664973$ 2.514172357 \( \frac{2222449}{45056} a + \frac{42043605}{45056} \) \( \bigl[1\) , \( a - 1\) , \( a\) , \( 67 a + 44\) , \( 336 a - 52\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(67a+44\right){x}+336a-52$
23716.4-b5 23716.4-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.723451393$ $0.574664973$ 2.514172357 \( -\frac{998361}{7744} a + \frac{23448551}{7744} \) \( \bigl[1\) , \( -a\) , \( a + 1\) , \( 72 a - 169\) , \( 363 a - 416\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(72a-169\right){x}+363a-416$
23716.4-b6 23716.4-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $4.340708360$ $0.191554991$ 2.514172357 \( -\frac{74168468086089}{22330474496} a + \frac{45400743717419}{11165237248} \) \( \bigl[1\) , \( -a - 1\) , \( a\) , \( -205 a - 1510\) , \( 2006 a + 23450\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-205a-1510\right){x}+2006a+23450$
23716.4-b7 23716.4-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.446902786$ $0.574664973$ 2.514172357 \( \frac{7153263}{2816} a + \frac{40910099}{1408} \) \( \bigl[1\) , \( -a - 1\) , \( a\) , \( 180 a + 30\) , \( -10 a + 1680\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(180a+30\right){x}-10a+1680$
23716.4-b8 23716.4-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.446902786$ $0.287332486$ 2.514172357 \( -\frac{67333244623}{117128} a + \frac{557731279327}{117128} \) \( \bigl[1\) , \( -a\) , \( a + 1\) , \( 1052 a - 2409\) , \( 27439 a - 38104\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(1052a-2409\right){x}+27439a-38104$
23716.4-c1 23716.4-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $0.786053931$ 1.188401839 \( \frac{1804271}{256} a - \frac{176701}{128} \) \( \bigl[1\) , \( -a + 1\) , \( a\) , \( -85 a + 28\) , \( 246 a - 462\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-85a+28\right){x}+246a-462$
23716.4-c2 23716.4-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.262017977$ 1.188401839 \( -\frac{244445227817}{16777216} a + \frac{189604608459}{8388608} \) \( \bigl[1\) , \( -a + 1\) , \( a\) , \( 265 a + 1043\) , \( 10921 a - 11431\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(265a+1043\right){x}+10921a-11431$
23716.4-d1 23716.4-d \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $5.427371109$ $0.095007311$ 4.677445842 \( \frac{3249994516225}{8589934592} a - \frac{36175316196699}{8589934592} \) \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -2160 a + 6587\) , \( 127480 a + 80853\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2160a+6587\right){x}+127480a+80853$
23716.4-d2 23716.4-d \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $1.809123703$ $0.285021933$ 4.677445842 \( -\frac{89671}{2048} a + \frac{3045277}{2048} \) \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 185 a - 588\) , \( -1159 a - 578\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(185a-588\right){x}-1159a-578$
23716.4-e1 23716.4-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.001846424$ 3.026507316 \( \frac{16471}{4} a - 3375 \) \( \bigl[1\) , \( a\) , \( 1\) , \( -9 a - 5\) , \( 13 a - 4\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-9a-5\right){x}+13a-4$
23716.4-e2 23716.4-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.001846424$ 3.026507316 \( -\frac{16471}{4} a + \frac{2971}{4} \) \( \bigl[1\) , \( 0\) , \( a + 1\) , \( -12 a + 6\) , \( 12 a - 22\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-12a+6\right){x}+12a-22$
23716.4-e3 23716.4-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.285978060$ 3.026507316 \( \frac{1875341}{16384} a + \frac{13640585}{8192} \) \( \bigl[1\) , \( a\) , \( 1\) , \( 361 a - 505\) , \( -787 a + 1306\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(361a-505\right){x}-787a+1306$
23716.4-e4 23716.4-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.285978060$ 3.026507316 \( -\frac{1875341}{16384} a + \frac{29156511}{16384} \) \( \bigl[1\) , \( 0\) , \( a + 1\) , \( 178 a + 436\) , \( -1168 a + 428\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(178a+436\right){x}-1168a+428$
23716.4-f1 23716.4-f \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.985370750$ 1.489740546 \( \frac{1804271}{256} a - \frac{176701}{128} \) \( \bigl[1\) , \( -a\) , \( 0\) , \( -8 a - 67\) , \( -30 a - 201\bigr] \) ${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-8a-67\right){x}-30a-201$
23716.4-f2 23716.4-f \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.328456916$ 1.489740546 \( -\frac{244445227817}{16777216} a + \frac{189604608459}{8388608} \) \( \bigl[1\) , \( -a\) , \( 0\) , \( -498 a + 668\) , \( -324 a - 8384\bigr] \) ${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-498a+668\right){x}-324a-8384$
23716.4-g1 23716.4-g \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.099763041$ 2.714895745 \( -\frac{548347731625}{1835008} \) \( \bigl[1\) , \( a + 1\) , \( 1\) , \( -9548 a + 1193\) , \( -415905 a + 422021\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-9548a+1193\right){x}-415905a+422021$
23716.4-g2 23716.4-g \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.299289124$ 2.714895745 \( \frac{10538337875}{200704} a - \frac{36575498625}{200704} \) \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 835 a - 1164\) , \( -14225 a + 9941\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(835a-1164\right){x}-14225a+9941$
23716.4-g3 23716.4-g \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.299289124$ 2.714895745 \( -\frac{10538337875}{200704} a - \frac{13018580375}{100352} \) \( \bigl[1\) , \( a - 1\) , \( 1\) , \( 414 a + 1006\) , \( -11079 a + 16329\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(414a+1006\right){x}-11079a+16329$
23716.4-g4 23716.4-g \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.897867372$ 2.714895745 \( \frac{831875}{112} a - \frac{499125}{56} \) \( \bigl[1\) , \( a - 1\) , \( 1\) , \( 64 a - 9\) , \( -103 a - 289\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(64a-9\right){x}-103a-289$
23716.4-g5 23716.4-g \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.897867372$ 2.714895745 \( -\frac{831875}{112} a - \frac{166375}{112} \) \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 65 a - 9\) , \( 41 a + 323\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(65a-9\right){x}+41a+323$
23716.4-g6 23716.4-g \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.897867372$ 2.714895745 \( -\frac{15625}{28} \) \( \bigl[1\) , \( a + 1\) , \( 1\) , \( -28 a + 3\) , \( 119 a - 121\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-28a+3\right){x}+119a-121$
23716.4-g7 23716.4-g \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.299289124$ 2.714895745 \( \frac{9938375}{21952} \) \( \bigl[1\) , \( a + 1\) , \( 1\) , \( 252 a - 32\) , \( -2737 a + 2777\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(252a-32\right){x}-2737a+2777$
23716.4-g8 23716.4-g \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.099763041$ 2.714895745 \( \frac{70135314719125}{481036337152} a + \frac{288417990127625}{481036337152} \) \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -1965 a + 3421\) , \( -76203 a + 47545\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1965a+3421\right){x}-76203a+47545$
23716.4-g9 23716.4-g \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.099763041$ 2.714895745 \( -\frac{70135314719125}{481036337152} a + \frac{179276652423375}{240518168576} \) \( \bigl[1\) , \( a - 1\) , \( 1\) , \( -706 a - 3089\) , \( -63187 a + 91873\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-706a-3089\right){x}-63187a+91873$
23716.4-g10 23716.4-g \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.149644562$ 2.714895745 \( \frac{4956477625}{941192} \) \( \bigl[1\) , \( a + 1\) , \( 1\) , \( -1988 a + 248\) , \( -33201 a + 33689\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1988a+248\right){x}-33201a+33689$
23716.4-g11 23716.4-g \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.448933686$ 2.714895745 \( \frac{128787625}{98} \) \( \bigl[1\) , \( a + 1\) , \( 1\) , \( -588 a + 73\) , \( 5831 a - 5917\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-588a+73\right){x}+5831a-5917$
23716.4-g12 23716.4-g \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.049881520$ 2.714895745 \( \frac{2251439055699625}{25088} \) \( \bigl[1\) , \( a + 1\) , \( 1\) , \( -152908 a + 19113\) , \( -26249377 a + 26635397\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-152908a+19113\right){x}-26249377a+26635397$
23716.4-h1 23716.4-h \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.306221512$ 3.472225579 \( -\frac{14992796757}{32768} a - \frac{10971811273}{32768} \) \( \bigl[1\) , \( a - 1\) , \( 1\) , \( 1026 a + 385\) , \( -1559 a + 25303\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(1026a+385\right){x}-1559a+25303$
23716.4-h2 23716.4-h \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.918664538$ 3.472225579 \( -\frac{51957}{32} a - \frac{18265}{32} \) \( \bigl[1\) , \( a - 1\) , \( 1\) , \( -4 a + 60\) , \( 173 a - 21\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a+60\right){x}+173a-21$
23716.4-i1 23716.4-i \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.123209096$ $0.833685772$ 10.24943837 \( \frac{3249994516225}{8589934592} a - \frac{36175316196699}{8589934592} \) \( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -59 a + 13\) , \( -261 a + 315\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-59a+13\right){x}-261a+315$
23716.4-i2 23716.4-i \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.041069698$ $2.501057318$ 10.24943837 \( -\frac{89671}{2048} a + \frac{3045277}{2048} \) \( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 6 a - 2\) , \( 5 a - 7\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6a-2\right){x}+5a-7$
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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.