The results below are complete, since the LMFDB contains all elliptic curves with conductor norm at most 100000 over imaginary quadratic fields with absolute discriminant 4

Note: The completeness Only modular elliptic curves are included

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Results (1-50 of 62 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
83200.6-a1 83200.6-a \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) $2$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.198263600$ $1.658422915$ 5.260878384 \( -\frac{1027380}{169} a - \frac{6481828}{169} \) \( \bigl[0\) , \( -i\) , \( 0\) , \( 8 i + 32\) , \( 60 i - 24\bigr] \) ${y}^2={x}^{3}-i{x}^{2}+\left(8i+32\right){x}+60i-24$
83200.6-a2 83200.6-a \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) $2$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.198263600$ $3.316845831$ 5.260878384 \( -\frac{7840}{13} a + \frac{1984}{13} \) \( \bigl[0\) , \( -i\) , \( 0\) , \( -2 i + 2\) , \( -4\bigr] \) ${y}^2={x}^{3}-i{x}^{2}+\left(-2i+2\right){x}-4$
83200.6-b1 83200.6-b \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.523383249$ $0.935054592$ 3.915135291 \( -\frac{109298}{1625} a + \frac{1963264}{1625} \) \( \bigl[0\) , \( -i\) , \( 0\) , \( 8 i - 48\) , \( 100 i + 16\bigr] \) ${y}^2={x}^{3}-i{x}^{2}+\left(8i-48\right){x}+100i+16$
83200.6-b2 83200.6-b \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.046766499$ $0.467527296$ 3.915135291 \( \frac{321047281}{2640625} a + \frac{6395175767}{2640625} \) \( \bigl[0\) , \( -i\) , \( 0\) , \( -32 i + 232\) , \( 660 i + 96\bigr] \) ${y}^2={x}^{3}-i{x}^{2}+\left(-32i+232\right){x}+660i+96$
83200.6-c1 83200.6-c \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.715032601$ $0.161777167$ 3.513842264 \( \frac{133474836631120}{137858491849} a - \frac{557894869971688}{137858491849} \) \( \bigl[0\) , \( i - 1\) , \( 0\) , \( 70 i - 2153\) , \( -63 i - 44951\bigr] \) ${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(70i-2153\right){x}-63i-44951$
83200.6-c2 83200.6-c \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.086013040$ $1.617771671$ 3.513842264 \( \frac{18944}{13} a + \frac{30656}{13} \) \( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 10 i + 17\) , \( -13 i + 33\bigr] \) ${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(10i+17\right){x}-13i+33$
83200.6-c3 83200.6-c \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.543006520$ $0.808885835$ 3.513842264 \( -\frac{3782000}{169} a + \frac{2403032}{169} \) \( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 30 i + 127\) , \( 503 i - 129\bigr] \) ${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(30i+127\right){x}+503i-129$
83200.6-c4 83200.6-c \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $5.430065202$ $0.323554334$ 3.513842264 \( -\frac{3444078286336}{371293} a + \frac{8030740546496}{371293} \) \( \bigl[0\) , \( i - 1\) , \( 0\) , \( 50 i - 2263\) , \( 621 i - 40689\bigr] \) ${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(50i-2263\right){x}+621i-40689$
83200.6-d1 83200.6-d \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) $2$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.861184100$ $0.849779646$ 5.854533762 \( -\frac{8646624}{4225} a - \frac{66027268}{4225} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -76 i + 74\) , \( 182 i + 388\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(-76i+74\right){x}+182i+388$
83200.6-d2 83200.6-d \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) $2$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.215296025$ $0.212444911$ 5.854533762 \( \frac{94078100761841}{20393268025} a - \frac{11284537597913}{20393268025} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 1044 i - 766\) , \( 17486 i - 5940\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(1044i-766\right){x}+17486i-5940$
83200.6-d3 83200.6-d \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) $2$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.861184100$ $0.424889823$ 5.854533762 \( -\frac{15461171586}{17850625} a - \frac{9080741152}{17850625} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -196 i - 86\) , \( 1902 i + 348\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(-196i-86\right){x}+1902i+348$
83200.6-d4 83200.6-d \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) $2$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.215296025$ $1.699559292$ 5.854533762 \( \frac{75008}{65} a - \frac{29104}{65} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 4 i + 14\) , \( -22 i + 16\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(4i+14\right){x}-22i+16$
83200.6-d5 83200.6-d \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) $2$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.861184100$ $0.212444911$ 5.854533762 \( \frac{143087370512191}{66015625} a + \frac{29292377558137}{66015625} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -3356 i - 1966\) , \( 94478 i + 1516\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(-3356i-1966\right){x}+94478i+1516$
83200.6-d6 83200.6-d \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) $2$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.861184100$ $0.424889823$ 5.854533762 \( \frac{4355686402}{65} a + \frac{17124606704}{65} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -1236 i + 1194\) , \( 10238 i + 25196\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(-1236i+1194\right){x}+10238i+25196$
83200.6-e1 83200.6-e \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) $2$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.730381696$ $0.864984338$ 5.987012267 \( \frac{35676140}{13} a - \frac{81459452}{13} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -116 i - 246\) , \( 1022 i + 1284\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(-116i-246\right){x}+1022i+1284$
83200.6-e2 83200.6-e \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) $2$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.432595424$ $1.729968676$ 5.987012267 \( -\frac{219264}{13} a - \frac{16384}{13} \) \( \bigl[0\) , \( -i\) , \( 0\) , \( -6 i + 25\) , \( 39 i + 18\bigr] \) ${y}^2={x}^{3}-i{x}^{2}+\left(-6i+25\right){x}+39i+18$
83200.6-e3 83200.6-e \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) $2$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.108148856$ $0.864984338$ 5.987012267 \( -\frac{34116572}{28561} a + \frac{12300412}{28561} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -16 i + 54\) , \( 94 i + 180\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(-16i+54\right){x}+94i+180$
83200.6-e4 83200.6-e \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) $2$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.432595424$ $1.729968676$ 5.987012267 \( \frac{420000}{169} a + \frac{218432}{169} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -6 i - 16\) , \( 18 i + 12\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(-6i-16\right){x}+18i+12$
83200.6-f1 83200.6-f \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.609236210$ $0.544697640$ 3.982194316 \( \frac{906876}{2197} a + \frac{1118799}{2197} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 104 i - 53\) , \( 374 i - 568\bigr] \) ${y}^2={x}^{3}+\left(104i-53\right){x}+374i-568$
83200.6-f2 83200.6-f \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.218472421$ $0.272348820$ 3.982194316 \( -\frac{10047446145}{4826809} a + \frac{17756992962}{4826809} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -776 i + 107\) , \( 4630 i - 5160\bigr] \) ${y}^2={x}^{3}+\left(-776i+107\right){x}+4630i-5160$
83200.6-g1 83200.6-g \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.539036824$ 2.156147299 \( -\frac{9109431098}{8125} a - \frac{703641086}{8125} \) \( \bigl[0\) , \( i + 1\) , \( 0\) , \( -242 i - 493\) , \( 2893 i + 3755\bigr] \) ${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(-242i-493\right){x}+2893i+3755$
83200.6-g2 83200.6-g \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.078073649$ 2.156147299 \( -\frac{2630664}{4225} a + \frac{6709952}{4225} \) \( \bigl[0\) , \( i + 1\) , \( 0\) , \( -22 i - 33\) , \( -7 i + 55\bigr] \) ${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(-22i-33\right){x}-7i+55$
83200.6-g3 83200.6-g \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.156147299$ 2.156147299 \( \frac{42112}{65} a + \frac{108224}{65} \) \( \bigl[0\) , \( i + 1\) , \( 0\) , \( 8 i + 7\) , \( 7 i + 7\bigr] \) ${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(8i+7\right){x}+7i+7$
83200.6-g4 83200.6-g \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.539036824$ 2.156147299 \( \frac{9896441706}{142805} a + \frac{2615329822}{142805} \) \( \bigl[0\) , \( i + 1\) , \( 0\) , \( -282 i - 213\) , \( -2683 i - 413\bigr] \) ${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(-282i-213\right){x}-2683i-413$
83200.6-h1 83200.6-h \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.059999824$ 2.119999649 \( \frac{2224}{13} a + \frac{356}{13} \) \( \bigl[0\) , \( -i\) , \( 0\) , \( 4 i - 20\) , \( 60 i + 96\bigr] \) ${y}^2={x}^{3}-i{x}^{2}+\left(4i-20\right){x}+60i+96$
83200.6-h2 83200.6-h \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.529999912$ 2.119999649 \( -\frac{47776420}{169} a + \frac{17266442}{169} \) \( \bigl[0\) , \( -i\) , \( 0\) , \( -76 i - 460\) , \( 1084 i + 3728\bigr] \) ${y}^2={x}^{3}-i{x}^{2}+\left(-76i-460\right){x}+1084i+3728$
83200.6-i1 83200.6-i \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.107412475$ 1.933424563 \( -\frac{276861163011391}{13000000000} a - \frac{33515586556057}{812500000} \) \( \bigl[0\) , \( i - 1\) , \( 0\) , \( -1074 i - 8145\) , \( -56883 i - 283111\bigr] \) ${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(-1074i-8145\right){x}-56883i-283111$
83200.6-i2 83200.6-i \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.322237427$ 1.933424563 \( \frac{37525044319}{2197000} a - \frac{7169596274}{274625} \) \( \bigl[0\) , \( i - 1\) , \( 0\) , \( -754 i - 385\) , \( 9773 i - 503\bigr] \) ${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(-754i-385\right){x}+9773i-503$
83200.6-i3 83200.6-i \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.161118713$ 1.933424563 \( \frac{133816114442969}{301675562500} a - \frac{19082395919017}{301675562500} \) \( \bigl[0\) , \( i - 1\) , \( 0\) , \( -914 i + 735\) , \( 23565 i + 21353\bigr] \) ${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(-914i+735\right){x}+23565i+21353$
83200.6-i4 83200.6-i \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.053706237$ 1.933424563 \( -\frac{8418015312387897223}{20629882812500000} a + \frac{2783266907131437289}{20629882812500000} \) \( \bigl[0\) , \( i - 1\) , \( 0\) , \( 7886 i - 6865\) , \( -699187 i - 407783\bigr] \) ${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(7886i-6865\right){x}-699187i-407783$
83200.6-i5 83200.6-i \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.966712281$ 1.933424563 \( \frac{31409}{130} a + \frac{101344}{65} \) \( \bigl[0\) , \( i - 1\) , \( 0\) , \( 46 i + 15\) , \( 45 i - 7\bigr] \) ${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(46i+15\right){x}+45i-7$
83200.6-i6 83200.6-i \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.483356140$ 1.933424563 \( \frac{4406742137}{8450} a + \frac{1310300809}{8450} \) \( \bigl[0\) , \( i - 1\) , \( 0\) , \( 606 i + 95\) , \( 2909 i + 4745\bigr] \) ${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(606i+95\right){x}+2909i+4745$
83200.6-j1 83200.6-j \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.414094126$ $0.866425513$ 4.305380593 \( -\frac{216464652}{4826809} a + \frac{109560836}{4826809} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -20 i + 2\) , \( 194 i + 20\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(-20i+2\right){x}+194i+20$
83200.6-j2 83200.6-j \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.207047063$ $1.732851027$ 4.305380593 \( -\frac{127480096}{2197} a + \frac{36670528}{2197} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -10 i + 32\) , \( -62 i - 44\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(-10i+32\right){x}-62i-44$
83200.6-k1 83200.6-k \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.636680645$ $0.951386247$ 4.845833680 \( -\frac{18805284}{4225} a - \frac{16444188}{4225} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 20 i - 65\) , \( -122 i + 204\bigr] \) ${y}^2={x}^{3}+\left(20i-65\right){x}-122i+204$
83200.6-k2 83200.6-k \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.318340322$ $1.902772494$ 4.845833680 \( \frac{23328}{65} a - \frac{74304}{65} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 10 i + 5\) , \( 4 i + 22\bigr] \) ${y}^2={x}^{3}+\left(10i+5\right){x}+4i+22$
83200.6-l1 83200.6-l \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $3.080288958$ $0.387477269$ 4.774167816 \( -\frac{216464652}{4826809} a + \frac{109560836}{4826809} \) \( \bigl[0\) , \( i - 1\) , \( 0\) , \( 66 i + 75\) , \( 2249 i - 235\bigr] \) ${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(66i+75\right){x}+2249i-235$
83200.6-l2 83200.6-l \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.540144479$ $0.774954538$ 4.774167816 \( -\frac{127480096}{2197} a + \frac{36670528}{2197} \) \( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 156 i - 55\) , \( -715 i - 203\bigr] \) ${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(156i-55\right){x}-715i-203$
83200.6-m1 83200.6-m \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.611205147$ 2.444820591 \( \frac{510916}{2640625} a + \frac{1029212}{2640625} \) \( \bigl[0\) , \( -i\) , \( 0\) , \( 8\) , \( -136 i + 568\bigr] \) ${y}^2={x}^{3}-i{x}^{2}+8{x}-136i+568$
83200.6-m2 83200.6-m \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.222410295$ 2.444820591 \( -\frac{2652512}{1625} a + \frac{67882816}{1625} \) \( \bigl[0\) , \( -i\) , \( 0\) , \( 10 i - 62\) , \( -24 i + 184\bigr] \) ${y}^2={x}^{3}-i{x}^{2}+\left(10i-62\right){x}-24i+184$
83200.6-n1 83200.6-n \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.829939029$ $1.556159794$ 5.166071001 \( \frac{3752}{65} a - \frac{7136}{65} \) \( \bigl[0\) , \( i\) , \( 0\) , \( 8\) , \( -32 i + 8\bigr] \) ${y}^2={x}^{3}+i{x}^{2}+8{x}-32i+8$
83200.6-n2 83200.6-n \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.414969514$ $0.778079897$ 5.166071001 \( \frac{109815566}{4225} a + \frac{7969262}{4225} \) \( \bigl[0\) , \( i\) , \( 0\) , \( -140 i - 12\) , \( -496 i + 456\bigr] \) ${y}^2={x}^{3}+i{x}^{2}+\left(-140i-12\right){x}-496i+456$
83200.6-o1 83200.6-o \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.490435845$ $2.370231664$ 4.649786281 \( \frac{2224}{13} a + \frac{356}{13} \) \( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 2 i + 3\) , \( 3 i + 11\bigr] \) ${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(2i+3\right){x}+3i+11$
83200.6-o2 83200.6-o \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.980871690$ $1.185115832$ 4.649786281 \( -\frac{47776420}{169} a + \frac{17266442}{169} \) \( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 82 i + 43\) , \( 35 i + 387\bigr] \) ${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(82i+43\right){x}+35i+387$
83200.6-p1 83200.6-p \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.546310423$ 1.546310423 \( -\frac{2662912}{65} a - \frac{16922944}{65} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 36 i + 40\) , \( 80 i - 122\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(36i+40\right){x}+80i-122$
83200.6-p2 83200.6-p \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.773155211$ 1.546310423 \( -\frac{20996208}{8125} a - \frac{1102494856}{8125} \) \( \bigl[0\) , \( i\) , \( 0\) , \( 56 i - 184\) , \( -504 i + 912\bigr] \) ${y}^2={x}^{3}+i{x}^{2}+\left(56i-184\right){x}-504i+912$
83200.6-p3 83200.6-p \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.546310423$ 1.546310423 \( \frac{631296}{4225} a + \frac{2516672}{4225} \) \( \bigl[0\) , \( i\) , \( 0\) , \( -4 i - 14\) , \( -32 i + 8\bigr] \) ${y}^2={x}^{3}+i{x}^{2}+\left(-4i-14\right){x}-32i+8$
83200.6-p4 83200.6-p \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.773155211$ 1.546310423 \( -\frac{110967056}{142805} a + \frac{597885848}{142805} \) \( \bigl[0\) , \( i\) , \( 0\) , \( 16 i + 96\) , \( -252 i + 48\bigr] \) ${y}^2={x}^{3}+i{x}^{2}+\left(16i+96\right){x}-252i+48$
83200.6-q1 83200.6-q \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $4.573968510$ $0.277158023$ 5.070848289 \( -\frac{10359522503116}{3570125} a - \frac{4364617727362}{3570125} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 1616 i - 1770\) , \( -41002 i + 20676\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(1616i-1770\right){x}-41002i+20676$
83200.6-q2 83200.6-q \(\Q(\sqrt{-1}) \) \( 2^{8} \cdot 5^{2} \cdot 13 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $4.573968510$ $0.277158023$ 5.070848289 \( \frac{2896194844812}{3173828125} a + \frac{3398200522034}{3173828125} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -144 i + 550\) , \( -4314 i + 1460\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(-144i+550\right){x}-4314i+1460$
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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.