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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
5202.5-a1 5202.5-a \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/2\Z$ $1$ $0.887997728$ 0.627909215 \( -\frac{288090894583}{323606016} a + \frac{3514414555109}{1294424064} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -33 a + 50\) , \( -36 a - 134\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-33a+50\right){x}-36a-134$
5202.5-a2 5202.5-a \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/2\Z$ $1$ $0.443998864$ 0.627909215 \( -\frac{311615647507297603}{88465794624} a + \frac{41779045002361607}{22116448656} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -513 a + 690\) , \( -3204 a - 11142\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-513a+690\right){x}-3204a-11142$
5202.5-b1 5202.5-b \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/2\Z$ $1$ $0.887997728$ 0.627909215 \( \frac{288090894583}{323606016} a + \frac{3514414555109}{1294424064} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( 33 a + 50\) , \( 36 a - 134\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(33a+50\right){x}+36a-134$
5202.5-b2 5202.5-b \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/2\Z$ $1$ $0.443998864$ 0.627909215 \( \frac{311615647507297603}{88465794624} a + \frac{41779045002361607}{22116448656} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( 513 a + 690\) , \( 3204 a - 11142\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(513a+690\right){x}+3204a-11142$
5202.5-c1 5202.5-c \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $1$ $\Z/2\Z$ $0.573015571$ $1.151150664$ 1.865707623 \( -\frac{118666603548005}{1095962562} a - \frac{91723455040024}{547981281} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -25 a + 88\) , \( 199 a + 230\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-25a+88\right){x}+199a+230$
5202.5-c2 5202.5-c \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $1$ $\Z/2\Z$ $0.573015571$ $1.151150664$ 1.865707623 \( \frac{118666603548005}{1095962562} a - \frac{91723455040024}{547981281} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( 25 a + 88\) , \( -199 a + 230\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(25a+88\right){x}-199a+230$
5202.5-c3 5202.5-c \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.286507785$ $2.302301329$ 1.865707623 \( \frac{46268279}{46818} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( 8\) , \( 10\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+8{x}+10$
5202.5-c4 5202.5-c \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $1$ $\Z/2\Z$ $0.143253892$ $4.604602658$ 1.865707623 \( \frac{1771561}{612} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -2\) , \( 0\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}-2{x}$
5202.5-d1 5202.5-d \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $1$ $\Z/2\Z$ $4.545067097$ $0.069311322$ 3.564096622 \( -\frac{795638018697416056308875}{122322703950862781472} a - \frac{740752568391229768255000}{3822584498464461921} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -8560 a + 22289\) , \( -811360 a - 1058718\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-8560a+22289\right){x}-811360a-1058718$
5202.5-d2 5202.5-d \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $1$ $\Z/2\Z$ $4.545067097$ $0.069311322$ 3.564096622 \( \frac{795638018697416056308875}{122322703950862781472} a - \frac{740752568391229768255000}{3822584498464461921} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 8560 a + 22289\) , \( 811360 a - 1058718\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(8560a+22289\right){x}+811360a-1058718$
5202.5-d3 5202.5-d \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $1$ $\Z/6\Z$ $1.515022365$ $0.207933967$ 3.564096622 \( -\frac{410311536960329978125}{94355189265718404} a - \frac{136155893118005119000}{23588797316429601} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -1090 a + 104\) , \( -12160 a + 18366\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-1090a+104\right){x}-12160a+18366$
5202.5-d4 5202.5-d \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $1$ $\Z/6\Z$ $1.515022365$ $0.207933967$ 3.564096622 \( \frac{410311536960329978125}{94355189265718404} a - \frac{136155893118005119000}{23588797316429601} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 1090 a + 104\) , \( 12160 a + 18366\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(1090a+104\right){x}+12160a+18366$
5202.5-d5 5202.5-d \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $1$ $\Z/2\Z\oplus\Z/6\Z$ $0.757511182$ $0.415867934$ 3.564096622 \( -\frac{1107111813625}{1228691592} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -216\) , \( 2062\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-216{x}+2062$
5202.5-d6 5202.5-d \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $2.272533548$ $0.138622644$ 3.564096622 \( \frac{655215969476375}{1001033261568} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 1809\) , \( -37790\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+1809{x}-37790$
5202.5-d7 5202.5-d \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $1$ $\Z/2\Z$ $4.545067097$ $0.277245289$ 3.564096622 \( \frac{46753267515625}{11591221248} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -751\) , \( -6046\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-751{x}-6046$
5202.5-d8 5202.5-d \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $1$ $\Z/6\Z$ $1.515022365$ $0.831735869$ 3.564096622 \( \frac{1845026709625}{793152} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -256\) , \( 1550\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-256{x}+1550$
5202.5-e1 5202.5-e \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/2\Z$ $1$ $0.318337197$ 1.800787128 \( \frac{28973973968878862165}{10170654348978} a - \frac{227019597633725057126}{5085327174489} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( 1776 a - 186\) , \( -26138 a - 30473\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(1776a-186\right){x}-26138a-30473$
5202.5-e2 5202.5-e \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/4\Z$ $1$ $2.546697580$ 1.800787128 \( -\frac{63405599}{7803} a - \frac{2377909445}{124848} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -9 a + 4\) , \( -15\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-9a+4\right){x}-15$
5202.5-e3 5202.5-e \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $1.273348790$ 1.800787128 \( -\frac{21406940170}{60886809} a - \frac{61807844839}{243547236} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -9 a - 16\) , \( -28 a - 63\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-9a-16\right){x}-28a-63$
5202.5-e4 5202.5-e \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.636674395$ 1.800787128 \( \frac{208995993887450}{44386483761} a + \frac{92858826184591}{88772967522} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( 111 a - 6\) , \( -398 a - 431\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(111a-6\right){x}-398a-431$
5202.5-e5 5202.5-e \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/2\Z$ $1$ $0.318337197$ 1.800787128 \( -\frac{689132974759173725}{163244272086018} a + \frac{92030074203444902}{81622136043009} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( 366 a + 334\) , \( -738 a + 5859\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(366a+334\right){x}-738a+5859$
5202.5-e6 5202.5-e \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/4\Z$ $1$ $0.636674395$ 1.800787128 \( \frac{132789029221532066}{188345450907} a + \frac{141186623119318075}{376690901814} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -129 a - 346\) , \( -1450 a - 2367\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-129a-346\right){x}-1450a-2367$
5202.5-f1 5202.5-f \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/2\Z$ $1$ $0.318337197$ 1.800787128 \( -\frac{28973973968878862165}{10170654348978} a - \frac{227019597633725057126}{5085327174489} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -1777 a - 186\) , \( 26137 a - 30473\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-1777a-186\right){x}+26137a-30473$
5202.5-f2 5202.5-f \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/4\Z$ $1$ $2.546697580$ 1.800787128 \( \frac{63405599}{7803} a - \frac{2377909445}{124848} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( 8 a + 4\) , \( -a - 15\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(8a+4\right){x}-a-15$
5202.5-f3 5202.5-f \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $1.273348790$ 1.800787128 \( \frac{21406940170}{60886809} a - \frac{61807844839}{243547236} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( 8 a - 16\) , \( 27 a - 63\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(8a-16\right){x}+27a-63$
5202.5-f4 5202.5-f \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.636674395$ 1.800787128 \( -\frac{208995993887450}{44386483761} a + \frac{92858826184591}{88772967522} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -112 a - 6\) , \( 397 a - 431\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-112a-6\right){x}+397a-431$
5202.5-f5 5202.5-f \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/2\Z$ $1$ $0.318337197$ 1.800787128 \( \frac{689132974759173725}{163244272086018} a + \frac{92030074203444902}{81622136043009} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -367 a + 334\) , \( 737 a + 5859\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-367a+334\right){x}+737a+5859$
5202.5-f6 5202.5-f \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/4\Z$ $1$ $0.636674395$ 1.800787128 \( -\frac{132789029221532066}{188345450907} a + \frac{141186623119318075}{376690901814} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( 128 a - 346\) , \( 1449 a - 2367\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(128a-346\right){x}+1449a-2367$
5202.5-g1 5202.5-g \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/2\Z$ $1$ $0.545397751$ 3.856544483 \( -\frac{32297532210782725}{72553009816008} a + \frac{60468973557987577}{18138252454002} \) \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 89 a - 137\) , \( -532 a + 213\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(89a-137\right){x}-532a+213$
5202.5-g2 5202.5-g \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/2\Z$ $1$ $1.090795502$ 3.856544483 \( \frac{2091127194353}{409563864} a + \frac{36587816460805}{1638255456} \) \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 29 a - 57\) , \( 100 a - 131\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(29a-57\right){x}+100a-131$
5202.5-h1 5202.5-h \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/2\Z$ $1$ $0.545397751$ 3.856544483 \( \frac{32297532210782725}{72553009816008} a + \frac{60468973557987577}{18138252454002} \) \( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -90 a - 137\) , \( 531 a + 213\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-90a-137\right){x}+531a+213$
5202.5-h2 5202.5-h \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/2\Z$ $1$ $1.090795502$ 3.856544483 \( -\frac{2091127194353}{409563864} a + \frac{36587816460805}{1638255456} \) \( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -30 a - 57\) , \( -101 a - 131\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-30a-57\right){x}-101a-131$
5202.5-i1 5202.5-i \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.183754147$ 4.157881714 \( -\frac{491411892194497}{125563633938} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -1644\) , \( -30942\bigr] \) ${y}^2+{x}{y}={x}^{3}-1644{x}-30942$
5202.5-i2 5202.5-i \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/2\Z$ $1$ $0.091877073$ 4.157881714 \( -\frac{61437923106397764191713}{291967151254001210886} a - \frac{146204680417750243067160}{48661191875666868481} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( 4305 a - 924\) , \( -137739 a - 127314\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(4305a-924\right){x}-137739a-127314$
5202.5-i3 5202.5-i \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/2\Z$ $1$ $0.091877073$ 4.157881714 \( \frac{61437923106397764191713}{291967151254001210886} a - \frac{146204680417750243067160}{48661191875666868481} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -4305 a - 924\) , \( 137739 a - 127314\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-4305a-924\right){x}+137739a-127314$
5202.5-i4 5202.5-i \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/8\Z$ $1$ $0.367508294$ 4.157881714 \( \frac{1276229915423}{2927177028} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( 226\) , \( -2232\bigr] \) ${y}^2+{x}{y}={x}^{3}+226{x}-2232$
5202.5-i5 5202.5-i \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/2\Z\oplus\Z/8\Z$ $1$ $0.735016588$ 4.157881714 \( \frac{163936758817}{30338064} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -114\) , \( -396\bigr] \) ${y}^2+{x}{y}={x}^{3}-114{x}-396$
5202.5-i6 5202.5-i \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/8\Z$ $1$ $1.470033177$ 4.157881714 \( \frac{4354703137}{352512} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( 68\bigr] \) ${y}^2+{x}{y}={x}^{3}-34{x}+68$
5202.5-i7 5202.5-i \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $0.367508294$ 4.157881714 \( \frac{576615941610337}{27060804} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -1734\) , \( -27936\bigr] \) ${y}^2+{x}{y}={x}^{3}-1734{x}-27936$
5202.5-i8 5202.5-i \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 17^{2} \) $0$ $\Z/4\Z$ $1$ $0.183754147$ 4.157881714 \( \frac{2361739090258884097}{5202} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -27744\) , \( -1781010\bigr] \) ${y}^2+{x}{y}={x}^{3}-27744{x}-1781010$
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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.