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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
273.2-a2 273.2-a \(\Q(\sqrt{-3}) \) \( 3 \cdot 7 \cdot 13 \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $1.774212068$ 0.682894543 \( \frac{7478174461}{842751} a - \frac{150471620027}{22754277} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 24 a - 15\) , \( 36 a - 9\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(24a-15\right){x}+36a-9$
273.2-a8 273.2-a \(\Q(\sqrt{-3}) \) \( 3 \cdot 7 \cdot 13 \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $0.591404022$ 0.682894543 \( -\frac{12174283995544342099}{273683771825373} a + \frac{1235018026428367060}{30409307980597} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -111 a - 195\) , \( 837 a + 1080\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-111a-195\right){x}+837a+1080$
273.3-a2 273.3-a \(\Q(\sqrt{-3}) \) \( 3 \cdot 7 \cdot 13 \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $1.774212068$ 0.682894543 \( -\frac{7478174461}{842751} a + \frac{51439090420}{22754277} \) \( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( -24 a + 10\) , \( -51 a + 51\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-24a+10\right){x}-51a+51$
273.3-a8 273.3-a \(\Q(\sqrt{-3}) \) \( 3 \cdot 7 \cdot 13 \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $0.591404022$ 0.682894543 \( \frac{12174283995544342099}{273683771825373} a - \frac{1059121757689038559}{273683771825373} \) \( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 111 a - 305\) , \( -1032 a + 1806\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(111a-305\right){x}-1032a+1806$
300.1-a1 300.1-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $1.294290140$ 0.747258760 \( -\frac{273359449}{1536000} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -14\) , \( -64\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-14{x}-64$
300.1-a2 300.1-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $3.882870421$ 0.747258760 \( \frac{357911}{2160} \) \( \bigl[a + 1\) , \( -a\) , \( 1\) , \( a - 2\) , \( 2\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(a-2\right){x}+2$
14196.2-f3 14196.2-f \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7 \cdot 13^{2} \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $0.297286955$ 2.059664444 \( \frac{13114301472005393}{297763030656} a - \frac{1022733290806164619}{9528416980992} \) \( \bigl[a\) , \( a + 1\) , \( 0\) , \( -913 a + 1382\) , \( 9312 a + 10425\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-913a+1382\right){x}+9312a+10425$
14196.2-f6 14196.2-f \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7 \cdot 13^{2} \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $0.891860865$ 2.059664444 \( \frac{35254619411}{139518288} a + \frac{66721467262}{78479037} \) \( \bigl[a\) , \( a + 1\) , \( 0\) , \( 32 a - 58\) , \( 60 a + 48\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(32a-58\right){x}+60a+48$
14196.5-f3 14196.5-f \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7 \cdot 13^{2} \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $0.297286955$ 2.059664444 \( -\frac{13114301472005393}{297763030656} a - \frac{201025214567330681}{3176138993664} \) \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 469 a - 1382\) , \( -9312 a + 19737\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(469a-1382\right){x}-9312a+19737$
14196.5-f6 14196.5-f \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7 \cdot 13^{2} \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $0.891860865$ 2.059664444 \( -\frac{35254619411}{139518288} a + \frac{1384835050891}{1255664592} \) \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -26 a + 58\) , \( -60 a + 108\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-26a+58\right){x}-60a+108$
14700.2-i1 14700.2-i \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 7^{2} \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $0.049562042$ 2.747007217 \( -\frac{932348627918877961}{358766164249920} \) \( \bigl[a\) , \( 0\) , \( 1\) , \( 20352 a\) , \( -1443724\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+20352a{x}-1443724$
14700.2-i2 14700.2-i \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 7^{2} \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $0.148686127$ 2.747007217 \( \frac{785793873833639}{637994920500} \) \( \bigl[a\) , \( 0\) , \( 1\) , \( -1923 a\) , \( 20756\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-1923a{x}+20756$
650.3-a2 650.3-a \(\Q(\sqrt{-1}) \) \( 2 \cdot 5^{2} \cdot 13 \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $2.892849288$ 1.446424644 \( -\frac{171697}{6500} a + \frac{2279159}{104000} \) \( \bigl[1\) , \( 0\) , \( i + 1\) , \( -2 i - 1\) , \( 3 i + 4\bigr] \) ${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-2i-1\right){x}+3i+4$
650.3-a4 650.3-a \(\Q(\sqrt{-1}) \) \( 2 \cdot 5^{2} \cdot 13 \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $0.723212322$ 1.446424644 \( -\frac{20122730162024161}{27891601562500} a + \frac{104798752060117927}{27891601562500} \) \( \bigl[1\) , \( 0\) , \( i + 1\) , \( 108 i + 9\) , \( -171 i - 274\bigr] \) ${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(108i+9\right){x}-171i-274$
650.4-a2 650.4-a \(\Q(\sqrt{-1}) \) \( 2 \cdot 5^{2} \cdot 13 \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $2.892849288$ 1.446424644 \( \frac{171697}{6500} a + \frac{2279159}{104000} \) \( \bigl[1\) , \( 0\) , \( i + 1\) , \( i - 1\) , \( -4 i + 4\bigr] \) ${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}-4i+4$
650.4-a4 650.4-a \(\Q(\sqrt{-1}) \) \( 2 \cdot 5^{2} \cdot 13 \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $0.723212322$ 1.446424644 \( \frac{20122730162024161}{27891601562500} a + \frac{104798752060117927}{27891601562500} \) \( \bigl[1\) , \( 0\) , \( i + 1\) , \( -109 i + 9\) , \( 170 i - 274\bigr] \) ${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-109i+9\right){x}+170i-274$
4050.2-c1 4050.2-c \(\Q(\sqrt{-1}) \) \( 2 \cdot 3^{4} \cdot 5^{2} \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $0.431430046$ 2.588580280 \( -\frac{273359449}{1536000} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -122\) , \( 1721\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-122{x}+1721$
4050.2-c3 4050.2-c \(\Q(\sqrt{-1}) \) \( 2 \cdot 3^{4} \cdot 5^{2} \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $0.107857511$ 2.588580280 \( \frac{10316097499609}{5859375000} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -4082\) , \( 14681\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-4082{x}+14681$
8450.5-a4 8450.5-a \(\Q(\sqrt{-1}) \) \( 2 \cdot 5^{2} \cdot 13^{2} \) $1$ $\Z/12\Z$ $\mathrm{SU}(2)$ $1.170464153$ $0.473037374$ 2.214693161 \( -\frac{321714644118649477}{13945800781250} a + \frac{162841521219476968}{6972900390625} \) \( \bigl[i\) , \( 0\) , \( i\) , \( -370 i + 148\) , \( 732 i - 2932\bigr] \) ${y}^2+i{x}{y}+i{y}={x}^{3}+\left(-370i+148\right){x}+732i-2932$
8450.5-a5 8450.5-a \(\Q(\sqrt{-1}) \) \( 2 \cdot 5^{2} \cdot 13^{2} \) $1$ $\Z/12\Z$ $\mathrm{SU}(2)$ $1.170464153$ $0.473037374$ 2.214693161 \( \frac{321714644118649477}{13945800781250} a + \frac{162841521219476968}{6972900390625} \) \( \bigl[i\) , \( 0\) , \( i\) , \( 370 i + 148\) , \( -732 i - 2932\bigr] \) ${y}^2+i{x}{y}+i{y}={x}^{3}+\left(370i+148\right){x}-732i-2932$
22050.2-b2 22050.2-b \(\Q(\sqrt{-1}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) $1$ $\Z/12\Z$ $\mathrm{SU}(2)$ $1.696399518$ $0.148686127$ 3.026772894 \( \frac{785793873833639}{637994920500} \) \( \bigl[i\) , \( 0\) , \( i\) , \( 1923\) , \( -20756\bigr] \) ${y}^2+i{x}{y}+i{y}={x}^{3}+1923{x}-20756$
22050.2-b5 22050.2-b \(\Q(\sqrt{-1}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) $1$ $\Z/12\Z$ $\mathrm{SU}(2)$ $1.696399518$ $0.148686127$ 3.026772894 \( \frac{9150443179640281}{184570312500} \) \( \bigl[i\) , \( 0\) , \( i\) , \( -4357\) , \( 109132\bigr] \) ${y}^2+i{x}{y}+i{y}={x}^{3}-4357{x}+109132$
39650.5-g1 39650.5-g \(\Q(\sqrt{-1}) \) \( 2 \cdot 5^{2} \cdot 13 \cdot 61 \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $0.144205299$ 3.460927196 \( \frac{76911185482379738283023}{175777278320312500} a - \frac{17069327857089274127939}{175777278320312500} \) \( \bigl[1\) , \( 0\) , \( i + 1\) , \( 962 i - 6628\) , \( 44990 i - 206754\bigr] \) ${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(962i-6628\right){x}+44990i-206754$
39650.5-g6 39650.5-g \(\Q(\sqrt{-1}) \) \( 2 \cdot 5^{2} \cdot 13 \cdot 61 \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $0.576821199$ 3.460927196 \( \frac{1036917664614083}{217777625000} a + \frac{8700158718205027}{1742221000000} \) \( \bigl[i\) , \( 0\) , \( i + 1\) , \( 132 i + 143\) , \( -333 i + 888\bigr] \) ${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+\left(132i+143\right){x}-333i+888$
39650.8-g1 39650.8-g \(\Q(\sqrt{-1}) \) \( 2 \cdot 5^{2} \cdot 13 \cdot 61 \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $0.144205299$ 3.460927196 \( -\frac{76911185482379738283023}{175777278320312500} a - \frac{17069327857089274127939}{175777278320312500} \) \( \bigl[1\) , \( 0\) , \( i + 1\) , \( -963 i - 6628\) , \( -44991 i - 206754\bigr] \) ${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-963i-6628\right){x}-44991i-206754$
39650.8-g6 39650.8-g \(\Q(\sqrt{-1}) \) \( 2 \cdot 5^{2} \cdot 13 \cdot 61 \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $0.576821199$ 3.460927196 \( -\frac{1036917664614083}{217777625000} a + \frac{8700158718205027}{1742221000000} \) \( \bigl[i\) , \( 0\) , \( i + 1\) , \( -133 i + 143\) , \( 332 i + 888\bigr] \) ${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-133i+143\right){x}+332i+888$
68450.5-h1 68450.5-h \(\Q(\sqrt{-1}) \) \( 2 \cdot 5^{2} \cdot 37^{2} \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $0.207070166$ 4.969683988 \( -\frac{818871339068490287063}{3660470703125000} a - \frac{45099024956931216152}{457558837890625} \) \( \bigl[i\) , \( 0\) , \( 0\) , \( -920 i + 2805\) , \( 54952 i + 28239\bigr] \) ${y}^2+i{x}{y}={x}^{3}+\left(-920i+2805\right){x}+54952i+28239$
68450.5-h2 68450.5-h \(\Q(\sqrt{-1}) \) \( 2 \cdot 5^{2} \cdot 37^{2} \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $0.207070166$ 4.969683988 \( \frac{818871339068490287063}{3660470703125000} a - \frac{45099024956931216152}{457558837890625} \) \( \bigl[i\) , \( 0\) , \( 0\) , \( 920 i + 2805\) , \( -54952 i + 28239\bigr] \) ${y}^2+i{x}{y}={x}^{3}+\left(920i+2805\right){x}-54952i+28239$
44.3-a3 44.3-a \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11 \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $5.042664675$ 0.635316032 \( \frac{2222449}{45056} a + \frac{42043605}{45056} \) \( \bigl[1\) , \( a\) , \( 0\) , \( 1\) , \( 1\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+{x}+1$
44.4-a3 44.4-a \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11 \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $5.042664675$ 0.635316032 \( -\frac{2222449}{45056} a + \frac{22133027}{22528} \) \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 1\) , \( 1\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+{x}+1$
644.3-b6 644.3-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7 \cdot 23 \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $1.883441247$ 2.847495514 \( -\frac{9858228523}{4616192} a + \frac{2914425481}{4616192} \) \( \bigl[1\) , \( a\) , \( a\) , \( -11 a + 6\) , \( -17 a + 30\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-11a+6\right){x}-17a+30$
644.4-b6 644.4-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7 \cdot 23 \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $1.883441247$ 2.847495514 \( \frac{9858228523}{4616192} a - \frac{3471901521}{2308096} \) \( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 10 a - 5\) , \( 16 a + 13\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(10a-5\right){x}+16a+13$
2772.3-c2 2772.3-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 7 \cdot 11 \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $0.645013956$ 1.950338880 \( \frac{482697730182277}{244158824448} a - \frac{330906907974815}{122079412224} \) \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 63 a + 63\) , \( 135 a - 621\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(63a+63\right){x}+135a-621$
2772.4-d2 2772.4-d \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 7 \cdot 11 \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $0.645013956$ 1.950338880 \( -\frac{482697730182277}{244158824448} a - \frac{8529337417493}{11626610688} \) \( \bigl[1\) , \( a\) , \( 0\) , \( -63 a + 126\) , \( -135 a - 486\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-63a+126\right){x}-135a-486$
6300.2-b2 6300.2-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7 \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $0.148686127$ 0.899169179 \( \frac{785793873833639}{637994920500} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 1922\) , \( 20756\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+1922{x}+20756$
6300.2-d3 6300.2-d \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7 \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $1.090738100$ 4.947123017 \( \frac{7633736209}{3870720} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -41\) , \( -39\bigr] \) ${y}^2+{x}{y}={x}^{3}-41{x}-39$
8100.2-b1 8100.2-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{4} \cdot 5^{2} \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $0.431430046$ 3.913565526 \( -\frac{273359449}{1536000} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -122\) , \( 1721\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-122{x}+1721$
108.2-a8 108.2-a \(\Q(\sqrt{-2}) \) \( 2^{2} \cdot 3^{3} \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $1.488316936$ 1.052398998 \( \frac{715706108}{531441} a + \frac{421307996}{531441} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 2 a - 21\) , \( 13 a + 37\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a-21\right){x}+13a+37$
108.3-a7 108.3-a \(\Q(\sqrt{-2}) \) \( 2^{2} \cdot 3^{3} \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $1.488316936$ 1.052398998 \( -\frac{715706108}{531441} a + \frac{421307996}{531441} \) \( \bigl[a\) , \( a + 1\) , \( a\) , \( -2 a - 21\) , \( -13 a + 37\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a-21\right){x}-13a+37$
450.2-a4 450.2-a \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $0.970717605$ 1.372802002 \( \frac{35578826569}{5314410} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -69\) , \( -194\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-69{x}-194$
594.3-c6 594.3-c \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{3} \cdot 11 \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $1.704113391$ 2.409980269 \( -\frac{84007489}{128304} a + \frac{468710027}{513216} \) \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 9 a + 4\) , \( -4 a + 27\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(9a+4\right){x}-4a+27$
594.6-c6 594.6-c \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{3} \cdot 11 \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $1.704113391$ 2.409980269 \( \frac{84007489}{128304} a + \frac{468710027}{513216} \) \( \bigl[1\) , \( a + 1\) , \( 1\) , \( -9 a + 4\) , \( 4 a + 27\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-9a+4\right){x}+4a+27$
4050.3-c1 4050.3-c \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{4} \cdot 5^{2} \) $1$ $\Z/12\Z$ $\mathrm{SU}(2)$ $0.940639818$ $0.431430046$ 4.591332359 \( -\frac{273359449}{1536000} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -122\) , \( 1721\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-122{x}+1721$
7524.5-c2 7524.5-c \(\Q(\sqrt{-2}) \) \( 2^{2} \cdot 3^{2} \cdot 11 \cdot 19 \) $1$ $\Z/12\Z$ $\mathrm{SU}(2)$ $1.393610825$ $0.433086737$ 5.121328620 \( -\frac{9232718736054548}{761837148171} a - \frac{17532010176936668}{761837148171} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( 63 a - 452\) , \( 828 a - 3639\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(63a-452\right){x}+828a-3639$
7524.8-c2 7524.8-c \(\Q(\sqrt{-2}) \) \( 2^{2} \cdot 3^{2} \cdot 11 \cdot 19 \) $1$ $\Z/12\Z$ $\mathrm{SU}(2)$ $1.393610825$ $0.433086737$ 5.121328620 \( \frac{9232718736054548}{761837148171} a - \frac{17532010176936668}{761837148171} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( -63 a - 452\) , \( -828 a - 3639\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-63a-452\right){x}-828a-3639$
10098.8-j6 10098.8-j \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{3} \cdot 11 \cdot 17 \) $1$ $\Z/12\Z$ $\mathrm{SU}(2)$ $0.996659843$ $0.408314069$ 6.906174528 \( \frac{68070478181263}{229765327704} a + \frac{394438305984299}{1838122621632} \) \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 112 a - 97\) , \( 849 a - 1385\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(112a-97\right){x}+849a-1385$
10098.9-i6 10098.9-i \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{3} \cdot 11 \cdot 17 \) $1$ $\Z/12\Z$ $\mathrm{SU}(2)$ $0.996659843$ $0.408314069$ 6.906174528 \( -\frac{68070478181263}{229765327704} a + \frac{394438305984299}{1838122621632} \) \( \bigl[1\) , \( a + 1\) , \( 1\) , \( -112 a - 97\) , \( -849 a - 1385\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-112a-97\right){x}-849a-1385$
22050.2-b2 22050.2-b \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) $1$ $\Z/12\Z$ $\mathrm{SU}(2)$ $1.029804775$ $0.148686127$ 5.196986521 \( \frac{785793873833639}{637994920500} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 1922\) , \( 20756\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+1922{x}+20756$
22050.2-e1 22050.2-e \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $0.272684525$ 4.627609845 \( -\frac{58818484369}{18600435000} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -81\) , \( 6561\bigr] \) ${y}^2+{x}{y}={x}^{3}-81{x}+6561$
7425.5-h8 7425.5-h \(\Q(\sqrt{-11}) \) \( 3^{3} \cdot 5^{2} \cdot 11 \) $1$ $\Z/12\Z$ $\mathrm{SU}(2)$ $1.407799633$ $0.256794058$ 5.232035875 \( -\frac{1032777340820292487}{1427209716796875} a + \frac{1521986905848333643}{475736572265625} \) \( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -138 a + 853\) , \( -2710 a - 2479\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-138a+853\right){x}-2710a-2479$
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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.