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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
10.1-a1 10.1-a \(\Q(\sqrt{-31}) \) \( 2 \cdot 5 \) $0$ $\Z/2\Z$ $1$ $1.385680830$ 1.742129368 \( -\frac{780929100411181}{1280000000} a - \frac{1907478885001083}{1280000000} \) \( \bigl[a\) , \( a - 1\) , \( a\) , \( -67 a + 360\) , \( 905 a + 1396\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3+\left(a-1\right){x}^2+\left(-67a+360\right){x}+905a+1396$
10.1-a2 10.1-a \(\Q(\sqrt{-31}) \) \( 2 \cdot 5 \) $0$ $\Z/2\Z$ $1$ $9.699765812$ 1.742129368 \( \frac{2911}{20} a - \frac{193027}{20} \) \( \bigl[a\) , \( a - 1\) , \( a\) , \( -2 a\) , \( -a + 4\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3+\left(a-1\right){x}^2-2a{x}-a+4$
10.1-a3 10.1-a \(\Q(\sqrt{-31}) \) \( 2 \cdot 5 \) $0$ $\Z/2\Z$ $1$ $9.699765812$ 1.742129368 \( -\frac{19951}{50} a - \frac{47943}{50} \) \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( a - 3\) , \( 1\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+\left(-a-1\right){x}^2+\left(a-3\right){x}+1$
10.1-a4 10.1-a \(\Q(\sqrt{-31}) \) \( 2 \cdot 5 \) $0$ $\Z/2\Z$ $1$ $1.385680830$ 1.742129368 \( \frac{379001974281391}{781250000000} a - \frac{103373105456887}{781250000000} \) \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -4 a + 17\) , \( 12 a - 1\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+\left(-a-1\right){x}^2+\left(-4a+17\right){x}+12a-1$
10.4-a1 10.4-a \(\Q(\sqrt{-31}) \) \( 2 \cdot 5 \) $0$ $\Z/2\Z$ $1$ $1.385680830$ 1.742129368 \( \frac{780929100411181}{1280000000} a - \frac{336050998176533}{160000000} \) \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 62 a + 289\) , \( -550 a + 1785\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+a{x}^2+\left(62a+289\right){x}-550a+1785$
10.4-a2 10.4-a \(\Q(\sqrt{-31}) \) \( 2 \cdot 5 \) $0$ $\Z/2\Z$ $1$ $9.699765812$ 1.742129368 \( -\frac{2911}{20} a - \frac{47529}{5} \) \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -3 a - 6\) , \( -4 a + 7\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+a{x}^2+\left(-3a-6\right){x}-4a+7$
10.4-a3 10.4-a \(\Q(\sqrt{-31}) \) \( 2 \cdot 5 \) $0$ $\Z/2\Z$ $1$ $9.699765812$ 1.742129368 \( \frac{19951}{50} a - \frac{33947}{25} \) \( \bigl[1\) , \( a + 1\) , \( 0\) , \( a - 2\) , \( -1\bigr] \) ${y}^2+{x}{y}={x}^3+\left(a+1\right){x}^2+\left(a-2\right){x}-1$
10.4-a4 10.4-a \(\Q(\sqrt{-31}) \) \( 2 \cdot 5 \) $0$ $\Z/2\Z$ $1$ $1.385680830$ 1.742129368 \( -\frac{379001974281391}{781250000000} a + \frac{34453608603063}{97656250000} \) \( \bigl[1\) , \( a + 1\) , \( 0\) , \( 6 a + 13\) , \( -7 a + 24\bigr] \) ${y}^2+{x}{y}={x}^3+\left(a+1\right){x}^2+\left(6a+13\right){x}-7a+24$
14.2-a1 14.2-a \(\Q(\sqrt{-31}) \) \( 2 \cdot 7 \) $0$ $\Z/3\Z$ $1$ $1.122170831$ 0.806191324 \( -\frac{3429643149944533}{10578455953408} a - \frac{436912252725523}{10578455953408} \) \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -a + 29\) , \( -24 a - 42\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(-a+29\right){x}-24a-42$
14.2-a2 14.2-a \(\Q(\sqrt{-31}) \) \( 2 \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $0.374056943$ 0.806191324 \( \frac{1524255431343666912883}{6178938688752320512} a + \frac{1865190650273146662373}{6178938688752320512} \) \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 4 a - 266\) , \( 467 a + 1516\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(4a-266\right){x}+467a+1516$
14.2-a3 14.2-a \(\Q(\sqrt{-31}) \) \( 2 \cdot 7 \) $0$ $\Z/3\Z$ $1$ $10.09953748$ 0.806191324 \( \frac{17387}{28} a + \frac{61997}{28} \) \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -a - 1\) , \( 0\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(-a-1\right){x}$
14.2-a4 14.2-a \(\Q(\sqrt{-31}) \) \( 2 \cdot 7 \) $0$ $\Z/3\Z$ $1$ $3.366512495$ 0.806191324 \( -\frac{25508811437}{21952} a + \frac{14931496453}{21952} \) \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 4 a + 4\) , \( -a - 38\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(4a+4\right){x}-a-38$
14.3-a1 14.3-a \(\Q(\sqrt{-31}) \) \( 2 \cdot 7 \) $0$ $\Z/3\Z$ $1$ $3.366512495$ 0.806191324 \( \frac{25508811437}{21952} a - \frac{1322164373}{2744} \) \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -5 a + 9\) , \( a - 39\bigr] \) ${y}^2+a{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2+\left(-5a+9\right){x}+a-39$
14.3-a2 14.3-a \(\Q(\sqrt{-31}) \) \( 2 \cdot 7 \) $0$ $\Z/3\Z$ $1$ $1.122170831$ 0.806191324 \( \frac{3429643149944533}{10578455953408} a - \frac{483319425333757}{1322306994176} \) \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 29\) , \( 24 a - 66\bigr] \) ${y}^2+a{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2+29{x}+24a-66$
14.3-a3 14.3-a \(\Q(\sqrt{-31}) \) \( 2 \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $0.374056943$ 0.806191324 \( -\frac{1524255431343666912883}{6178938688752320512} a + \frac{423680760202101696907}{772367336094040064} \) \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -5 a - 261\) , \( -467 a + 1983\bigr] \) ${y}^2+a{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2+\left(-5a-261\right){x}-467a+1983$
14.3-a4 14.3-a \(\Q(\sqrt{-31}) \) \( 2 \cdot 7 \) $0$ $\Z/3\Z$ $1$ $10.09953748$ 0.806191324 \( -\frac{17387}{28} a + \frac{19846}{7} \) \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -1\) , \( 0\bigr] \) ${y}^2+a{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2-{x}$
20.3-a1 20.3-a \(\Q(\sqrt{-31}) \) \( 2^{2} \cdot 5 \) $1$ $\Z/2\Z$ $0.463053980$ $2.448298200$ 0.814469976 \( \frac{4201360591}{8000000} a + \frac{36727033713}{8000000} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 4 a + 40\) , \( -38 a + 48\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3+\left(-a+1\right){x}^2+\left(4a+40\right){x}-38a+48$
20.3-a2 20.3-a \(\Q(\sqrt{-31}) \) \( 2^{2} \cdot 5 \) $1$ $\Z/6\Z$ $1.389161942$ $7.344894602$ 0.814469976 \( -\frac{240871}{200} a + \frac{1256497}{200} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -a\) , \( 0\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3+\left(-a+1\right){x}^2-a{x}$
20.3-a3 20.3-a \(\Q(\sqrt{-31}) \) \( 2^{2} \cdot 5 \) $1$ $\Z/6\Z$ $2.778323884$ $7.344894602$ 0.814469976 \( \frac{566667}{320} a + \frac{2148781}{320} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -4 a - 4\) , \( 16\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a-1\right){x}^2+\left(-4a-4\right){x}+16$
20.3-a4 20.3-a \(\Q(\sqrt{-31}) \) \( 2^{2} \cdot 5 \) $1$ $\Z/2\Z$ $0.926107961$ $2.448298200$ 0.814469976 \( -\frac{55081295373}{32768000} a + \frac{423698409061}{32768000} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 11 a + 21\) , \( -5 a + 45\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a-1\right){x}^2+\left(11a+21\right){x}-5a+45$
20.3-b1 20.3-b \(\Q(\sqrt{-31}) \) \( 2^{2} \cdot 5 \) $0$ $\Z/2\Z$ $1$ $1.138318178$ 1.226687881 \( \frac{5721159718441}{512000} a - \frac{17013218122889}{64000} \) \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 78 a - 963\) , \( -1718 a + 12067\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(78a-963\right){x}-1718a+12067$
20.3-b2 20.3-b \(\Q(\sqrt{-31}) \) \( 2^{2} \cdot 5 \) $0$ $\Z/6\Z$ $1$ $3.414954535$ 1.226687881 \( \frac{94333009}{12800} a - \frac{23122663}{12800} \) \( \bigl[a\) , \( 0\) , \( a\) , \( 3 a + 29\) , \( 16 a - 58\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3+\left(3a+29\right){x}+16a-58$
20.3-b3 20.3-b \(\Q(\sqrt{-31}) \) \( 2^{2} \cdot 5 \) $0$ $\Z/6\Z$ $1$ $3.414954535$ 1.226687881 \( \frac{7985051}{1310720} a - \frac{205461507}{1310720} \) \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -2 a - 3\) , \( -6 a + 35\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(-2a-3\right){x}-6a+35$
20.3-b4 20.3-b \(\Q(\sqrt{-31}) \) \( 2^{2} \cdot 5 \) $0$ $\Z/2\Z$ $1$ $1.138318178$ 1.226687881 \( -\frac{1520638086962303}{262144000000} a + \frac{87855796164087}{32768000000} \) \( \bigl[a\) , \( 0\) , \( a\) , \( 68 a - 171\) , \( 452 a - 346\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3+\left(68a-171\right){x}+452a-346$
20.4-a1 20.4-a \(\Q(\sqrt{-31}) \) \( 2^{2} \cdot 5 \) $1$ $\Z/6\Z$ $1.389161942$ $7.344894602$ 0.814469976 \( \frac{240871}{200} a + \frac{507813}{100} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -a - 1\) , \( -a\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}-a$
20.4-a2 20.4-a \(\Q(\sqrt{-31}) \) \( 2^{2} \cdot 5 \) $1$ $\Z/2\Z$ $0.463053980$ $2.448298200$ 0.814469976 \( -\frac{4201360591}{8000000} a + \frac{639506161}{125000} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -6 a + 44\) , \( 37 a + 10\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-6a+44\right){x}+37a+10$
20.4-a3 20.4-a \(\Q(\sqrt{-31}) \) \( 2^{2} \cdot 5 \) $1$ $\Z/6\Z$ $2.778323884$ $7.344894602$ 0.814469976 \( -\frac{566667}{320} a + \frac{339431}{40} \) \( \bigl[a\) , \( a + 1\) , \( a\) , \( a\) , \( 0\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3+\left(a+1\right){x}^2+a{x}$
20.4-a4 20.4-a \(\Q(\sqrt{-31}) \) \( 2^{2} \cdot 5 \) $1$ $\Z/2\Z$ $0.926107961$ $2.448298200$ 0.814469976 \( \frac{55081295373}{32768000} a + \frac{46077139211}{4096000} \) \( \bigl[a\) , \( a + 1\) , \( a\) , \( -14 a + 40\) , \( 30 a + 144\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3+\left(a+1\right){x}^2+\left(-14a+40\right){x}+30a+144$
20.4-b1 20.4-b \(\Q(\sqrt{-31}) \) \( 2^{2} \cdot 5 \) $0$ $\Z/2\Z$ $1$ $1.138318178$ 1.226687881 \( -\frac{5721159718441}{512000} a - \frac{130384585264671}{512000} \) \( \bigl[a\) , \( -a\) , \( a\) , \( -80 a - 883\) , \( 1717 a + 10350\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3-a{x}^2+\left(-80a-883\right){x}+1717a+10350$
20.4-b2 20.4-b \(\Q(\sqrt{-31}) \) \( 2^{2} \cdot 5 \) $0$ $\Z/2\Z$ $1$ $1.138318178$ 1.226687881 \( \frac{1520638086962303}{262144000000} a - \frac{817791717649607}{262144000000} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -70 a - 103\) , \( -453 a + 106\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-a{x}^2+\left(-70a-103\right){x}-453a+106$
20.4-b3 20.4-b \(\Q(\sqrt{-31}) \) \( 2^{2} \cdot 5 \) $0$ $\Z/6\Z$ $1$ $3.414954535$ 1.226687881 \( -\frac{7985051}{1310720} a - \frac{24684557}{163840} \) \( \bigl[a\) , \( -a\) , \( a\) , \( -3\) , \( 5 a + 30\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3-a{x}^2-3{x}+5a+30$
20.4-b4 20.4-b \(\Q(\sqrt{-31}) \) \( 2^{2} \cdot 5 \) $0$ $\Z/6\Z$ $1$ $3.414954535$ 1.226687881 \( -\frac{94333009}{12800} a + \frac{35605173}{6400} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -5 a + 32\) , \( -17 a - 42\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-a{x}^2+\left(-5a+32\right){x}-17a-42$
32.2-a1 32.2-a \(\Q(\sqrt{-31}) \) \( 2^{5} \) $0$ $\Z/2\Z$ $1$ $3.684514436$ 1.323516656 \( \frac{514073}{32} a - 48120 \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -2 a + 8\) , \( 4\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3+\left(-a+1\right){x}^2+\left(-2a+8\right){x}+4$
32.2-a2 32.2-a \(\Q(\sqrt{-31}) \) \( 2^{5} \) $0$ $\Z/2\Z$ $1$ $3.684514436$ 1.323516656 \( -\frac{514073}{32} a - \frac{1025767}{32} \) \( \bigl[a\) , \( 0\) , \( a\) , \( 2 a + 32\) , \( -20 a + 16\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3+\left(2a+32\right){x}-20a+16$
32.2-a3 32.2-a \(\Q(\sqrt{-31}) \) \( 2^{5} \) $0$ $\Z/2\Z$ $1$ $3.684514436$ 1.323516656 \( \frac{85169}{1024} a + \frac{12167}{128} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 8\) , \( -4 a + 16\bigr] \) ${y}^2={x}^3-{x}^2+8{x}-4a+16$
32.2-a4 32.2-a \(\Q(\sqrt{-31}) \) \( 2^{5} \) $0$ $\Z/2\Z$ $1$ $3.684514436$ 1.323516656 \( -\frac{85169}{1024} a + \frac{182505}{1024} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 8\) , \( -4 a - 12\bigr] \) ${y}^2={x}^3+{x}^2+8{x}-4a-12$
32.3-a1 32.3-a \(\Q(\sqrt{-31}) \) \( 2^{5} \) $1$ $\mathsf{trivial}$ $0.139158379$ $8.191609121$ 1.637901283 \( 1536 a + 1280 \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -a + 3\) , \( -3\bigr] \) ${y}^2={x}^3-{x}^2+\left(-a+3\right){x}-3$
32.4-a1 32.4-a \(\Q(\sqrt{-31}) \) \( 2^{5} \) $1$ $\mathsf{trivial}$ $0.139158379$ $8.191609121$ 1.637901283 \( -1536 a + 2816 \) \( \bigl[0\) , \( -1\) , \( 0\) , \( a + 2\) , \( -3\bigr] \) ${y}^2={x}^3-{x}^2+\left(a+2\right){x}-3$
32.5-a1 32.5-a \(\Q(\sqrt{-31}) \) \( 2^{5} \) $0$ $\Z/2\Z$ $1$ $3.684514436$ 1.323516656 \( \frac{514073}{32} a - 48120 \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -4 a + 34\) , \( 19 a - 4\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-a{x}^2+\left(-4a+34\right){x}+19a-4$
32.5-a2 32.5-a \(\Q(\sqrt{-31}) \) \( 2^{5} \) $0$ $\Z/2\Z$ $1$ $3.684514436$ 1.323516656 \( -\frac{514073}{32} a - \frac{1025767}{32} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 6\) , \( -a + 4\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+6{x}-a+4$
32.5-a3 32.5-a \(\Q(\sqrt{-31}) \) \( 2^{5} \) $0$ $\Z/2\Z$ $1$ $3.684514436$ 1.323516656 \( \frac{85169}{1024} a + \frac{12167}{128} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 8\) , \( 4 a - 16\bigr] \) ${y}^2={x}^3+{x}^2+8{x}+4a-16$
32.5-a4 32.5-a \(\Q(\sqrt{-31}) \) \( 2^{5} \) $0$ $\Z/2\Z$ $1$ $3.684514436$ 1.323516656 \( -\frac{85169}{1024} a + \frac{182505}{1024} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 8\) , \( 4 a + 12\bigr] \) ${y}^2={x}^3-{x}^2+8{x}+4a+12$
49.1-a1 49.1-a \(\Q(\sqrt{-31}) \) \( 7^{2} \) $0$ $\mathsf{trivial}$ $1$ $3.185341100$ 2.288416601 \( \frac{38637}{343} a + \frac{563544}{343} \) \( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 2 a + 2\) , \( -2 a + 7\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(2a+2\right){x}-2a+7$
49.3-a1 49.3-a \(\Q(\sqrt{-31}) \) \( 7^{2} \) $0$ $\mathsf{trivial}$ $1$ $3.185341100$ 2.288416601 \( -\frac{38637}{343} a + \frac{602181}{343} \) \( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -2 a - 4\) , \( -a + 2\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+{x}^2+\left(-2a-4\right){x}-a+2$
50.1-a1 50.1-a \(\Q(\sqrt{-31}) \) \( 2 \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $0.619695306$ 1.558207877 \( -\frac{780929100411181}{1280000000} a - \frac{1907478885001083}{1280000000} \) \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -609 a + 1079\) , \( -674 a + 33097\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a-1\right){x}^2+\left(-609a+1079\right){x}-674a+33097$
50.1-a2 50.1-a \(\Q(\sqrt{-31}) \) \( 2 \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $4.337867144$ 1.558207877 \( \frac{2911}{20} a - \frac{193027}{20} \) \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( a - 11\) , \( -9\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a-1\right){x}^2+\left(a-11\right){x}-9$
50.1-a3 50.1-a \(\Q(\sqrt{-31}) \) \( 2 \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $4.337867144$ 1.558207877 \( -\frac{19951}{50} a - \frac{47943}{50} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( a + 8\) , \( -8 a\bigr] \) ${y}^2+a{x}{y}={x}^3+\left(-a+1\right){x}^2+\left(a+8\right){x}-8a$
50.1-a4 50.1-a \(\Q(\sqrt{-31}) \) \( 2 \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $0.619695306$ 1.558207877 \( \frac{379001974281391}{781250000000} a - \frac{103373105456887}{781250000000} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -144 a - 112\) , \( 1415 a - 3512\bigr] \) ${y}^2+a{x}{y}={x}^3+\left(-a+1\right){x}^2+\left(-144a-112\right){x}+1415a-3512$
50.6-a1 50.6-a \(\Q(\sqrt{-31}) \) \( 2 \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $0.619695306$ 1.558207877 \( \frac{780929100411181}{1280000000} a - \frac{336050998176533}{160000000} \) \( \bigl[a\) , \( a + 1\) , \( 0\) , \( 605 a + 472\) , \( 1753 a + 27576\bigr] \) ${y}^2+a{x}{y}={x}^3+\left(a+1\right){x}^2+\left(605a+472\right){x}+1753a+27576$
50.6-a2 50.6-a \(\Q(\sqrt{-31}) \) \( 2 \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $4.337867144$ 1.558207877 \( -\frac{2911}{20} a - \frac{47529}{5} \) \( \bigl[a\) , \( a + 1\) , \( 0\) , \( -5 a - 8\) , \( -11 a + 24\bigr] \) ${y}^2+a{x}{y}={x}^3+\left(a+1\right){x}^2+\left(-5a-8\right){x}-11a+24$
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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.