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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
9.1-a1 9.1-a \(\Q(\sqrt{2}) \) \( 3^{2} \) $0$ $\Z/2\Z$ $1$ $1.266923342$ 0.223962521 \( -\frac{873722816}{59049} \) \( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -40 a - 60\) , \( -153 a - 220\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-40a-60\right){x}-153a-220$
9.1-a2 9.1-a \(\Q(\sqrt{2}) \) \( 3^{2} \) $0$ $\Z/10\Z$ $1$ $31.67308356$ 0.223962521 \( \frac{64}{9} \) \( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}$
9.1-a3 9.1-a \(\Q(\sqrt{2}) \) \( 3^{2} \) $0$ $\Z/10\Z$ $1$ $63.34616712$ 0.223962521 \( \frac{85184}{3} \) \( \bigl[a\) , \( a\) , \( a + 1\) , \( -2 a - 3\) , \( 0\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-2a-3\right){x}$
9.1-a4 9.1-a \(\Q(\sqrt{2}) \) \( 3^{2} \) $0$ $\Z/2\Z$ $1$ $2.533846685$ 0.223962521 \( \frac{58591911104}{243} \) \( \bigl[a\) , \( a\) , \( a + 1\) , \( -162 a - 243\) , \( -1495 a - 2130\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-162a-243\right){x}-1495a-2130$
17.1-a1 17.1-a \(\Q(\sqrt{2}) \) \( 17 \) $0$ $\Z/6\Z$ $1$ $22.23161552$ 0.436670169 \( -\frac{94464}{289} a + \frac{58688}{289} \) \( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -2 a + 1\) , \( -a\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a+1\right){x}-a$
17.1-a2 17.1-a \(\Q(\sqrt{2}) \) \( 17 \) $0$ $\Z/2\Z$ $1$ $2.470179502$ 0.436670169 \( \frac{1522678220544}{24137569} a - \frac{2147745195712}{24137569} \) \( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 13 a - 19\) , \( 47 a - 69\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(13a-19\right){x}+47a-69$
17.1-a3 17.1-a \(\Q(\sqrt{2}) \) \( 17 \) $0$ $\Z/2\Z$ $1$ $4.940359004$ 0.436670169 \( -\frac{55615383938816}{4913} a + \frac{78652069441856}{4913} \) \( \bigl[a\) , \( -1\) , \( a + 1\) , \( -34 a - 53\) , \( -113 a - 163\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-34a-53\right){x}-113a-163$
17.1-a4 17.1-a \(\Q(\sqrt{2}) \) \( 17 \) $0$ $\Z/6\Z$ $1$ $44.46323104$ 0.436670169 \( \frac{3690752}{17} a + \frac{5287232}{17} \) \( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( a - 1\) , \( -1\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a-1\right){x}-1$
17.2-a1 17.2-a \(\Q(\sqrt{2}) \) \( 17 \) $0$ $\Z/2\Z$ $1$ $2.470179502$ 0.436670169 \( -\frac{1522678220544}{24137569} a - \frac{2147745195712}{24137569} \) \( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( -14 a - 19\) , \( -48 a - 69\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-14a-19\right){x}-48a-69$
17.2-a2 17.2-a \(\Q(\sqrt{2}) \) \( 17 \) $0$ $\Z/6\Z$ $1$ $22.23161552$ 0.436670169 \( \frac{94464}{289} a + \frac{58688}{289} \) \( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( a + 1\) , \( 0\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+1\right){x}$
17.2-a3 17.2-a \(\Q(\sqrt{2}) \) \( 17 \) $0$ $\Z/6\Z$ $1$ $44.46323104$ 0.436670169 \( -\frac{3690752}{17} a + \frac{5287232}{17} \) \( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -2 a - 1\) , \( -a - 1\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a-1\right){x}-a-1$
17.2-a4 17.2-a \(\Q(\sqrt{2}) \) \( 17 \) $0$ $\Z/2\Z$ $1$ $4.940359004$ 0.436670169 \( \frac{55615383938816}{4913} a + \frac{78652069441856}{4913} \) \( \bigl[a\) , \( -1\) , \( a + 1\) , \( 33 a - 53\) , \( 112 a - 163\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(33a-53\right){x}+112a-163$
28.1-a1 28.1-a \(\Q(\sqrt{2}) \) \( 2^{2} \cdot 7 \) $0$ $\Z/4\Z$ $1$ $2.155441053$ 0.571547619 \( -\frac{29518306565684}{13841287201} a + \frac{41622722395132}{13841287201} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -9 a - 18\) , \( -320 a - 467\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-9a-18\right){x}-320a-467$
28.1-a2 28.1-a \(\Q(\sqrt{2}) \) \( 2^{2} \cdot 7 \) $0$ $\Z/12\Z$ $1$ $19.39896948$ 0.571547619 \( -\frac{861093316}{2401} a + \frac{1217791012}{2401} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( a + 2\) , \( 12 a + 17\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(a+2\right){x}+12a+17$
28.1-a3 28.1-a \(\Q(\sqrt{2}) \) \( 2^{2} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $2.155441053$ 0.571547619 \( -\frac{91481168031853524}{343} a + \frac{129373908533024396}{343} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -19 a - 148\) , \( 318 a - 201\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-19a-148\right){x}+318a-201$
28.1-a4 28.1-a \(\Q(\sqrt{2}) \) \( 2^{2} \cdot 7 \) $0$ $\Z/6\Z$ $1$ $19.39896948$ 0.571547619 \( \frac{4096}{7} a + \frac{16384}{7} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -2 a + 3\) , \( 0\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(-2a+3\right){x}$
28.1-a5 28.1-a \(\Q(\sqrt{2}) \) \( 2^{2} \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/6\Z$ $1$ $38.79793896$ 0.571547619 \( \frac{435744}{49} a + \frac{712688}{49} \) \( \bigl[a\) , \( -1\) , \( a\) , \( 2 a - 4\) , \( -a + 1\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(2a-4\right){x}-a+1$
28.1-a6 28.1-a \(\Q(\sqrt{2}) \) \( 2^{2} \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $4.310882107$ 0.571547619 \( -\frac{1137747277344}{117649} a + \frac{1622386617968}{117649} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -34 a - 53\) , \( -133 a - 203\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-34a-53\right){x}-133a-203$
28.1-a7 28.1-a \(\Q(\sqrt{2}) \) \( 2^{2} \cdot 7 \) $0$ $\Z/6\Z$ $1$ $19.39896948$ 0.571547619 \( \frac{1720664028}{7} a + \frac{2434028852}{7} \) \( \bigl[a\) , \( -1\) , \( a\) , \( 17 a - 29\) , \( 49 a - 66\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(17a-29\right){x}+49a-66$
28.1-a8 28.1-a \(\Q(\sqrt{2}) \) \( 2^{2} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $2.155441053$ 0.571547619 \( \frac{1545435312128}{343} a + \frac{2185574023168}{343} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 18 a - 37\) , \( 68 a - 108\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(18a-37\right){x}+68a-108$
28.2-a1 28.2-a \(\Q(\sqrt{2}) \) \( 2^{2} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $2.155441053$ 0.571547619 \( -\frac{1545435312128}{343} a + \frac{2185574023168}{343} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -18 a - 37\) , \( -68 a - 108\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(-18a-37\right){x}-68a-108$
28.2-a2 28.2-a \(\Q(\sqrt{2}) \) \( 2^{2} \cdot 7 \) $0$ $\Z/6\Z$ $1$ $19.39896948$ 0.571547619 \( -\frac{4096}{7} a + \frac{16384}{7} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 2 a + 3\) , \( 0\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(2a+3\right){x}$
28.2-a3 28.2-a \(\Q(\sqrt{2}) \) \( 2^{2} \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/6\Z$ $1$ $38.79793896$ 0.571547619 \( -\frac{435744}{49} a + \frac{712688}{49} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -2 a - 4\) , \( a + 1\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-2a-4\right){x}+a+1$
28.2-a4 28.2-a \(\Q(\sqrt{2}) \) \( 2^{2} \cdot 7 \) $0$ $\Z/4\Z$ $1$ $2.155441053$ 0.571547619 \( \frac{29518306565684}{13841287201} a + \frac{41622722395132}{13841287201} \) \( \bigl[a\) , \( a + 1\) , \( 0\) , \( 9 a - 18\) , \( 320 a - 467\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(9a-18\right){x}+320a-467$
28.2-a5 28.2-a \(\Q(\sqrt{2}) \) \( 2^{2} \cdot 7 \) $0$ $\Z/6\Z$ $1$ $19.39896948$ 0.571547619 \( -\frac{1720664028}{7} a + \frac{2434028852}{7} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -17 a - 29\) , \( -49 a - 66\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-17a-29\right){x}-49a-66$
28.2-a6 28.2-a \(\Q(\sqrt{2}) \) \( 2^{2} \cdot 7 \) $0$ $\Z/12\Z$ $1$ $19.39896948$ 0.571547619 \( \frac{861093316}{2401} a + \frac{1217791012}{2401} \) \( \bigl[a\) , \( a + 1\) , \( 0\) , \( -a + 2\) , \( -12 a + 17\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-a+2\right){x}-12a+17$
28.2-a7 28.2-a \(\Q(\sqrt{2}) \) \( 2^{2} \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $4.310882107$ 0.571547619 \( \frac{1137747277344}{117649} a + \frac{1622386617968}{117649} \) \( \bigl[a\) , \( a + 1\) , \( 0\) , \( 34 a - 53\) , \( 133 a - 203\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(34a-53\right){x}+133a-203$
28.2-a8 28.2-a \(\Q(\sqrt{2}) \) \( 2^{2} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $2.155441053$ 0.571547619 \( \frac{91481168031853524}{343} a + \frac{129373908533024396}{343} \) \( \bigl[a\) , \( a + 1\) , \( 0\) , \( 19 a - 148\) , \( -318 a - 201\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(19a-148\right){x}-318a-201$
31.1-a1 31.1-a \(\Q(\sqrt{2}) \) \( 31 \) $0$ $\Z/2\Z$ $1$ $2.544454463$ 0.449800251 \( -\frac{78588372777605}{923521} a + \frac{111138046783591}{923521} \) \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -7 a - 21\) , \( -31 a - 52\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-7a-21\right){x}-31a-52$
31.1-a2 31.1-a \(\Q(\sqrt{2}) \) \( 31 \) $0$ $\Z/4\Z$ $1$ $20.35563570$ 0.449800251 \( \frac{47780}{31} a + \frac{69151}{31} \) \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -2 a - 1\) , \( -a - 2\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a-1\right){x}-a-2$
31.1-a3 31.1-a \(\Q(\sqrt{2}) \) \( 31 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $10.17781785$ 0.449800251 \( \frac{4423034250}{961} a + \frac{6270751283}{961} \) \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 10 a - 14\) , \( 21 a - 30\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(10a-14\right){x}+21a-30$
31.1-a4 31.1-a \(\Q(\sqrt{2}) \) \( 31 \) $0$ $\Z/2\Z$ $1$ $5.088908926$ 0.449800251 \( \frac{1861812264958875}{31} a + \frac{2633000155833143}{31} \) \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 25 a - 49\) , \( -79 a + 100\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(25a-49\right){x}-79a+100$
31.2-a1 31.2-a \(\Q(\sqrt{2}) \) \( 31 \) $0$ $\Z/4\Z$ $1$ $20.35563570$ 0.449800251 \( -\frac{47780}{31} a + \frac{69151}{31} \) \( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}$
31.2-a2 31.2-a \(\Q(\sqrt{2}) \) \( 31 \) $0$ $\Z/2\Z$ $1$ $5.088908926$ 0.449800251 \( -\frac{1861812264958875}{31} a + \frac{2633000155833143}{31} \) \( \bigl[1\) , \( a - 1\) , \( 1\) , \( -25 a - 49\) , \( 79 a + 100\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-25a-49\right){x}+79a+100$
31.2-a3 31.2-a \(\Q(\sqrt{2}) \) \( 31 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $10.17781785$ 0.449800251 \( -\frac{4423034250}{961} a + \frac{6270751283}{961} \) \( \bigl[1\) , \( a - 1\) , \( 1\) , \( -10 a - 14\) , \( -21 a - 30\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-10a-14\right){x}-21a-30$
31.2-a4 31.2-a \(\Q(\sqrt{2}) \) \( 31 \) $0$ $\Z/2\Z$ $1$ $2.544454463$ 0.449800251 \( \frac{78588372777605}{923521} a + \frac{111138046783591}{923521} \) \( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 5 a - 20\) , \( 10 a - 40\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(5a-20\right){x}+10a-40$
32.1-a1 32.1-a \(\Q(\sqrt{2}) \) \( 2^{5} \) $0$ $\Z/2\Z$ $-64$ $1$ $3.437592909$ 0.607686314 \( -29071392966 a + 41113158120 \) \( \bigl[a\) , \( 1\) , \( 0\) , \( 15 a - 22\) , \( 46 a - 69\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(15a-22\right){x}+46a-69$
32.1-a2 32.1-a \(\Q(\sqrt{2}) \) \( 2^{5} \) $0$ $\Z/4\Z$ $-64$ $1$ $27.50074327$ 0.607686314 \( -29071392966 a + 41113158120 \) \( \bigl[a\) , \( 1\) , \( a\) , \( 15 a - 23\) , \( -31 a + 46\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(15a-23\right){x}-31a+46$
32.1-a3 32.1-a \(\Q(\sqrt{2}) \) \( 2^{5} \) $0$ $\Z/4\Z$ $-4$ $1$ $13.75037163$ 0.607686314 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2={x}^{3}+{x}$
32.1-a4 32.1-a \(\Q(\sqrt{2}) \) \( 2^{5} \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $-4$ $1$ $27.50074327$ 0.607686314 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \) ${y}^2={x}^{3}-{x}$
32.1-a5 32.1-a \(\Q(\sqrt{2}) \) \( 2^{5} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $-16$ $1$ $13.75037163$ 0.607686314 \( 287496 \) \( \bigl[a\) , \( 1\) , \( 0\) , \( -2\) , \( -3\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}-2{x}-3$
32.1-a6 32.1-a \(\Q(\sqrt{2}) \) \( 2^{5} \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $-16$ $1$ $55.00148654$ 0.607686314 \( 287496 \) \( \bigl[a\) , \( 1\) , \( a\) , \( -3\) , \( 0\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-3{x}$
32.1-a7 32.1-a \(\Q(\sqrt{2}) \) \( 2^{5} \) $0$ $\Z/2\Z$ $-64$ $1$ $3.437592909$ 0.607686314 \( 29071392966 a + 41113158120 \) \( \bigl[a\) , \( 1\) , \( 0\) , \( -15 a - 22\) , \( -46 a - 69\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-15a-22\right){x}-46a-69$
32.1-a8 32.1-a \(\Q(\sqrt{2}) \) \( 2^{5} \) $0$ $\Z/4\Z$ $-64$ $1$ $27.50074327$ 0.607686314 \( 29071392966 a + 41113158120 \) \( \bigl[a\) , \( 1\) , \( a\) , \( -15 a - 23\) , \( 31 a + 46\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-15a-23\right){x}+31a+46$
34.1-a1 34.1-a \(\Q(\sqrt{2}) \) \( 2 \cdot 17 \) $0$ $\Z/2\Z$ $1$ $2.790055734$ 0.493216832 \( -\frac{9756993259}{1257728} a - \frac{25455932221}{2515456} \) \( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -16 a + 19\) , \( -25 a + 31\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-16a+19\right){x}-25a+31$
34.1-a2 34.1-a \(\Q(\sqrt{2}) \) \( 2 \cdot 17 \) $0$ $\Z/6\Z$ $1$ $25.11050160$ 0.493216832 \( \frac{2939047}{68} a - \frac{8089117}{136} \) \( \bigl[1\) , \( a - 1\) , \( 0\) , \( 2 a + 4\) , \( 0\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2a+4\right){x}$
34.1-a3 34.1-a \(\Q(\sqrt{2}) \) \( 2 \cdot 17 \) $0$ $\Z/6\Z$ $1$ $25.11050160$ 0.493216832 \( -\frac{6018090689657}{1156} a + \frac{4255433785057}{578} \) \( \bigl[1\) , \( a - 1\) , \( 0\) , \( -8 a - 16\) , \( -10 a - 4\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-8a-16\right){x}-10a-4$
34.1-a4 34.1-a \(\Q(\sqrt{2}) \) \( 2 \cdot 17 \) $0$ $\Z/2\Z$ $1$ $2.790055734$ 0.493216832 \( \frac{130087595511310753}{772402208} a + \frac{91987087285468997}{386201104} \) \( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 64 a - 141\) , \( -457 a + 479\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(64a-141\right){x}-457a+479$
34.2-a1 34.2-a \(\Q(\sqrt{2}) \) \( 2 \cdot 17 \) $0$ $\Z/6\Z$ $1$ $25.11050160$ 0.493216832 \( -\frac{2939047}{68} a - \frac{8089117}{136} \) \( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -2 a + 4\) , \( 0\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a+4\right){x}$
34.2-a2 34.2-a \(\Q(\sqrt{2}) \) \( 2 \cdot 17 \) $0$ $\Z/2\Z$ $1$ $2.790055734$ 0.493216832 \( \frac{9756993259}{1257728} a - \frac{25455932221}{2515456} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 15 a + 20\) , \( 44 a + 62\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(15a+20\right){x}+44a+62$
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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.