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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
1.1-a1 1.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 1 \) $0$ $\Z/2\Z$ $1$ $0.925503519$ 0.283435452 \( -4572291148814851641920 a^{3} + 10462525154672292268320 a^{2} + 3492919624948937785472 a - 7992658002021083838208 \) \( \bigl[\frac{1}{2} a^{3} - a\) , \( -a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 1\) , \( \frac{85}{2} a^{3} + \frac{51}{2} a^{2} - 284 a - 304\) , \( \frac{951}{2} a^{3} + \frac{589}{2} a^{2} - 2911 a - 2650\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-a\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(\frac{85}{2}a^{3}+\frac{51}{2}a^{2}-284a-304\right){x}+\frac{951}{2}a^{3}+\frac{589}{2}a^{2}-2911a-2650$
1.1-a2 1.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 1 \) $0$ $\Z/2\Z$ $1$ $0.925503519$ 0.283435452 \( 4572291148814851641920 a^{3} + 10462525154672292268320 a^{2} - 3492919624948937785472 a - 7992658002021083838208 \) \( \bigl[\frac{1}{2} a^{3} - a\) , \( a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 1\) , \( -43 a^{3} + \frac{51}{2} a^{2} + 284 a - 304\) , \( -\frac{951}{2} a^{3} + \frac{589}{2} a^{2} + 2910 a - 2650\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-a\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-43a^{3}+\frac{51}{2}a^{2}+284a-304\right){x}-\frac{951}{2}a^{3}+\frac{589}{2}a^{2}+2910a-2650$
1.1-a3 1.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 1 \) $0$ $\Z/14\Z$ $1$ $2222.133950$ 0.283435452 \( 820352 a^{3} - 717600 a^{2} - 4294784 a + 3756992 \) \( \bigl[\frac{1}{2} a^{3} - a\) , \( \frac{1}{2} a^{3} - 2 a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - a\) , \( \frac{1}{2} a^{2} + a - 1\) , \( 0\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-a\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-a\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-2a\right){x}^{2}+\left(\frac{1}{2}a^{2}+a-1\right){x}$
1.1-a4 1.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 1 \) $0$ $\Z/14\Z$ $1$ $2222.133950$ 0.283435452 \( -820352 a^{3} - 717600 a^{2} + 4294784 a + 3756992 \) \( \bigl[\frac{1}{2} a^{3} - a\) , \( -\frac{1}{2} a^{3} + 2 a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - a\) , \( -a^{3} + \frac{1}{2} a^{2} - 1\) , \( -a^{3} + a\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-a\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-a\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+2a\right){x}^{2}+\left(-a^{3}+\frac{1}{2}a^{2}-1\right){x}-a^{3}+a$
1.1-a5 1.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 1 \) $0$ $\Z/14\Z$ $1$ $2222.133950$ 0.283435452 \( 313664 a^{3} + 717600 a^{2} - 241280 a - 548608 \) \( \bigl[a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 1\) , \( \frac{1}{2} a^{2} + a - 1\) , \( \frac{1}{2} a^{3} - a^{2} + 1\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} + 1\bigr] \) ${y}^2+a{x}{y}+\left(\frac{1}{2}a^{2}+a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-1\right){x}^{2}+\left(\frac{1}{2}a^{3}-a^{2}+1\right){x}+\frac{1}{2}a^{3}-\frac{3}{2}a^{2}+1$
1.1-a6 1.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 1 \) $0$ $\Z/14\Z$ $1$ $2222.133950$ 0.283435452 \( -313664 a^{3} + 717600 a^{2} + 241280 a - 548608 \) \( \bigl[a\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 2 a - 1\) , \( \frac{1}{2} a^{2} + a - 1\) , \( -a^{3} - a^{2} + a + 1\) , \( -a^{3} - \frac{3}{2} a^{2} + a + 1\bigr] \) ${y}^2+a{x}{y}+\left(\frac{1}{2}a^{2}+a-1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+2a-1\right){x}^{2}+\left(-a^{3}-a^{2}+a+1\right){x}-a^{3}-\frac{3}{2}a^{2}+a+1$
1.1-a7 1.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 1 \) $0$ $\Z/2\Z$ $1$ $0.925503519$ 0.283435452 \( 11970413633970086033024 a^{3} - 10462525154672292268320 a^{2} - 62677899506190812914304 a + 54782492926012669771712 \) \( \bigl[a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a\) , \( \frac{1}{2} a^{2} + a\) , \( \frac{25}{2} a^{3} - 25 a^{2} - 164 a - 151\) , \( -28 a^{3} - 421 a^{2} - 984 a - 681\bigr] \) ${y}^2+a{x}{y}+\left(\frac{1}{2}a^{2}+a\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-3a\right){x}^{2}+\left(\frac{25}{2}a^{3}-25a^{2}-164a-151\right){x}-28a^{3}-421a^{2}-984a-681$
1.1-a8 1.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 1 \) $0$ $\Z/2\Z$ $1$ $0.925503519$ 0.283435452 \( -11970413633970086033024 a^{3} - 10462525154672292268320 a^{2} + 62677899506190812914304 a + 54782492926012669771712 \) \( \bigl[a\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 3 a\) , \( \frac{1}{2} a^{2} + a\) , \( -13 a^{3} - 25 a^{2} + 164 a - 151\) , \( \frac{55}{2} a^{3} - 421 a^{2} + 984 a - 681\bigr] \) ${y}^2+a{x}{y}+\left(\frac{1}{2}a^{2}+a\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+3a\right){x}^{2}+\left(-13a^{3}-25a^{2}+164a-151\right){x}+\frac{55}{2}a^{3}-421a^{2}+984a-681$
16.1-a1 16.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 2^{4} \) $0$ $\Z/4\Z$ $1$ $533.1660961$ 0.833072025 \( -1153708403565030 a^{3} - 1008378119767100 a^{2} + 6040895627231640 a + 5279936382223900 \) \( \bigl[\frac{1}{2} a^{3} - 2 a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - a - 2\) , \( 0\) , \( 14 a^{3} - 12 a^{2} - 72 a + 60\) , \( -9 a^{3} + 8 a^{2} + 44 a - 34\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-2a\right){x}{y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-a-2\right){x}^{2}+\left(14a^{3}-12a^{2}-72a+60\right){x}-9a^{3}+8a^{2}+44a-34$
16.1-a2 16.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 2^{4} \) $0$ $\Z/4\Z$ $1$ $533.1660961$ 0.833072025 \( 1153708403565030 a^{3} - 1008378119767100 a^{2} - 6040895627231640 a + 5279936382223900 \) \( \bigl[\frac{1}{2} a^{3} - 2 a\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + a - 2\) , \( 0\) , \( -14 a^{3} - 12 a^{2} + 72 a + 60\) , \( 9 a^{3} + 8 a^{2} - 44 a - 34\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-2a\right){x}{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+a-2\right){x}^{2}+\left(-14a^{3}-12a^{2}+72a+60\right){x}+9a^{3}+8a^{2}-44a-34$
16.1-a3 16.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $133.2915240$ 0.833072025 \( 7753056320 a^{3} + 17740898400 a^{2} - 5922808160 a - 13552840400 \) \( \bigl[\frac{1}{2} a^{3} - 2 a\) , \( \frac{1}{2} a^{3} - 3 a + 1\) , \( \frac{1}{2} a^{3} - 2 a\) , \( 2 a^{3} - 2 a^{2} - 10 a + 8\) , \( \frac{15}{2} a^{3} - 7 a^{2} - 38 a + 33\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-2a\right){x}{y}+\left(\frac{1}{2}a^{3}-2a\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-3a+1\right){x}^{2}+\left(2a^{3}-2a^{2}-10a+8\right){x}+\frac{15}{2}a^{3}-7a^{2}-38a+33$
16.1-a4 16.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 2^{4} \) $0$ $\Z/4\Z$ $1$ $533.1660961$ 0.833072025 \( 440677397079270 a^{3} + 1008378119767100 a^{2} - 336647575345560 a - 770332336378700 \) \( \bigl[\frac{1}{2} a^{3} - 2 a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - a + 1\) , \( 0\) , \( -\frac{11}{2} a^{3} + 14 a^{2} + 4 a - 18\) , \( 10 a^{3} - 25 a^{2} - 6 a + 25\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-2a\right){x}{y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-a+1\right){x}^{2}+\left(-\frac{11}{2}a^{3}+14a^{2}+4a-18\right){x}+10a^{3}-25a^{2}-6a+25$
16.1-a5 16.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 2^{4} \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $2132.664384$ 0.833072025 \( -7507920 a^{3} + 60063360 a + 47486000 \) \( \bigl[\frac{1}{2} a^{3} - 2 a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - a + 1\) , \( 0\) , \( 2 a^{3} - a^{2} - 6 a - 3\) , \( -\frac{5}{2} a^{3} + 3 a^{2} + 6 a + 1\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-2a\right){x}{y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-a+1\right){x}^{2}+\left(2a^{3}-a^{2}-6a-3\right){x}-\frac{5}{2}a^{3}+3a^{2}+6a+1$
16.1-a6 16.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $133.2915240$ 0.833072025 \( -20297764880 a^{3} - 17740898400 a^{2} + 106280476640 a + 92892550000 \) \( \bigl[\frac{1}{2} a^{3} - 2 a\) , \( -a + 1\) , \( \frac{1}{2} a^{3} - 2 a\) , \( -a^{3} + 2 a^{2} + 2 a - 4\) , \( -\frac{7}{2} a^{3} + 7 a^{2} + 6 a - 9\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-2a\right){x}{y}+\left(\frac{1}{2}a^{3}-2a\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a^{3}+2a^{2}+2a-4\right){x}-\frac{7}{2}a^{3}+7a^{2}+6a-9$
16.1-a7 16.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 2^{4} \) $0$ $\Z/4\Z$ $1$ $533.1660961$ 0.833072025 \( -440677397079270 a^{3} + 1008378119767100 a^{2} + 336647575345560 a - 770332336378700 \) \( \bigl[\frac{1}{2} a^{3} - 2 a\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + a + 1\) , \( 0\) , \( \frac{11}{2} a^{3} + 14 a^{2} - 4 a - 18\) , \( -10 a^{3} - 25 a^{2} + 6 a + 25\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-2a\right){x}{y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+a+1\right){x}^{2}+\left(\frac{11}{2}a^{3}+14a^{2}-4a-18\right){x}-10a^{3}-25a^{2}+6a+25$
16.1-a8 16.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 2^{4} \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $2132.664384$ 0.833072025 \( 7507920 a^{3} - 60063360 a + 47486000 \) \( \bigl[\frac{1}{2} a^{3} - 2 a\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + a + 1\) , \( 0\) , \( -2 a^{3} - a^{2} + 6 a - 3\) , \( \frac{5}{2} a^{3} + 3 a^{2} - 6 a + 1\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-2a\right){x}{y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+a+1\right){x}^{2}+\left(-2a^{3}-a^{2}+6a-3\right){x}+\frac{5}{2}a^{3}+3a^{2}-6a+1$
16.1-a9 16.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $133.2915240$ 0.833072025 \( 20297764880 a^{3} - 17740898400 a^{2} - 106280476640 a + 92892550000 \) \( \bigl[\frac{1}{2} a^{3} - 2 a\) , \( a + 1\) , \( \frac{1}{2} a^{3} - 2 a\) , \( a^{3} + 2 a^{2} - 2 a - 4\) , \( \frac{7}{2} a^{3} + 7 a^{2} - 6 a - 9\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-2a\right){x}{y}+\left(\frac{1}{2}a^{3}-2a\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a^{3}+2a^{2}-2a-4\right){x}+\frac{7}{2}a^{3}+7a^{2}-6a-9$
16.1-a10 16.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $133.2915240$ 0.833072025 \( -7753056320 a^{3} + 17740898400 a^{2} + 5922808160 a - 13552840400 \) \( \bigl[\frac{1}{2} a^{3} - 2 a\) , \( -\frac{1}{2} a^{3} + 3 a + 1\) , \( \frac{1}{2} a^{3} - 2 a\) , \( -2 a^{3} - 2 a^{2} + 10 a + 8\) , \( -\frac{15}{2} a^{3} - 7 a^{2} + 38 a + 33\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-2a\right){x}{y}+\left(\frac{1}{2}a^{3}-2a\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+3a+1\right){x}^{2}+\left(-2a^{3}-2a^{2}+10a+8\right){x}-\frac{15}{2}a^{3}-7a^{2}+38a+33$
16.1-a11 16.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 2^{4} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $533.1660961$ 0.833072025 \( 30720 a^{3} - 245760 a + 204800 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -a^{3} - 3 a^{2} - 2 a\) , \( 4 a^{3} + 10 a^{2} - 5\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-a^{3}-3a^{2}-2a\right){x}+4a^{3}+10a^{2}-5$
16.1-a12 16.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 2^{4} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $533.1660961$ 0.833072025 \( -30720 a^{3} + 245760 a + 204800 \) \( \bigl[0\) , \( -\frac{1}{2} a^{3} + 3 a\) , \( 0\) , \( -4 a^{3} + 3 a^{2} + 22 a - 18\) , \( 12 a^{3} - 10 a^{2} - 64 a + 55\bigr] \) ${y}^2={x}^{3}+\left(-\frac{1}{2}a^{3}+3a\right){x}^{2}+\left(-4a^{3}+3a^{2}+22a-18\right){x}+12a^{3}-10a^{2}-64a+55$
31.1-a1 31.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 31 \) $0$ $\Z/2\Z$ $1$ $21.32891754$ 1.066445877 \( -\frac{505219547793146787969}{1847042} a^{3} + \frac{1156066776906178179193}{1847042} a^{2} + \frac{192976118760042249464}{923521} a - \frac{441577709639777226006}{923521} \) \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 1\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 3 a + 2\) , \( \frac{1}{2} a^{3} - a\) , \( 43 a^{3} + \frac{93}{2} a^{2} - 208 a - 211\) , \( -226 a^{3} - \frac{349}{2} a^{2} + 1236 a + 1026\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-1\right){x}{y}+\left(\frac{1}{2}a^{3}-a\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+3a+2\right){x}^{2}+\left(43a^{3}+\frac{93}{2}a^{2}-208a-211\right){x}-226a^{3}-\frac{349}{2}a^{2}+1236a+1026$
31.1-a2 31.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 31 \) $0$ $\Z/2\Z$ $1$ $170.6313403$ 1.066445877 \( \frac{248777767711978335}{59582} a^{3} + \frac{569082138084219041}{59582} a^{2} - \frac{95151399194580063}{29791} a - \frac{217251974013061967}{29791} \) \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a\) , \( -\frac{1}{2} a^{2} + 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a\) , \( \frac{1709}{2} a^{3} - \frac{3885}{2} a^{2} - 671 a + 1460\) , \( -43216 a^{3} + 98857 a^{2} + 33055 a - 75482\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+2\right){x}^{2}+\left(\frac{1709}{2}a^{3}-\frac{3885}{2}a^{2}-671a+1460\right){x}-43216a^{3}+98857a^{2}+33055a-75482$
31.1-a3 31.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 31 \) $0$ $\Z/4\Z$ $1$ $682.5253613$ 1.066445877 \( \frac{11686086}{31} a^{3} + \frac{31460719}{62} a^{2} - \frac{43571072}{31} a - \frac{42296544}{31} \) \( \bigl[1\) , \( \frac{1}{2} a^{2}\) , \( \frac{1}{2} a^{2} + a - 1\) , \( a^{3} - \frac{3}{2} a^{2} - 2 a + 1\) , \( 2 a^{3} - \frac{11}{2} a^{2} - a + 4\bigr] \) ${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}+a-1\right){y}={x}^{3}+\frac{1}{2}a^{2}{x}^{2}+\left(a^{3}-\frac{3}{2}a^{2}-2a+1\right){x}+2a^{3}-\frac{11}{2}a^{2}-a+4$
31.1-a4 31.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 31 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $341.2626806$ 1.066445877 \( \frac{408946009712709}{887503681} a^{3} + \frac{1814035747952571}{1775007362} a^{2} - \frac{348963373631244}{887503681} a - \frac{646404289554322}{887503681} \) \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a\) , \( -\frac{1}{2} a^{2} + 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a\) , \( 72 a^{3} - 165 a^{2} - 56 a + 125\) , \( -162 a^{3} + 370 a^{2} + 124 a - 283\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+2\right){x}^{2}+\left(72a^{3}-165a^{2}-56a+125\right){x}-162a^{3}+370a^{2}+124a-283$
31.1-a5 31.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 31 \) $0$ $\Z/2\Z$ $1$ $21.32891754$ 1.066445877 \( -\frac{14383414343925670643585}{1575325567577099522} a^{3} + \frac{29872156558690483602305}{1575325567577099522} a^{2} + \frac{6561729841950628185729}{787662783788549761} a - \frac{8912263801297866015903}{787662783788549761} \) \( \bigl[\frac{1}{2} a^{2}\) , \( -a + 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 1\) , \( -\frac{27}{2} a^{3} + 2 a^{2} + 46 a - 59\) , \( -43 a^{3} - \frac{69}{2} a^{2} + 108 a - 83\bigr] \) ${y}^2+\frac{1}{2}a^{2}{x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-\frac{27}{2}a^{3}+2a^{2}+46a-59\right){x}-43a^{3}-\frac{69}{2}a^{2}+108a-83$
31.1-a6 31.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 31 \) $0$ $\Z/4\Z$ $1$ $682.5253613$ 1.066445877 \( \frac{2944222}{29791} a^{3} + \frac{36603857}{59582} a^{2} - \frac{1351764}{29791} a - \frac{13276467}{29791} \) \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - a\) , \( \frac{1}{2} a^{3} - 2 a + 1\) , \( -a^{3} + 2 a^{2} + 2 a - 3\) , \( 3 a^{3} - \frac{7}{2} a^{2} - 13 a + 12\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-1\right){x}{y}+\left(\frac{1}{2}a^{3}-2a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-a\right){x}^{2}+\left(-a^{3}+2a^{2}+2a-3\right){x}+3a^{3}-\frac{7}{2}a^{2}-13a+12$
31.1-a7 31.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 31 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $341.2626806$ 1.066445877 \( -\frac{469486995236469}{961} a^{3} - \frac{820671155387481}{1922} a^{2} + \frac{2458250110522194}{961} a + \frac{2148580931607341}{961} \) \( \bigl[1\) , \( \frac{1}{2} a^{2}\) , \( \frac{1}{2} a^{2} + a - 1\) , \( 16 a^{3} - 29 a^{2} - 22 a + 11\) , \( \frac{199}{2} a^{3} - 241 a^{2} - 57 a + 197\bigr] \) ${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}+a-1\right){y}={x}^{3}+\frac{1}{2}a^{2}{x}^{2}+\left(16a^{3}-29a^{2}-22a+11\right){x}+\frac{199}{2}a^{3}-241a^{2}-57a+197$
31.1-a8 31.1-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 31 \) $0$ $\Z/2\Z$ $1$ $170.6313403$ 1.066445877 \( -\frac{115679900627333053956710625}{62} a^{3} - \frac{101107940561583547666668071}{62} a^{2} + \frac{302853911657568218576001528}{31} a + \frac{264704024922729858633502426}{31} \) \( \bigl[\frac{1}{2} a^{3} - 2 a + 1\) , \( -\frac{1}{2} a^{3} + a\) , \( 1\) , \( -38 a^{3} + \frac{49}{2} a^{2} + 185 a - 164\) , \( 125 a^{3} - \frac{275}{2} a^{2} - 686 a + 630\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-2a+1\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a\right){x}^{2}+\left(-38a^{3}+\frac{49}{2}a^{2}+185a-164\right){x}+125a^{3}-\frac{275}{2}a^{2}-686a+630$
31.2-a1 31.2-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 31 \) $0$ $\Z/2\Z$ $1$ $170.6313403$ 1.066445877 \( \frac{44185790224430943294130347}{62} a^{3} + \frac{101107940561583547666668071}{62} a^{2} - \frac{16877470045959775925680416}{31} a - \frac{38619796762020784366501787}{31} \) \( \bigl[\frac{1}{2} a^{3} - 2 a + 1\) , \( \frac{1}{2} a^{3} - 3 a\) , \( 1\) , \( 21 a^{3} - \frac{49}{2} a^{2} - 51 a - 17\) , \( -32 a^{3} + \frac{275}{2} a^{2} - 58 a - 195\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-2a+1\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{2}a^{3}-3a\right){x}^{2}+\left(21a^{3}-\frac{49}{2}a^{2}-51a-17\right){x}-32a^{3}+\frac{275}{2}a^{2}-58a-195$
31.2-a2 31.2-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 31 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $341.2626806$ 1.066445877 \( \frac{179335930448310}{961} a^{3} + \frac{820671155387481}{1922} a^{2} - \frac{137041592216922}{961} a - \frac{313432534555102}{961} \) \( \bigl[\frac{1}{2} a^{3} - 2 a + 1\) , \( \frac{1}{2} a^{3} - 3 a\) , \( 1\) , \( 6 a^{3} - 12 a^{2} - 6 a + 3\) , \( \frac{43}{2} a^{3} - \frac{115}{2} a^{2} + a + 41\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-2a+1\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{2}a^{3}-3a\right){x}^{2}+\left(6a^{3}-12a^{2}-6a+3\right){x}+\frac{43}{2}a^{3}-\frac{115}{2}a^{2}+a+41$
31.2-a3 31.2-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 31 \) $0$ $\Z/4\Z$ $1$ $682.5253613$ 1.066445877 \( -\frac{8156784}{29791} a^{3} - \frac{36603857}{59582} a^{2} + \frac{43052260}{29791} a + \frac{96535104}{29791} \) \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a\) , \( a + 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - a + 1\) , \( -\frac{1}{2} a^{3} + 3 a^{2} - 2\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-a-1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-a+1\right){x}-\frac{1}{2}a^{3}+3a^{2}-2$
31.2-a4 31.2-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 31 \) $0$ $\Z/2\Z$ $1$ $21.32891754$ 1.066445877 \( \frac{18294256594913191872513}{787662783788549761} a^{3} - \frac{29872156558690483602305}{1575325567577099522} a^{2} - \frac{95382125225553480591493}{787662783788549761} a + \frac{80704205874773584791012}{787662783788549761} \) \( \bigl[\frac{1}{2} a^{3} - 2 a + 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - a - 1\) , \( -7 a^{3} - 10 a^{2} + 8 a - 14\) , \( -\frac{73}{2} a^{3} - 62 a^{2} + 48 a - 4\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-2a+1\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-1\right){x}^{2}+\left(-7a^{3}-10a^{2}+8a-14\right){x}-\frac{73}{2}a^{3}-62a^{2}+48a-4$
31.2-a5 31.2-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 31 \) $0$ $\Z/4\Z$ $1$ $682.5253613$ 1.066445877 \( -\frac{13272722}{31} a^{3} - \frac{31460719}{62} a^{2} + \frac{56264160}{31} a + \frac{52085613}{31} \) \( \bigl[\frac{1}{2} a^{3} - 2 a + 1\) , \( \frac{1}{2} a^{3} - 3 a\) , \( 1\) , \( a^{3} + \frac{1}{2} a^{2} - 6 a - 2\) , \( -\frac{1}{2} a^{3} - \frac{9}{2} a^{2} + 8 a + 11\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-2a+1\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{2}a^{3}-3a\right){x}^{2}+\left(a^{3}+\frac{1}{2}a^{2}-6a-2\right){x}-\frac{1}{2}a^{3}-\frac{9}{2}a^{2}+8a+11$
31.2-a6 31.2-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 31 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $341.2626806$ 1.066445877 \( -\frac{1052356342322505}{887503681} a^{3} - \frac{1814035747952571}{1775007362} a^{2} + \frac{5496246034509612}{887503681} a + \frac{4795702954303391}{887503681} \) \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a\) , \( a + 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - a - 1\) , \( \frac{11}{2} a^{3} - 12 a^{2} - a + 6\) , \( -\frac{53}{2} a^{3} + \frac{125}{2} a^{2} + 20 a - 49\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-a-1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(\frac{11}{2}a^{3}-12a^{2}-a+6\right){x}-\frac{53}{2}a^{3}+\frac{125}{2}a^{2}+20a-49$
31.2-a7 31.2-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 31 \) $0$ $\Z/2\Z$ $1$ $170.6313403$ 1.066445877 \( -\frac{325590951970677471}{29791} a^{3} - \frac{569082138084219041}{59582} a^{2} + \frac{1704767944112086491}{29791} a + \frac{1489994440239595156}{29791} \) \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a\) , \( a + 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - a - 1\) , \( 88 a^{3} - 207 a^{2} - 36 a + 111\) , \( -1609 a^{3} + \frac{7485}{2} a^{2} + 1071 a - 2772\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-a-1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(88a^{3}-207a^{2}-36a+111\right){x}-1609a^{3}+\frac{7485}{2}a^{2}+1071a-2772$
31.2-a8 31.2-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 31 \) $0$ $\Z/2\Z$ $1$ $21.32891754$ 1.066445877 \( \frac{1322682524619398114443}{1847042} a^{3} - \frac{1156066776906178179193}{1847042} a^{2} - \frac{3462828026065047555360}{923521} a + \frac{3026622621078757311573}{923521} \) \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - a - 1\) , \( \frac{1}{2} a^{2} + a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a\) , \( -\frac{147}{2} a^{3} - 54 a^{2} + 381 a + 272\) , \( -423 a^{3} - 342 a^{2} + 2215 a + 1788\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-a-1\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}+a-1\right){x}^{2}+\left(-\frac{147}{2}a^{3}-54a^{2}+381a+272\right){x}-423a^{3}-342a^{2}+2215a+1788$
31.3-a1 31.3-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 31 \) $0$ $\Z/2\Z$ $1$ $170.6313403$ 1.066445877 \( -\frac{44185790224430943294130347}{62} a^{3} + \frac{101107940561583547666668071}{62} a^{2} + \frac{16877470045959775925680416}{31} a - \frac{38619796762020784366501787}{31} \) \( \bigl[\frac{1}{2} a^{3} - 2 a + 1\) , \( \frac{1}{2} a^{3} - a\) , \( \frac{1}{2} a^{3} - 2 a + 1\) , \( -21 a^{3} - \frac{45}{2} a^{2} + 51 a - 22\) , \( -\frac{3}{2} a^{3} + \frac{209}{2} a^{2} + 145 a - 213\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-2a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-2a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-a\right){x}^{2}+\left(-21a^{3}-\frac{45}{2}a^{2}+51a-22\right){x}-\frac{3}{2}a^{3}+\frac{209}{2}a^{2}+145a-213$
31.3-a2 31.3-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 31 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $341.2626806$ 1.066445877 \( -\frac{179335930448310}{961} a^{3} + \frac{820671155387481}{1922} a^{2} + \frac{137041592216922}{961} a - \frac{313432534555102}{961} \) \( \bigl[\frac{1}{2} a^{3} - 2 a + 1\) , \( \frac{1}{2} a^{3} - a\) , \( \frac{1}{2} a^{3} - 2 a + 1\) , \( -6 a^{3} - 10 a^{2} + 6 a - 2\) , \( -\frac{65}{2} a^{3} - \frac{151}{2} a^{2} + 21 a + 53\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-2a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-2a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-a\right){x}^{2}+\left(-6a^{3}-10a^{2}+6a-2\right){x}-\frac{65}{2}a^{3}-\frac{151}{2}a^{2}+21a+53$
31.3-a3 31.3-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 31 \) $0$ $\Z/4\Z$ $1$ $682.5253613$ 1.066445877 \( \frac{8156784}{29791} a^{3} - \frac{36603857}{59582} a^{2} - \frac{43052260}{29791} a + \frac{96535104}{29791} \) \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a\) , \( -\frac{1}{2} a^{3} + 3 a + 1\) , \( \frac{1}{2} a^{2} + a - 1\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 3 a + 4\) , \( \frac{1}{2} a^{3} + 2 a^{2} + 2 a\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a\right){x}{y}+\left(\frac{1}{2}a^{2}+a-1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+3a+1\right){x}^{2}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+3a+4\right){x}+\frac{1}{2}a^{3}+2a^{2}+2a$
31.3-a4 31.3-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 31 \) $0$ $\Z/2\Z$ $1$ $21.32891754$ 1.066445877 \( -\frac{18294256594913191872513}{787662783788549761} a^{3} - \frac{29872156558690483602305}{1575325567577099522} a^{2} + \frac{95382125225553480591493}{787662783788549761} a + \frac{80704205874773584791012}{787662783788549761} \) \( \bigl[\frac{1}{2} a^{2} + a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - a + 2\) , \( \frac{1}{2} a^{3} - 2 a + 1\) , \( 45 a^{3} - \frac{199}{2} a^{2} - 37 a + 75\) , \( \frac{673}{2} a^{3} - \frac{1537}{2} a^{2} - 256 a + 582\bigr] \) ${y}^2+\left(\frac{1}{2}a^{2}+a-1\right){x}{y}+\left(\frac{1}{2}a^{3}-2a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-a+2\right){x}^{2}+\left(45a^{3}-\frac{199}{2}a^{2}-37a+75\right){x}+\frac{673}{2}a^{3}-\frac{1537}{2}a^{2}-256a+582$
31.3-a5 31.3-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 31 \) $0$ $\Z/4\Z$ $1$ $682.5253613$ 1.066445877 \( \frac{13272722}{31} a^{3} - \frac{31460719}{62} a^{2} - \frac{56264160}{31} a + \frac{52085613}{31} \) \( \bigl[\frac{1}{2} a^{3} - 2 a + 1\) , \( \frac{1}{2} a^{3} - a\) , \( \frac{1}{2} a^{3} - 2 a + 1\) , \( -a^{3} + \frac{5}{2} a^{2} + 6 a - 7\) , \( -\frac{1}{2} a^{3} - \frac{5}{2} a^{2} - a + 3\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-2a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-2a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-a\right){x}^{2}+\left(-a^{3}+\frac{5}{2}a^{2}+6a-7\right){x}-\frac{1}{2}a^{3}-\frac{5}{2}a^{2}-a+3$
31.3-a6 31.3-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 31 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $341.2626806$ 1.066445877 \( \frac{1052356342322505}{887503681} a^{3} - \frac{1814035747952571}{1775007362} a^{2} - \frac{5496246034509612}{887503681} a + \frac{4795702954303391}{887503681} \) \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - a - 1\) , \( a - 1\) , \( \frac{1}{2} a^{2} + a\) , \( 4 a^{3} + 5 a^{2} - 23 a - 29\) , \( -\frac{5}{2} a^{3} - \frac{3}{2} a^{2} + 12 a + 5\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-a-1\right){x}{y}+\left(\frac{1}{2}a^{2}+a\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(4a^{3}+5a^{2}-23a-29\right){x}-\frac{5}{2}a^{3}-\frac{3}{2}a^{2}+12a+5$
31.3-a7 31.3-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 31 \) $0$ $\Z/2\Z$ $1$ $170.6313403$ 1.066445877 \( \frac{325590951970677471}{29791} a^{3} - \frac{569082138084219041}{59582} a^{2} - \frac{1704767944112086491}{29791} a + \frac{1489994440239595156}{29791} \) \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - a - 1\) , \( a - 1\) , \( \frac{1}{2} a^{2} + a\) , \( 34 a^{3} + \frac{85}{2} a^{2} - 238 a - 359\) , \( -586 a^{3} - 312 a^{2} + 3301 a + 2167\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-a-1\right){x}{y}+\left(\frac{1}{2}a^{2}+a\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(34a^{3}+\frac{85}{2}a^{2}-238a-359\right){x}-586a^{3}-312a^{2}+3301a+2167$
31.3-a8 31.3-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 31 \) $0$ $\Z/2\Z$ $1$ $21.32891754$ 1.066445877 \( -\frac{1322682524619398114443}{1847042} a^{3} - \frac{1156066776906178179193}{1847042} a^{2} + \frac{3462828026065047555360}{923521} a + \frac{3026622621078757311573}{923521} \) \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a\) , \( a\) , \( \frac{1}{2} a^{3} - a\) , \( 26 a^{3} - \frac{93}{2} a^{2} - 67 a + 69\) , \( -107 a^{3} + 262 a^{2} - 22 a - 121\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a\right){x}{y}+\left(\frac{1}{2}a^{3}-a\right){y}={x}^{3}+a{x}^{2}+\left(26a^{3}-\frac{93}{2}a^{2}-67a+69\right){x}-107a^{3}+262a^{2}-22a-121$
31.4-a1 31.4-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 31 \) $0$ $\Z/2\Z$ $1$ $21.32891754$ 1.066445877 \( \frac{505219547793146787969}{1847042} a^{3} + \frac{1156066776906178179193}{1847042} a^{2} - \frac{192976118760042249464}{923521} a - \frac{441577709639777226006}{923521} \) \( \bigl[\frac{1}{2} a^{2} + a\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 2 a + 1\) , \( a\) , \( -34 a^{3} + 57 a^{2} + 53 a - 69\) , \( -140 a^{3} + 302 a^{2} + 22 a - 161\bigr] \) ${y}^2+\left(\frac{1}{2}a^{2}+a\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+2a+1\right){x}^{2}+\left(-34a^{3}+57a^{2}+53a-69\right){x}-140a^{3}+302a^{2}+22a-161$
31.4-a2 31.4-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 31 \) $0$ $\Z/2\Z$ $1$ $170.6313403$ 1.066445877 \( -\frac{248777767711978335}{59582} a^{3} + \frac{569082138084219041}{59582} a^{2} + \frac{95151399194580063}{29791} a - \frac{217251974013061967}{29791} \) \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - a - 1\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + a + 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - a - 1\) , \( -153 a^{3} - 248 a^{2} + 243 a + 22\) , \( 2540 a^{3} + \frac{10239}{2} a^{2} - 2876 a - 2955\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-a-1\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-a-1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+a+1\right){x}^{2}+\left(-153a^{3}-248a^{2}+243a+22\right){x}+2540a^{3}+\frac{10239}{2}a^{2}-2876a-2955$
31.4-a3 31.4-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 31 \) $0$ $\Z/4\Z$ $1$ $682.5253613$ 1.066445877 \( -\frac{11686086}{31} a^{3} + \frac{31460719}{62} a^{2} + \frac{43571072}{31} a - \frac{42296544}{31} \) \( \bigl[1\) , \( \frac{1}{2} a^{2}\) , \( \frac{1}{2} a^{2} + a - 1\) , \( -a^{3} - \frac{3}{2} a^{2} + a + 1\) , \( -\frac{5}{2} a^{3} - \frac{11}{2} a^{2} + 2 a + 4\bigr] \) ${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}+a-1\right){y}={x}^{3}+\frac{1}{2}a^{2}{x}^{2}+\left(-a^{3}-\frac{3}{2}a^{2}+a+1\right){x}-\frac{5}{2}a^{3}-\frac{11}{2}a^{2}+2a+4$
31.4-a4 31.4-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 31 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $341.2626806$ 1.066445877 \( -\frac{408946009712709}{887503681} a^{3} + \frac{1814035747952571}{1775007362} a^{2} + \frac{348963373631244}{887503681} a - \frac{646404289554322}{887503681} \) \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - a - 1\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + a + 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - a - 1\) , \( -13 a^{3} - 23 a^{2} + 18 a + 7\) , \( \frac{11}{2} a^{3} + 2 a^{2} - 19 a + 12\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-a-1\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-a-1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+a+1\right){x}^{2}+\left(-13a^{3}-23a^{2}+18a+7\right){x}+\frac{11}{2}a^{3}+2a^{2}-19a+12$
31.4-a5 31.4-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 31 \) $0$ $\Z/2\Z$ $1$ $21.32891754$ 1.066445877 \( \frac{14383414343925670643585}{1575325567577099522} a^{3} + \frac{29872156558690483602305}{1575325567577099522} a^{2} - \frac{6561729841950628185729}{787662783788549761} a - \frac{8912263801297866015903}{787662783788549761} \) \( \bigl[1\) , \( \frac{1}{2} a^{3} - 3 a - 1\) , \( \frac{1}{2} a^{3} - a + 1\) , \( \frac{69}{2} a^{3} - 76 a^{2} - 30 a + 51\) , \( \frac{903}{2} a^{3} - \frac{2075}{2} a^{2} - 339 a + 793\bigr] \) ${y}^2+{x}{y}+\left(\frac{1}{2}a^{3}-a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-3a-1\right){x}^{2}+\left(\frac{69}{2}a^{3}-76a^{2}-30a+51\right){x}+\frac{903}{2}a^{3}-\frac{2075}{2}a^{2}-339a+793$
31.4-a6 31.4-a \(\Q(\sqrt{2}, \sqrt{5})\) \( 31 \) $0$ $\Z/4\Z$ $1$ $682.5253613$ 1.066445877 \( -\frac{2944222}{29791} a^{3} + \frac{36603857}{59582} a^{2} + \frac{1351764}{29791} a - \frac{13276467}{29791} \) \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 1\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 3 a\) , \( a + 1\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + a + 3\) , \( -\frac{5}{2} a^{3} - \frac{5}{2} a^{2} + 13 a + 11\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-2a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+3a\right){x}^{2}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+a+3\right){x}-\frac{5}{2}a^{3}-\frac{5}{2}a^{2}+13a+11$
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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.