Elliptic curves over Q(2,5)\Q(\sqrt{2}, \sqrt{5})

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Label	Class	Class size	Class degree	Base field	Field degree	Field signature	Conductor	Conductor norm	Discriminant norm	Root analytic conductor	Bad primes	Rank	Torsion	CM	CM	Sato-Tate	$\Q$-curve	Base change	Semistable	Potentially good	Nonmax $\ell$	mod-$\ell$ images	$Ш_{\textrm{an}}$	Tamagawa	Regulator	Period	Leading coeff	j-invariant	Weierstrass coefficients	Weierstrass equation
1.1-a1	1.1-a	$8$	$42$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	1.1	$1$	$1$	$3.57436$	$\textsf{none}$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓	✓	$2, 3, 7$	2B, 3B, 7B.1.3	$49$	$1$	$1$	$0.925503519$	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	$8$	$42$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	1.1	$1$	$1$	$3.57436$	$\textsf{none}$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓	✓	$2, 3, 7$	2B, 3B, 7B.1.3	$49$	$1$	$1$	$0.925503519$	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	$8$	$42$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	1.1	$1$	$1$	$3.57436$	$\textsf{none}$	0	$\Z/14\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓	✓	$2, 3, 7$	2B, 3B, 7B.1.1	$1$	$1$	$1$	$2222.133950$	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	$8$	$42$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	1.1	$1$	$1$	$3.57436$	$\textsf{none}$	0	$\Z/14\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓	✓	$2, 3, 7$	2B, 3B, 7B.1.1	$1$	$1$	$1$	$2222.133950$	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	$8$	$42$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	1.1	$1$	$1$	$3.57436$	$\textsf{none}$	0	$\Z/14\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓	✓	$2, 3, 7$	2B, 3B, 7B.1.1	$1$	$1$	$1$	$2222.133950$	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	$8$	$42$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	1.1	$1$	$1$	$3.57436$	$\textsf{none}$	0	$\Z/14\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓	✓	$2, 3, 7$	2B, 3B, 7B.1.1	$1$	$1$	$1$	$2222.133950$	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	$8$	$42$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	1.1	$1$	$1$	$3.57436$	$\textsf{none}$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓	✓	$2, 3, 7$	2B, 3B, 7B.1.3	$49$	$1$	$1$	$0.925503519$	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	$8$	$42$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	1.1	$1$	$1$	$3.57436$	$\textsf{none}$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓	✓	$2, 3, 7$	2B, 3B, 7B.1.3	$49$	$1$	$1$	$0.925503519$	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	$12$	$24$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	16.1	$2^{4}$	$2^{16}$	$5.05491$	$(1/2a^3-2a)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2, 3$	2B, 3B	$1$	$1$	$1$	$533.1660961$	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	$12$	$24$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	16.1	$2^{4}$	$2^{16}$	$5.05491$	$(1/2a^3-2a)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2, 3$	2B, 3B	$1$	$1$	$1$	$533.1660961$	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	$12$	$24$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	16.1	$2^{4}$	$2^{8}$	$5.05491$	$(1/2a^3-2a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2, 3$	2B, 3B	$1$	$1$	$1$	$133.2915240$	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	$12$	$24$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	16.1	$2^{4}$	$2^{16}$	$5.05491$	$(1/2a^3-2a)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2, 3$	2B, 3B	$1$	$1$	$1$	$533.1660961$	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	$12$	$24$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	16.1	$2^{4}$	$2^{8}$	$5.05491$	$(1/2a^3-2a)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2, 3$	2Cs, 3B	$1$	$1$	$1$	$2132.664384$	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	$12$	$24$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	16.1	$2^{4}$	$2^{8}$	$5.05491$	$(1/2a^3-2a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2, 3$	2B, 3B	$1$	$1$	$1$	$133.2915240$	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	$12$	$24$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	16.1	$2^{4}$	$2^{16}$	$5.05491$	$(1/2a^3-2a)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2, 3$	2B, 3B	$1$	$1$	$1$	$533.1660961$	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	$12$	$24$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	16.1	$2^{4}$	$2^{8}$	$5.05491$	$(1/2a^3-2a)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2, 3$	2Cs, 3B	$1$	$1$	$1$	$2132.664384$	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	$12$	$24$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	16.1	$2^{4}$	$2^{8}$	$5.05491$	$(1/2a^3-2a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2, 3$	2B, 3B	$1$	$1$	$1$	$133.2915240$	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	$12$	$24$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	16.1	$2^{4}$	$2^{8}$	$5.05491$	$(1/2a^3-2a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2, 3$	2B, 3B	$1$	$1$	$1$	$133.2915240$	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	$12$	$24$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	16.1	$2^{4}$	$2^{16}$	$5.05491$	$(1/2a^3-2a)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2, 3$	2Cs, 3B	$1$	$1$	$1$	$533.1660961$	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	$12$	$24$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	16.1	$2^{4}$	$2^{16}$	$5.05491$	$(1/2a^3-2a)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2, 3$	2Cs, 3B	$1$	$1$	$1$	$533.1660961$	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	$8$	$12$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	31.1	$31$	$- 31^{4}$	$5.49059$	$(1/2a^3+1/2a^2-3a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$4$	$2$	$1$	$21.32891754$	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	$8$	$12$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	31.1	$31$	$31^{3}$	$5.49059$	$(1/2a^3+1/2a^2-3a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$1$	$1$	$1$	$170.6313403$	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	$8$	$12$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	31.1	$31$	$-31$	$5.49059$	$(1/2a^3+1/2a^2-3a)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$1$	$1$	$1$	$682.5253613$	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	$8$	$12$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	31.1	$31$	$31^{6}$	$5.49059$	$(1/2a^3+1/2a^2-3a)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2Cs, 3B	$1$	$2$	$1$	$341.2626806$	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	$8$	$12$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	31.1	$31$	$- 31^{12}$	$5.49059$	$(1/2a^3+1/2a^2-3a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$4$	$2$	$1$	$21.32891754$	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	$8$	$12$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	31.1	$31$	$- 31^{3}$	$5.49059$	$(1/2a^3+1/2a^2-3a)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$1$	$1$	$1$	$682.5253613$	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	$8$	$12$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	31.1	$31$	$31^{2}$	$5.49059$	$(1/2a^3+1/2a^2-3a)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2Cs, 3B	$1$	$2$	$1$	$341.2626806$	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	$8$	$12$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	31.1	$31$	$31$	$5.49059$	$(1/2a^3+1/2a^2-3a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$1$	$1$	$1$	$170.6313403$	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	$8$	$12$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	31.2	$31$	$31$	$5.49059$	$(1/2a^2+a-3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$1$	$1$	$1$	$170.6313403$	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	$8$	$12$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	31.2	$31$	$31^{2}$	$5.49059$	$(1/2a^2+a-3)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2Cs, 3B	$1$	$2$	$1$	$341.2626806$	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	$8$	$12$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	31.2	$31$	$- 31^{3}$	$5.49059$	$(1/2a^2+a-3)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$1$	$1$	$1$	$682.5253613$	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	$8$	$12$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	31.2	$31$	$- 31^{12}$	$5.49059$	$(1/2a^2+a-3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$4$	$2$	$1$	$21.32891754$	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	$8$	$12$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	31.2	$31$	$-31$	$5.49059$	$(1/2a^2+a-3)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$1$	$1$	$1$	$682.5253613$	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	$8$	$12$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	31.2	$31$	$31^{6}$	$5.49059$	$(1/2a^2+a-3)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2Cs, 3B	$1$	$2$	$1$	$341.2626806$	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	$8$	$12$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	31.2	$31$	$31^{3}$	$5.49059$	$(1/2a^2+a-3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$1$	$1$	$1$	$170.6313403$	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	$8$	$12$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	31.2	$31$	$- 31^{4}$	$5.49059$	$(1/2a^2+a-3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$4$	$2$	$1$	$21.32891754$	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	$8$	$12$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	31.3	$31$	$31$	$5.49059$	$(-1/2a^2+a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$1$	$1$	$1$	$170.6313403$	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	$8$	$12$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	31.3	$31$	$31^{2}$	$5.49059$	$(-1/2a^2+a+3)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2Cs, 3B	$1$	$2$	$1$	$341.2626806$	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	$8$	$12$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	31.3	$31$	$- 31^{3}$	$5.49059$	$(-1/2a^2+a+3)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$1$	$1$	$1$	$682.5253613$	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	$8$	$12$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	31.3	$31$	$- 31^{12}$	$5.49059$	$(-1/2a^2+a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$4$	$2$	$1$	$21.32891754$	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	$8$	$12$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	31.3	$31$	$-31$	$5.49059$	$(-1/2a^2+a+3)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$1$	$1$	$1$	$682.5253613$	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	$8$	$12$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	31.3	$31$	$31^{6}$	$5.49059$	$(-1/2a^2+a+3)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2Cs, 3B	$1$	$2$	$1$	$341.2626806$	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	$8$	$12$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	31.3	$31$	$31^{3}$	$5.49059$	$(-1/2a^2+a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$1$	$1$	$1$	$170.6313403$	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	$8$	$12$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	31.3	$31$	$- 31^{4}$	$5.49059$	$(-1/2a^2+a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$4$	$2$	$1$	$21.32891754$	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	$8$	$12$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	31.4	$31$	$- 31^{4}$	$5.49059$	$(1/2a^3-1/2a^2-3a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$4$	$2$	$1$	$21.32891754$	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	$8$	$12$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	31.4	$31$	$31^{3}$	$5.49059$	$(1/2a^3-1/2a^2-3a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$1$	$1$	$1$	$170.6313403$	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	$8$	$12$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	31.4	$31$	$-31$	$5.49059$	$(1/2a^3-1/2a^2-3a)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$1$	$1$	$1$	$682.5253613$	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	$8$	$12$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	31.4	$31$	$31^{6}$	$5.49059$	$(1/2a^3-1/2a^2-3a)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2Cs, 3B	$1$	$2$	$1$	$341.2626806$	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	$8$	$12$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	31.4	$31$	$- 31^{12}$	$5.49059$	$(1/2a^3-1/2a^2-3a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$4$	$2$	$1$	$21.32891754$	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	$8$	$12$	$\Q(\sqrt{2}, \sqrt{5})$	$4$	$[4, 0]$	31.4	$31$	$- 31^{3}$	$5.49059$	$(1/2a^3-1/2a^2-3a)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$1$	$1$	$1$	$682.5253613$	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.