Elliptic curves over Q(26)\Q(\sqrt{26})

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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	$2$	$5$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	1.1	$1$	$1$	$0.91129$	$\textsf{none}$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓	✓	$3, 5$	3Nn, 5B.1.2	$9$	$1$	$1$	$0.736148266$	0.649667488	$-23788477376$	$\bigl[a$ , $-a - 1$ , $a + 1$ , $595 a - 3050$ , $20142 a - 102714\bigr]$	${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(595a-3050\right){x}+20142a-102714$
1.1-a2	1.1-a	$2$	$5$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	1.1	$1$	$1$	$0.91129$	$\textsf{none}$	0	$\Z/5\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓	✓	$3, 5$	3Nn, 5B.1.1	$9$	$1$	$1$	$18.40370665$	0.649667488	$64$	$\bigl[a$ , $-a - 1$ , $a + 1$ , $-5 a + 10$ , $-3 a + 6\bigr]$	${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-5a+10\right){x}-3a+6$
1.1-b1	1.1-b	$2$	$5$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	1.1	$1$	$2^{12}$	$0.91129$	$\textsf{none}$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓	✓	$3, 5$	3Nn, 5B.4.2	$25$	$1$	$1$	$0.736148266$	1.804631911	$-23788477376$	$\bigl[0$ , $a - 1$ , $0$ , $2396 a - 12214$ , $139366 a - 710632\bigr]$	${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(2396a-12214\right){x}+139366a-710632$
1.1-b2	1.1-b	$2$	$5$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	1.1	$1$	$2^{12}$	$0.91129$	$\textsf{none}$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓	✓	$3, 5$	3Nn, 5B.4.1	$1$	$1$	$1$	$18.40370665$	1.804631911	$64$	$\bigl[0$ , $a - 1$ , $0$ , $-4 a + 26$ , $46 a - 232\bigr]$	${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a+26\right){x}+46a-232$
8.1-a1	8.1-a	$1$	$1$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	8.1	$2^{3}$	$2^{20}$	$1.53260$	$(2,a)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓			$1$	$2$	$1$	$8.909190355$	1.747235979	$-23504 a - 119652$	$\bigl[0$ , $a + 1$ , $0$ , $-2 a + 22$ , $-10 a + 58\bigr]$	${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a+22\right){x}-10a+58$
8.1-b1	8.1-b	$1$	$1$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	8.1	$2^{3}$	$2^{8}$	$1.53260$	$(2,a)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓			$1$	$2^{2}$	$0.309407382$	$8.909190355$	2.162430844	$23504 a - 119652$	$\bigl[a$ , $a$ , $0$ , $5 a + 26$ , $10 a + 51\bigr]$	${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(5a+26\right){x}+10a+51$
8.1-c1	8.1-c	$1$	$1$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	8.1	$2^{3}$	$2^{20}$	$1.53260$	$(2,a)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓			$1$	$2$	$1$	$8.909190355$	1.747235979	$23504 a - 119652$	$\bigl[0$ , $-a + 1$ , $0$ , $2 a + 22$ , $10 a + 58\bigr]$	${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a+22\right){x}+10a+58$
8.1-d1	8.1-d	$1$	$1$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	8.1	$2^{3}$	$2^{8}$	$1.53260$	$(2,a)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓			$1$	$2^{2}$	$0.309407382$	$8.909190355$	2.162430844	$-23504 a - 119652$	$\bigl[a$ , $-a$ , $0$ , $-5 a + 26$ , $-10 a + 51\bigr]$	${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-5a+26\right){x}-10a+51$
9.1-a1	9.1-a	$2$	$2$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	9.1	$3^{2}$	$3^{12}$	$1.57840$	$(3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2, 3$	2B, 3Nn	$4$	$2$	$1$	$21.40949540$	4.198747493	$-\frac{778688}{729}$	$\bigl[a$ , $-a - 1$ , $a + 1$ , $15 a - 92$ , $-104 a + 521\bigr]$	${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(15a-92\right){x}-104a+521$
9.1-a2	9.1-a	$2$	$2$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	9.1	$3^{2}$	$2^{12} \cdot 3^{6}$	$1.57840$	$(3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2, 3$	2B, 3Nn	$4$	$1$	$1$	$42.81899080$	4.198747493	$\frac{78402752}{27}$	$\bigl[0$ , $-a + 1$ , $0$ , $356 a - 1810$ , $-7554 a + 38516\bigr]$	${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(356a-1810\right){x}-7554a+38516$
9.1-b1	9.1-b	$2$	$2$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	9.1	$3^{2}$	$2^{12} \cdot 3^{12}$	$1.57840$	$(3)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2, 3$	2B, 3Nn	$1$	$2$	$0.327721564$	$21.40949540$	1.376020096	$-\frac{778688}{729}$	$\bigl[0$ , $a - 1$ , $0$ , $76 a - 382$ , $-1490 a + 7600\bigr]$	${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(76a-382\right){x}-1490a+7600$
9.1-b2	9.1-b	$2$	$2$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	9.1	$3^{2}$	$3^{6}$	$1.57840$	$(3)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2, 3$	2B, 3Nn	$1$	$1$	$0.327721564$	$42.81899080$	1.376020096	$\frac{78402752}{27}$	$\bigl[a$ , $a$ , $a + 1$ , $93 a - 445$ , $-988 a + 5086\bigr]$	${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(93a-445\right){x}-988a+5086$
10.1-a1	10.1-a	$2$	$5$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$- 2^{17} \cdot 5^{5}$	$1.62052$	$(2,a), (5,a+4)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$5$	5B.4.1	$1$	$1$	$1$	$17.05624564$	1.672502487	$-\frac{37617129}{25000} a + \frac{44393049}{6250}$	$\bigl[a$ , $1$ , $0$ , $5 a - 8$ , $26 a - 119\bigr]$	${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(5a-8\right){x}+26a-119$
10.1-a2	10.1-a	$2$	$5$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$- 2^{13} \cdot 5$	$1.62052$	$(2,a), (5,a+4)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$5$	5B.4.2	$25$	$1$	$1$	$0.682249825$	1.672502487	$-\frac{530618171482888843761}{10} a + \frac{1352816205329086378722}{5}$	$\bigl[a$ , $1$ , $0$ , $3145 a - 16048$ , $224946 a - 1147199\bigr]$	${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(3145a-16048\right){x}+224946a-1147199$
10.1-b1	10.1-b	$1$	$1$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$- 2^{25} \cdot 5$	$1.62052$	$(2,a), (5,a+4)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	$1$	$0.536698983$	$17.17500600$	1.807760930	$-\frac{391019}{640} a + \frac{357337}{80}$	$\bigl[a$ , $a - 1$ , $a$ , $1479 a - 7517$ , $-61002 a + 311088\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(1479a-7517\right){x}-61002a+311088$
10.1-c1	10.1-c	$2$	$5$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$- 2^{5} \cdot 5^{5}$	$1.62052$	$(2,a), (5,a+4)$	0	$\Z/5\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$5$	5B.1.1	$1$	$5^{2}$	$1$	$17.05624564$	1.672502487	$-\frac{37617129}{25000} a + \frac{44393049}{6250}$	$\bigl[a + 1$ , $a$ , $0$ , $8 a + 28$ , $12 a + 48\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(8a+28\right){x}+12a+48$
10.1-c2	10.1-c	$2$	$5$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$- 2 \cdot 5$	$1.62052$	$(2,a), (5,a+4)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$5$	5B.1.2	$25$	$1$	$1$	$0.682249825$	1.672502487	$-\frac{530618171482888843761}{10} a + \frac{1352816205329086378722}{5}$	$\bigl[a + 1$ , $a$ , $0$ , $793 a - 3982$ , $26907 a - 137142\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(793a-3982\right){x}+26907a-137142$
10.1-d1	10.1-d	$1$	$1$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$- 2^{13} \cdot 5$	$1.62052$	$(2,a), (5,a+4)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	$13$	$0.080526241$	$17.17500600$	3.526070609	$-\frac{391019}{640} a + \frac{357337}{80}$	$\bigl[1$ , $-a + 1$ , $1$ , $368 a - 1872$ , $-6871 a + 35033\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(368a-1872\right){x}-6871a+35033$
10.2-a1	10.2-a	$2$	$5$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	10.2	$2 \cdot 5$	$- 2^{17} \cdot 5^{5}$	$1.62052$	$(2,a), (5,a+1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$5$	5B.4.1	$1$	$1$	$1$	$17.05624564$	1.672502487	$\frac{37617129}{25000} a + \frac{44393049}{6250}$	$\bigl[a$ , $1$ , $0$ , $-5 a - 8$ , $-26 a - 119\bigr]$	${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-5a-8\right){x}-26a-119$
10.2-a2	10.2-a	$2$	$5$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	10.2	$2 \cdot 5$	$- 2^{13} \cdot 5$	$1.62052$	$(2,a), (5,a+1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$5$	5B.4.2	$25$	$1$	$1$	$0.682249825$	1.672502487	$\frac{530618171482888843761}{10} a + \frac{1352816205329086378722}{5}$	$\bigl[a$ , $1$ , $0$ , $-3145 a - 16048$ , $-224946 a - 1147199\bigr]$	${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-3145a-16048\right){x}-224946a-1147199$
10.2-b1	10.2-b	$1$	$1$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	10.2	$2 \cdot 5$	$- 2^{25} \cdot 5$	$1.62052$	$(2,a), (5,a+1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	$1$	$0.536698983$	$17.17500600$	1.807760930	$\frac{391019}{640} a + \frac{357337}{80}$	$\bigl[a$ , $-a$ , $a$ , $-8 a + 27$ , $-15 a + 70\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-8a+27\right){x}-15a+70$
10.2-c1	10.2-c	$2$	$5$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	10.2	$2 \cdot 5$	$- 2^{5} \cdot 5^{5}$	$1.62052$	$(2,a), (5,a+1)$	0	$\Z/5\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$5$	5B.1.1	$1$	$5^{2}$	$1$	$17.05624564$	1.672502487	$\frac{37617129}{25000} a + \frac{44393049}{6250}$	$\bigl[a + 1$ , $a$ , $a$ , $5 a + 15$ , $3 a + 9\bigr]$	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(5a+15\right){x}+3a+9$
10.2-c2	10.2-c	$2$	$5$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	10.2	$2 \cdot 5$	$- 2 \cdot 5$	$1.62052$	$(2,a), (5,a+1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$5$	5B.1.2	$25$	$1$	$1$	$0.682249825$	1.672502487	$\frac{530618171482888843761}{10} a + \frac{1352816205329086378722}{5}$	$\bigl[a + 1$ , $a$ , $a$ , $-780 a - 3995$ , $-30902 a - 157591\bigr]$	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-780a-3995\right){x}-30902a-157591$
10.2-d1	10.2-d	$1$	$1$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	10.2	$2 \cdot 5$	$- 2^{13} \cdot 5$	$1.62052$	$(2,a), (5,a+1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	$13$	$0.080526241$	$17.17500600$	3.526070609	$\frac{391019}{640} a + \frac{357337}{80}$	$\bigl[1$ , $a + 1$ , $1$ , $-368 a - 1872$ , $6871 a + 35033\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-368a-1872\right){x}+6871a+35033$
13.1-a1	13.1-a	$1$	$1$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	13.1	$13$	$13^{4}$	$1.73038$	$(13,a)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	$2^{2}$	$0.629188872$	$3.908720549$	1.929252060	$\frac{2292144}{169} a - \frac{11688353}{169}$	$\bigl[a + 1$ , $a + 1$ , $1$ , $20 a - 26$ , $70 a - 222\bigr]$	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(20a-26\right){x}+70a-222$
13.1-b1	13.1-b	$1$	$1$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	13.1	$13$	$13^{4}$	$1.73038$	$(13,a)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	$2^{2}$	$0.629188872$	$3.908720549$	1.929252060	$-\frac{2292144}{169} a - \frac{11688353}{169}$	$\bigl[a + 1$ , $a + 1$ , $a + 1$ , $-6 a - 39$ , $-109 a - 560\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-6a-39\right){x}-109a-560$
13.1-c1	13.1-c	$1$	$1$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	13.1	$13$	$2^{12} \cdot 13^{4}$	$1.73038$	$(13,a)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	$2$	$1$	$3.908720549$	0.766563167	$-\frac{2292144}{169} a - \frac{11688353}{169}$	$\bigl[a$ , $0$ , $a$ , $-51 a - 259$ , $-561 a - 2857\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-51a-259\right){x}-561a-2857$
13.1-d1	13.1-d	$1$	$1$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	13.1	$13$	$2^{12} \cdot 13^{4}$	$1.73038$	$(13,a)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	$2$	$1$	$3.908720549$	0.766563167	$\frac{2292144}{169} a - \frac{11688353}{169}$	$\bigl[a$ , $0$ , $a$ , $51 a - 259$ , $561 a - 2857\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(51a-259\right){x}+561a-2857$
16.1-a1	16.1-a	$1$	$1$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	16.1	$2^{4}$	$2^{20}$	$1.82257$	$(2,a)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓			$1$	$2$	$0.326166095$	$24.54409375$	3.139996309	$-23504 a - 119652$	$\bigl[0$ , $-a - 1$ , $0$ , $-2 a + 22$ , $10 a - 58\bigr]$	${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a+22\right){x}+10a-58$
16.1-b1	16.1-b	$2$	$5$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	16.1	$2^{4}$	$2^{24}$	$1.82257$	$(2,a)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$3, 5$	3Nn, 5B.4.2	$1$	$1$	$1$	$21.28911211$	2.087569194	$-23788477376$	$\bigl[0$ , $a - 1$ , $0$ , $9586 a - 48883$ , $-1173397 a + 5983175\bigr]$	${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(9586a-48883\right){x}-1173397a+5983175$
16.1-b2	16.1-b	$2$	$5$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	16.1	$2^{4}$	$2^{24}$	$1.82257$	$(2,a)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$3, 5$	3Nn, 5B.4.1	$1$	$1$	$1$	$21.28911211$	2.087569194	$64$	$\bigl[0$ , $a - 1$ , $0$ , $-14 a + 77$ , $-277 a + 1415\bigr]$	${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-14a+77\right){x}-277a+1415$
16.1-c1	16.1-c	$1$	$1$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	16.1	$2^{4}$	$2^{20}$	$1.82257$	$(2,a)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓			$1$	$2$	$0.326166095$	$24.54409375$	3.139996309	$23504 a - 119652$	$\bigl[0$ , $a - 1$ , $0$ , $2 a + 22$ , $-10 a - 58\bigr]$	${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(2a+22\right){x}-10a-58$
16.1-d1	16.1-d	$1$	$1$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	16.1	$2^{4}$	$2^{8}$	$1.82257$	$(2,a)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓			$1$	$2$	$0.269173633$	$24.54409375$	2.591330699	$23504 a - 119652$	$\bigl[a$ , $-a - 1$ , $0$ , $-3 a + 22$ , $-6 a + 13\bigr]$	${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3a+22\right){x}-6a+13$
16.1-e1	16.1-e	$2$	$5$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	16.1	$2^{4}$	$2^{12}$	$1.82257$	$(2,a)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$3, 5$	3Nn, 5B.4.2	$1$	$1$	$1$	$21.28911211$	2.087569194	$-23788477376$	$\bigl[0$ , $-a + 1$ , $0$ , $2396 a - 12214$ , $-139366 a + 710632\bigr]$	${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(2396a-12214\right){x}-139366a+710632$
16.1-e2	16.1-e	$2$	$5$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	16.1	$2^{4}$	$2^{12}$	$1.82257$	$(2,a)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$3, 5$	3Nn, 5B.4.1	$1$	$1$	$1$	$21.28911211$	2.087569194	$64$	$\bigl[0$ , $-a + 1$ , $0$ , $-4 a + 26$ , $-46 a + 232\bigr]$	${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a+26\right){x}-46a+232$
16.1-f1	16.1-f	$1$	$1$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	16.1	$2^{4}$	$2^{8}$	$1.82257$	$(2,a)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓			$1$	$2$	$0.269173633$	$24.54409375$	2.591330699	$-23504 a - 119652$	$\bigl[a$ , $a - 1$ , $0$ , $3 a + 22$ , $6 a + 13\bigr]$	${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(3a+22\right){x}+6a+13$
17.1-a1	17.1-a	$2$	$2$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	17.1	$17$	$- 2^{12} \cdot 17^{6}$	$1.85041$	$(a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3Nn	$4$	$2$	$1$	$8.036318802$	1.576051784	$-\frac{516632309525}{24137569} a + \frac{2632534734107}{24137569}$	$\bigl[a$ , $a$ , $a$ , $26 a - 103$ , $-111 a + 602\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(26a-103\right){x}-111a+602$
17.1-a2	17.1-a	$2$	$2$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	17.1	$17$	$2^{12} \cdot 17^{3}$	$1.85041$	$(a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3Nn	$4$	$1$	$1$	$16.07263760$	1.576051784	$\frac{123207298}{4913} a + \frac{636786691}{4913}$	$\bigl[a$ , $a$ , $a$ , $6 a - 3$ , $5 a + 6\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(6a-3\right){x}+5a+6$
17.1-b1	17.1-b	$2$	$2$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	17.1	$17$	$- 17^{6}$	$1.85041$	$(a+3)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3Nn	$1$	$2$	$2.202689616$	$8.036318802$	3.471552899	$-\frac{516632309525}{24137569} a + \frac{2632534734107}{24137569}$	$\bigl[a + 1$ , $1$ , $0$ , $8 a - 6$ , $-3 a + 53\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(8a-6\right){x}-3a+53$
17.1-b2	17.1-b	$2$	$2$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	17.1	$17$	$17^{3}$	$1.85041$	$(a+3)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3Nn	$1$	$1$	$2.202689616$	$16.07263760$	3.471552899	$\frac{123207298}{4913} a + \frac{636786691}{4913}$	$\bigl[a + 1$ , $1$ , $0$ , $3 a + 19$ , $4 a + 16\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(3a+19\right){x}+4a+16$
17.2-a1	17.2-a	$2$	$2$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	17.2	$17$	$2^{12} \cdot 17^{3}$	$1.85041$	$(a-3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3Nn	$4$	$1$	$1$	$16.07263760$	1.576051784	$-\frac{123207298}{4913} a + \frac{636786691}{4913}$	$\bigl[a$ , $-a$ , $a$ , $-6 a - 3$ , $-5 a + 6\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-6a-3\right){x}-5a+6$
17.2-a2	17.2-a	$2$	$2$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	17.2	$17$	$- 2^{12} \cdot 17^{6}$	$1.85041$	$(a-3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3Nn	$4$	$2$	$1$	$8.036318802$	1.576051784	$\frac{516632309525}{24137569} a + \frac{2632534734107}{24137569}$	$\bigl[a$ , $-a$ , $a$ , $-26 a - 103$ , $111 a + 602\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-26a-103\right){x}+111a+602$
17.2-b1	17.2-b	$2$	$2$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	17.2	$17$	$17^{3}$	$1.85041$	$(a-3)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3Nn	$1$	$1$	$2.202689616$	$16.07263760$	3.471552899	$-\frac{123207298}{4913} a + \frac{636786691}{4913}$	$\bigl[a + 1$ , $-a + 1$ , $0$ , $-3 a + 19$ , $-4 a + 16\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a+19\right){x}-4a+16$
17.2-b2	17.2-b	$2$	$2$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	17.2	$17$	$- 17^{6}$	$1.85041$	$(a-3)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3Nn	$1$	$2$	$2.202689616$	$8.036318802$	3.471552899	$\frac{516632309525}{24137569} a + \frac{2632534734107}{24137569}$	$\bigl[a + 1$ , $-a + 1$ , $0$ , $-8 a - 6$ , $3 a + 53\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-8a-6\right){x}+3a+53$
20.1-a1	20.1-a	$4$	$4$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	20.1	$2^{2} \cdot 5$	$- 2^{8} \cdot 5^{2}$	$1.92714$	$(2,a), (5,a+1)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2$	$9.101597095$	$14.39552905$	3.211948519	$-\frac{449312768164}{25} a + \frac{2291054610364}{25}$	$\bigl[a$ , $a$ , $a$ , $223 a - 1105$ , $-3866 a + 19765\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(223a-1105\right){x}-3866a+19765$
20.1-a2	20.1-a	$4$	$4$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	20.1	$2^{2} \cdot 5$	$2^{4} \cdot 5^{4}$	$1.92714$	$(2,a), (5,a+1)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	$2$	$4.550798547$	$28.79105811$	3.211948519	$-\frac{26162592}{625} a + \frac{134634992}{625}$	$\bigl[a$ , $a$ , $a$ , $18 a - 60$ , $-50 a + 306\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(18a-60\right){x}-50a+306$
20.1-a3	20.1-a	$4$	$4$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	20.1	$2^{2} \cdot 5$	$- 2^{8} \cdot 5^{8}$	$1.92714$	$(2,a), (5,a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2$	$2.275399273$	$14.39552905$	3.211948519	$\frac{3507883972}{390625} a + \frac{17822712628}{390625}$	$\bigl[a$ , $a$ , $a$ , $13 a - 35$ , $-98 a + 549\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(13a-35\right){x}-98a+549$
20.1-a4	20.1-a	$4$	$4$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	20.1	$2^{2} \cdot 5$	$2^{20} \cdot 5^{2}$	$1.92714$	$(2,a), (5,a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2$	$2.275399273$	$14.39552905$	3.211948519	$\frac{2494464}{25} a + \frac{12763136}{25}$	$\bigl[0$ , $a - 1$ , $0$ , $18 a - 87$ , $-49 a + 251\bigr]$	${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(18a-87\right){x}-49a+251$
20.1-b1	20.1-b	$4$	$4$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	20.1	$2^{2} \cdot 5$	$- 2^{20} \cdot 5^{2}$	$1.92714$	$(2,a), (5,a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2 \cdot 3$	$1$	$14.39552905$	2.117396641	$-\frac{449312768164}{25} a + \frac{2291054610364}{25}$	$\bigl[0$ , $a + 1$ , $0$ , $962 a + 4910$ , $-11906 a - 60710\bigr]$	${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(962a+4910\right){x}-11906a-60710$
20.1-b2	20.1-b	$4$	$4$	$\Q(\sqrt{26})$	$2$	$[2, 0]$	20.1	$2^{2} \cdot 5$	$2^{16} \cdot 5^{4}$	$1.92714$	$(2,a), (5,a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	$2^{2} \cdot 3$	$1$	$28.79105811$	2.117396641	$-\frac{26162592}{625} a + \frac{134634992}{625}$	$\bigl[0$ , $a + 1$ , $0$ , $-258 a - 1310$ , $-2318 a - 11822\bigr]$	${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-258a-1310\right){x}-2318a-11822$

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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.