Elliptic curves over Q(−5)\Q(\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
16.1-a1	16.1-a	$2$	$2$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	16.1	$2^{4}$	$2^{20}$	$0.79925$	$(2,a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$1$	$1$	$1$	$8.594800260$	0.960927881	$2048$	$\bigl[0$ , $-a$ , $0$ , $1$ , $-a\bigr]$	${y}^2={x}^3-a{x}^2+{x}-a$
16.1-a2	16.1-a	$2$	$2$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	16.1	$2^{4}$	$2^{4}$	$0.79925$	$(2,a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$1$	$1$	$1$	$8.594800260$	0.960927881	$78608$	$\bigl[a + 1$ , $1$ , $a + 1$ , $-a + 3$ , $1\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+{x}^2+\left(-a+3\right){x}+1$
16.1-b1	16.1-b	$2$	$2$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	16.1	$2^{4}$	$2^{20}$	$0.79925$	$(2,a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$1$	$1$	$1$	$8.594800260$	0.960927881	$2048$	$\bigl[0$ , $a$ , $0$ , $1$ , $a\bigr]$	${y}^2={x}^3+a{x}^2+{x}+a$
16.1-b2	16.1-b	$2$	$2$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	16.1	$2^{4}$	$2^{4}$	$0.79925$	$(2,a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$1$	$1$	$1$	$8.594800260$	0.960927881	$78608$	$\bigl[a + 1$ , $-a + 1$ , $a + 1$ , $-a + 3$ , $-a + 1\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+\left(-a+3\right){x}-a+1$
20.1-a1	20.1-a	$4$	$6$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	20.1	$2^{2} \cdot 5$	$2^{16} \cdot 5^{12}$	$0.84511$	$(2,a+1), (-a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B.1.1	$1$	$2$	$1$	$2.141031885$	0.478749283	$-\frac{20720464}{15625}$	$\bigl[0$ , $1$ , $0$ , $-36$ , $-140\bigr]$	${y}^2={x}^3+{x}^2-36{x}-140$
20.1-a2	20.1-a	$4$	$6$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	20.1	$2^{2} \cdot 5$	$2^{16} \cdot 5^{4}$	$0.84511$	$(2,a+1), (-a)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B.1.1	$1$	$2 \cdot 3$	$1$	$6.423095656$	0.478749283	$\frac{21296}{25}$	$\bigl[0$ , $1$ , $0$ , $4$ , $4\bigr]$	${y}^2={x}^3+{x}^2+4{x}+4$
20.1-a3	20.1-a	$4$	$6$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	20.1	$2^{2} \cdot 5$	$2^{8} \cdot 5^{2}$	$0.84511$	$(2,a+1), (-a)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B.1.1	$1$	$2 \cdot 3$	$1$	$6.423095656$	0.478749283	$\frac{16384}{5}$	$\bigl[0$ , $1$ , $0$ , $-1$ , $0\bigr]$	${y}^2={x}^3+{x}^2-{x}$
20.1-a4	20.1-a	$4$	$6$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	20.1	$2^{2} \cdot 5$	$2^{8} \cdot 5^{6}$	$0.84511$	$(2,a+1), (-a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B.1.1	$1$	$2$	$1$	$2.141031885$	0.478749283	$\frac{488095744}{125}$	$\bigl[0$ , $1$ , $0$ , $-41$ , $-116\bigr]$	${y}^2={x}^3+{x}^2-41{x}-116$
20.1-b1	20.1-b	$4$	$6$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	20.1	$2^{2} \cdot 5$	$2^{16} \cdot 5^{12}$	$0.84511$	$(2,a+1), (-a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B	$1$	$2 \cdot 3$	$1$	$2.141031885$	1.436247851	$-\frac{20720464}{15625}$	$\bigl[0$ , $-1$ , $0$ , $-36$ , $140\bigr]$	${y}^2={x}^3-{x}^2-36{x}+140$
20.1-b2	20.1-b	$4$	$6$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	20.1	$2^{2} \cdot 5$	$2^{16} \cdot 5^{4}$	$0.84511$	$(2,a+1), (-a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B	$1$	$2$	$1$	$6.423095656$	1.436247851	$\frac{21296}{25}$	$\bigl[0$ , $-1$ , $0$ , $4$ , $-4\bigr]$	${y}^2={x}^3-{x}^2+4{x}-4$
20.1-b3	20.1-b	$4$	$6$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	20.1	$2^{2} \cdot 5$	$2^{8} \cdot 5^{2}$	$0.84511$	$(2,a+1), (-a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B	$1$	$2$	$1$	$6.423095656$	1.436247851	$\frac{16384}{5}$	$\bigl[0$ , $-1$ , $0$ , $-1$ , $0\bigr]$	${y}^2={x}^3-{x}^2-{x}$
20.1-b4	20.1-b	$4$	$6$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	20.1	$2^{2} \cdot 5$	$2^{8} \cdot 5^{6}$	$0.84511$	$(2,a+1), (-a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B	$1$	$2 \cdot 3$	$1$	$2.141031885$	1.436247851	$\frac{488095744}{125}$	$\bigl[0$ , $-1$ , $0$ , $-41$ , $116\bigr]$	${y}^2={x}^3-{x}^2-41{x}+116$
40.1-a1	40.1-a	$4$	$4$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	40.1	$2^{3} \cdot 5$	$2^{20} \cdot 5^{8}$	$1.00501$	$(2,a+1), (-a)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{5}$	$0.233348375$	$2.996888981$	1.250980172	$\frac{237276}{625}$	$\bigl[0$ , $0$ , $0$ , $13$ , $-34\bigr]$	${y}^2={x}^3+13{x}-34$
40.1-a2	40.1-a	$4$	$4$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	40.1	$2^{3} \cdot 5$	$2^{16} \cdot 5^{4}$	$1.00501$	$(2,a+1), (-a)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{3}$	$0.466696751$	$5.993777963$	1.250980172	$\frac{148176}{25}$	$\bigl[0$ , $0$ , $0$ , $-7$ , $-6\bigr]$	${y}^2={x}^3-7{x}-6$
40.1-a3	40.1-a	$4$	$4$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	40.1	$2^{3} \cdot 5$	$2^{8} \cdot 5^{2}$	$1.00501$	$(2,a+1), (-a)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{2}$	$0.933393502$	$5.993777963$	1.250980172	$\frac{55296}{5}$	$\bigl[0$ , $0$ , $0$ , $-2$ , $1\bigr]$	${y}^2={x}^3-2{x}+1$
40.1-a4	40.1-a	$4$	$4$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	40.1	$2^{3} \cdot 5$	$2^{20} \cdot 5^{2}$	$1.00501$	$(2,a+1), (-a)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{3}$	$0.933393502$	$2.996888981$	1.250980172	$\frac{132304644}{5}$	$\bigl[0$ , $0$ , $0$ , $-107$ , $-426\bigr]$	${y}^2={x}^3-107{x}-426$
40.1-b1	40.1-b	$4$	$4$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	40.1	$2^{3} \cdot 5$	$2^{20} \cdot 5^{8}$	$1.00501$	$(2,a+1), (-a)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{4}$	$1$	$2.996888981$	1.340249496	$\frac{237276}{625}$	$\bigl[0$ , $0$ , $0$ , $13$ , $34\bigr]$	${y}^2={x}^3+13{x}+34$
40.1-b2	40.1-b	$4$	$4$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	40.1	$2^{3} \cdot 5$	$2^{16} \cdot 5^{4}$	$1.00501$	$(2,a+1), (-a)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{3}$	$1$	$5.993777963$	1.340249496	$\frac{148176}{25}$	$\bigl[0$ , $0$ , $0$ , $-7$ , $6\bigr]$	${y}^2={x}^3-7{x}+6$
40.1-b3	40.1-b	$4$	$4$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	40.1	$2^{3} \cdot 5$	$2^{8} \cdot 5^{2}$	$1.00501$	$(2,a+1), (-a)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{3}$	$1$	$5.993777963$	1.340249496	$\frac{55296}{5}$	$\bigl[0$ , $0$ , $0$ , $-2$ , $-1\bigr]$	${y}^2={x}^3-2{x}-1$
40.1-b4	40.1-b	$4$	$4$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	40.1	$2^{3} \cdot 5$	$2^{20} \cdot 5^{2}$	$1.00501$	$(2,a+1), (-a)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$4$	$2^{2}$	$1$	$2.996888981$	1.340249496	$\frac{132304644}{5}$	$\bigl[0$ , $0$ , $0$ , $-107$ , $426\bigr]$	${y}^2={x}^3-107{x}+426$
45.2-a1	45.2-a	$10$	$32$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	45.2	$3^{2} \cdot 5$	$3^{40} \cdot 5$	$1.03504$	$(3,a+1), (3,a+2), (-a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2$	2Cs	$4$	$2^{2}$	$1$	$0.279462714$	0.499918100	$-\frac{33987626912827121359}{9265100944259205} a - \frac{10358164733153980696}{1853020188851841}$	$\bigl[1$ , $1$ , $1$ , $-395 a + 90$ , $2916 a - 8170\bigr]$	${y}^2+{x}{y}+{y}={x}^3+{x}^2+\left(-395a+90\right){x}+2916a-8170$
45.2-a2	45.2-a	$10$	$32$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	45.2	$3^{2} \cdot 5$	$3^{40} \cdot 5$	$1.03504$	$(3,a+1), (3,a+2), (-a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2$	2Cs	$4$	$2^{2}$	$1$	$0.279462714$	0.499918100	$\frac{33987626912827121359}{9265100944259205} a - \frac{10358164733153980696}{1853020188851841}$	$\bigl[1$ , $1$ , $1$ , $395 a + 90$ , $-2916 a - 8170\bigr]$	${y}^2+{x}{y}+{y}={x}^3+{x}^2+\left(395a+90\right){x}-2916a-8170$
45.2-a3	45.2-a	$10$	$32$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	45.2	$3^{2} \cdot 5$	$3^{32} \cdot 5^{2}$	$1.03504$	$(3,a+1), (3,a+2), (-a)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$4$	$2^{3}$	$1$	$0.558925428$	0.499918100	$-\frac{147281603041}{215233605}$	$\bigl[1$ , $1$ , $1$ , $-110$ , $-880\bigr]$	${y}^2+{x}{y}+{y}={x}^3+{x}^2-110{x}-880$
45.2-a4	45.2-a	$10$	$32$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	45.2	$3^{2} \cdot 5$	$3^{2} \cdot 5^{2}$	$1.03504$	$(3,a+1), (3,a+2), (-a)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$1$	$2$	$1$	$8.942806850$	0.499918100	$-\frac{1}{15}$	$\bigl[1$ , $1$ , $1$ , $0$ , $0\bigr]$	${y}^2+{x}{y}+{y}={x}^3+{x}^2$
45.2-a5	45.2-a	$10$	$32$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	45.2	$3^{2} \cdot 5$	$3^{4} \cdot 5^{16}$	$1.03504$	$(3,a+1), (3,a+2), (-a)$	0	$\Z/8\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$1$	$2^{6}$	$1$	$1.117850856$	0.499918100	$\frac{4733169839}{3515625}$	$\bigl[1$ , $1$ , $1$ , $35$ , $-28\bigr]$	${y}^2+{x}{y}+{y}={x}^3+{x}^2+35{x}-28$
45.2-a6	45.2-a	$10$	$32$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	45.2	$3^{2} \cdot 5$	$3^{8} \cdot 5^{8}$	$1.03504$	$(3,a+1), (3,a+2), (-a)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$1$	$2^{5}$	$1$	$2.235701712$	0.499918100	$\frac{111284641}{50625}$	$\bigl[1$ , $1$ , $1$ , $-10$ , $-10\bigr]$	${y}^2+{x}{y}+{y}={x}^3+{x}^2-10{x}-10$
45.2-a7	45.2-a	$10$	$32$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	45.2	$3^{2} \cdot 5$	$3^{4} \cdot 5^{4}$	$1.03504$	$(3,a+1), (3,a+2), (-a)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$1$	$2^{4}$	$1$	$4.471403425$	0.499918100	$\frac{13997521}{225}$	$\bigl[1$ , $1$ , $1$ , $-5$ , $2\bigr]$	${y}^2+{x}{y}+{y}={x}^3+{x}^2-5{x}+2$
45.2-a8	45.2-a	$10$	$32$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	45.2	$3^{2} \cdot 5$	$3^{16} \cdot 5^{4}$	$1.03504$	$(3,a+1), (3,a+2), (-a)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$4$	$2^{4}$	$1$	$1.117850856$	0.499918100	$\frac{272223782641}{164025}$	$\bigl[1$ , $1$ , $1$ , $-135$ , $-660\bigr]$	${y}^2+{x}{y}+{y}={x}^3+{x}^2-135{x}-660$
45.2-a9	45.2-a	$10$	$32$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	45.2	$3^{2} \cdot 5$	$3^{2} \cdot 5^{2}$	$1.03504$	$(3,a+1), (3,a+2), (-a)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$4$	$2$	$1$	$2.235701712$	0.499918100	$\frac{56667352321}{15}$	$\bigl[1$ , $1$ , $1$ , $-80$ , $242\bigr]$	${y}^2+{x}{y}+{y}={x}^3+{x}^2-80{x}+242$
45.2-a10	45.2-a	$10$	$32$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	45.2	$3^{2} \cdot 5$	$3^{8} \cdot 5^{2}$	$1.03504$	$(3,a+1), (3,a+2), (-a)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$4$	$2^{3}$	$1$	$0.558925428$	0.499918100	$\frac{1114544804970241}{405}$	$\bigl[1$ , $1$ , $1$ , $-2160$ , $-39540\bigr]$	${y}^2+{x}{y}+{y}={x}^3+{x}^2-2160{x}-39540$
45.2-b1	45.2-b	$10$	$32$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	45.2	$3^{2} \cdot 5$	$3^{40} \cdot 5$	$1.03504$	$(3,a+1), (3,a+2), (-a)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2$	2Cs	$1$	$2^{8}$	$1$	$0.279462714$	1.999672402	$-\frac{33987626912827121359}{9265100944259205} a - \frac{10358164733153980696}{1853020188851841}$	$\bigl[a$ , $0$ , $a$ , $-395 a + 93$ , $-2916 a + 8171\bigr]$	${y}^2+a{x}{y}+a{y}={x}^3+\left(-395a+93\right){x}-2916a+8171$
45.2-b2	45.2-b	$10$	$32$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	45.2	$3^{2} \cdot 5$	$3^{40} \cdot 5$	$1.03504$	$(3,a+1), (3,a+2), (-a)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2$	2Cs	$1$	$2^{8}$	$1$	$0.279462714$	1.999672402	$\frac{33987626912827121359}{9265100944259205} a - \frac{10358164733153980696}{1853020188851841}$	$\bigl[a$ , $0$ , $a$ , $395 a + 93$ , $2916 a + 8171\bigr]$	${y}^2+a{x}{y}+a{y}={x}^3+\left(395a+93\right){x}+2916a+8171$
45.2-b3	45.2-b	$10$	$32$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	45.2	$3^{2} \cdot 5$	$3^{32} \cdot 5^{2}$	$1.03504$	$(3,a+1), (3,a+2), (-a)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$1$	$2^{9}$	$1$	$0.558925428$	1.999672402	$-\frac{147281603041}{215233605}$	$\bigl[a$ , $0$ , $a$ , $-107$ , $881\bigr]$	${y}^2+a{x}{y}+a{y}={x}^3-107{x}+881$
45.2-b4	45.2-b	$10$	$32$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	45.2	$3^{2} \cdot 5$	$3^{2} \cdot 5^{2}$	$1.03504$	$(3,a+1), (3,a+2), (-a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$1$	$2$	$1$	$8.942806850$	1.999672402	$-\frac{1}{15}$	$\bigl[a$ , $0$ , $a$ , $3$ , $1\bigr]$	${y}^2+a{x}{y}+a{y}={x}^3+3{x}+1$
45.2-b5	45.2-b	$10$	$32$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	45.2	$3^{2} \cdot 5$	$3^{4} \cdot 5^{16}$	$1.03504$	$(3,a+1), (3,a+2), (-a)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$1$	$2^{6}$	$1$	$1.117850856$	1.999672402	$\frac{4733169839}{3515625}$	$\bigl[a$ , $0$ , $a$ , $38$ , $29\bigr]$	${y}^2+a{x}{y}+a{y}={x}^3+38{x}+29$
45.2-b6	45.2-b	$10$	$32$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	45.2	$3^{2} \cdot 5$	$3^{8} \cdot 5^{8}$	$1.03504$	$(3,a+1), (3,a+2), (-a)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$1$	$2^{7}$	$1$	$2.235701712$	1.999672402	$\frac{111284641}{50625}$	$\bigl[a$ , $0$ , $a$ , $-7$ , $11\bigr]$	${y}^2+a{x}{y}+a{y}={x}^3-7{x}+11$
45.2-b7	45.2-b	$10$	$32$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	45.2	$3^{2} \cdot 5$	$3^{4} \cdot 5^{4}$	$1.03504$	$(3,a+1), (3,a+2), (-a)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$1$	$2^{4}$	$1$	$4.471403425$	1.999672402	$\frac{13997521}{225}$	$\bigl[a$ , $0$ , $a$ , $-2$ , $-1\bigr]$	${y}^2+a{x}{y}+a{y}={x}^3-2{x}-1$
45.2-b8	45.2-b	$10$	$32$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	45.2	$3^{2} \cdot 5$	$3^{16} \cdot 5^{4}$	$1.03504$	$(3,a+1), (3,a+2), (-a)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$1$	$2^{8}$	$1$	$1.117850856$	1.999672402	$\frac{272223782641}{164025}$	$\bigl[a$ , $0$ , $a$ , $-132$ , $661\bigr]$	${y}^2+a{x}{y}+a{y}={x}^3-132{x}+661$
45.2-b9	45.2-b	$10$	$32$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	45.2	$3^{2} \cdot 5$	$3^{2} \cdot 5^{2}$	$1.03504$	$(3,a+1), (3,a+2), (-a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$4$	$2$	$1$	$2.235701712$	1.999672402	$\frac{56667352321}{15}$	$\bigl[a$ , $0$ , $a$ , $-77$ , $-241\bigr]$	${y}^2+a{x}{y}+a{y}={x}^3-77{x}-241$
45.2-b10	45.2-b	$10$	$32$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	45.2	$3^{2} \cdot 5$	$3^{8} \cdot 5^{2}$	$1.03504$	$(3,a+1), (3,a+2), (-a)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$4$	$2^{5}$	$1$	$0.558925428$	1.999672402	$\frac{1114544804970241}{405}$	$\bigl[a$ , $0$ , $a$ , $-2157$ , $39541\bigr]$	${y}^2+a{x}{y}+a{y}={x}^3-2157{x}+39541$
50.1-a1	50.1-a	$4$	$15$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	50.1	$2 \cdot 5^{2}$	$2^{6} \cdot 5^{8}$	$1.06266$	$(2,a+1), (-a)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$3, 5$	3B.1.1, 5B.1.3	$1$	$2$	$1$	$1.424166746$	1.273813462	$-\frac{349938025}{8}$	$\bigl[1$ , $0$ , $1$ , $-126$ , $-552\bigr]$	${y}^2+{x}{y}+{y}={x}^3-126{x}-552$
50.1-a2	50.1-a	$4$	$15$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	50.1	$2 \cdot 5^{2}$	$2^{10} \cdot 5^{4}$	$1.06266$	$(2,a+1), (-a)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$3, 5$	3B.1.1, 5B.1.3	$1$	$2 \cdot 3$	$1$	$4.272500240$	1.273813462	$-\frac{121945}{32}$	$\bigl[a$ , $0$ , $a$ , $0$ , $0\bigr]$	${y}^2+a{x}{y}+a{y}={x}^3$
50.1-a3	50.1-a	$4$	$15$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	50.1	$2 \cdot 5^{2}$	$2^{2} \cdot 5^{8}$	$1.06266$	$(2,a+1), (-a)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$3, 5$	3B.1.1, 5B.1.3	$1$	$2 \cdot 3$	$1$	$4.272500240$	1.273813462	$-\frac{25}{2}$	$\bigl[1$ , $0$ , $1$ , $-1$ , $-2\bigr]$	${y}^2+{x}{y}+{y}={x}^3-{x}-2$
50.1-a4	50.1-a	$4$	$15$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	50.1	$2 \cdot 5^{2}$	$2^{30} \cdot 5^{4}$	$1.06266$	$(2,a+1), (-a)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$3, 5$	3B.1.1, 5B.1.3	$1$	$2$	$1$	$1.424166746$	1.273813462	$\frac{46969655}{32768}$	$\bigl[a$ , $0$ , $a$ , $25$ , $10\bigr]$	${y}^2+a{x}{y}+a{y}={x}^3+25{x}+10$
50.1-b1	50.1-b	$4$	$15$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	50.1	$2 \cdot 5^{2}$	$2^{6} \cdot 5^{8}$	$1.06266$	$(2,a+1), (-a)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$3, 5$	3B, 5B.1.2	$1$	$2 \cdot 3$	$0.194697629$	$1.424166746$	1.488050770	$-\frac{349938025}{8}$	$\bigl[a$ , $1$ , $a$ , $-123$ , $553\bigr]$	${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-123{x}+553$
50.1-b2	50.1-b	$4$	$15$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	50.1	$2 \cdot 5^{2}$	$2^{10} \cdot 5^{4}$	$1.06266$	$(2,a+1), (-a)$	$1$	$\Z/5\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$3, 5$	3B, 5B.1.2	$1$	$2 \cdot 3 \cdot 5$	$0.324496049$	$4.272500240$	1.488050770	$-\frac{121945}{32}$	$\bigl[1$ , $1$ , $1$ , $-3$ , $1\bigr]$	${y}^2+{x}{y}+{y}={x}^3+{x}^2-3{x}+1$
50.1-b3	50.1-b	$4$	$15$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	50.1	$2 \cdot 5^{2}$	$2^{2} \cdot 5^{8}$	$1.06266$	$(2,a+1), (-a)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$3, 5$	3B, 5B.1.2	$1$	$2 \cdot 3$	$0.064899209$	$4.272500240$	1.488050770	$-\frac{25}{2}$	$\bigl[a$ , $1$ , $a$ , $2$ , $3\bigr]$	${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+2{x}+3$
50.1-b4	50.1-b	$4$	$15$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	50.1	$2 \cdot 5^{2}$	$2^{30} \cdot 5^{4}$	$1.06266$	$(2,a+1), (-a)$	$1$	$\Z/5\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$3, 5$	3B, 5B.1.2	$1$	$2 \cdot 3 \cdot 5$	$0.973488147$	$1.424166746$	1.488050770	$\frac{46969655}{32768}$	$\bigl[1$ , $1$ , $1$ , $22$ , $-9\bigr]$	${y}^2+{x}{y}+{y}={x}^3+{x}^2+22{x}-9$
64.1-a1	64.1-a	$4$	$4$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	64.1	$2^{6}$	$2^{12}$	$1.13031$	$(2,a+1)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓	✓		✓	$2, 5$	2Cs, 5Ns.2.1	$1$	$2$	$1.899482172$	$6.875185818$	1.460073332	$1728$	$\bigl[0$ , $0$ , $0$ , $-1$ , $0\bigr]$	${y}^2={x}^3-{x}$
64.1-a2	64.1-a	$4$	$4$	$\Q(\sqrt{-5})$	$2$	$[0, 1]$	64.1	$2^{6}$	$2^{24}$	$1.13031$	$(2,a+1)$	$1$	$\Z/4\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓	✓		✓	$2, 5$	2Cs, 5Ns.2.1	$1$	$2^{2}$	$0.949741086$	$6.875185818$	1.460073332	$1728$	$\bigl[0$ , $0$ , $0$ , $4$ , $0\bigr]$	${y}^2={x}^3+4{x}$

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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.