Elliptic curves over Q(−1)\Q(\sqrt{-1}) of conductor 12544.1

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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
12544.1-a1	12544.1-a	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	12544.1	$2^{8} \cdot 7^{2}$	$2^{16} \cdot 7^{2}$	$1.89137$	$(a+1), (7)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2^{2}$	$0.186222298$	$4.016295718$	2.991695286	$\frac{432}{7}$	$\bigl[0$ , $0$ , $0$ , $-1$ , $2 i\bigr]$	${y}^2={x}^{3}-{x}+2i$
12544.1-a2	12544.1-a	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	12544.1	$2^{8} \cdot 7^{2}$	$2^{22} \cdot 7^{8}$	$1.89137$	$(a+1), (7)$	$2$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2^{4}$	$0.744889195$	$1.004073929$	2.991695286	$\frac{11090466}{2401}$	$\bigl[0$ , $0$ , $0$ , $59$ , $-138 i\bigr]$	${y}^2={x}^{3}+59{x}-138i$
12544.1-a3	12544.1-a	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	12544.1	$2^{8} \cdot 7^{2}$	$2^{20} \cdot 7^{4}$	$1.89137$	$(a+1), (7)$	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{3}$	$0.744889195$	$2.008147859$	2.991695286	$\frac{740772}{49}$	$\bigl[0$ , $0$ , $0$ , $19$ , $30 i\bigr]$	${y}^2={x}^{3}+19{x}+30i$
12544.1-a4	12544.1-a	$4$	$4$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	12544.1	$2^{8} \cdot 7^{2}$	$2^{22} \cdot 7^{2}$	$1.89137$	$(a+1), (7)$	$2$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2^{2}$	$2.979556781$	$1.004073929$	2.991695286	$\frac{1443468546}{7}$	$\bigl[0$ , $0$ , $0$ , $299$ , $1990 i\bigr]$	${y}^2={x}^{3}+299{x}+1990i$
12544.1-b1	12544.1-b	$2$	$2$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	12544.1	$2^{8} \cdot 7^{2}$	$2^{14} \cdot 7^{2}$	$1.89137$	$(a+1), (7)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$0.321742177$	$4.250988810$	2.735444791	$\frac{19872}{7} a + \frac{15296}{7}$	$\bigl[0$ , $-i + 1$ , $0$ , $-3$ , $i + 1\bigr]$	${y}^2={x}^{3}+\left(-i+1\right){x}^{2}-3{x}+i+1$
12544.1-b2	12544.1-b	$2$	$2$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	12544.1	$2^{8} \cdot 7^{2}$	$2^{19} \cdot 7^{4}$	$1.89137$	$(a+1), (7)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$0.643484354$	$2.125494405$	2.735444791	$-\frac{694948}{49} a + \frac{30148}{7}$	$\bigl[0$ , $-i + 1$ , $0$ , $10 i - 13$ , $31 i - 13\bigr]$	${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(10i-13\right){x}+31i-13$
12544.1-c1	12544.1-c	$2$	$2$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	12544.1	$2^{8} \cdot 7^{2}$	$2^{14} \cdot 7^{2}$	$1.89137$	$(a+1), (7)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$0.321742177$	$4.250988810$	2.735444791	$-\frac{19872}{7} a + \frac{15296}{7}$	$\bigl[0$ , $-i - 1$ , $0$ , $-3$ , $i - 1\bigr]$	${y}^2={x}^{3}+\left(-i-1\right){x}^{2}-3{x}+i-1$
12544.1-c2	12544.1-c	$2$	$2$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	12544.1	$2^{8} \cdot 7^{2}$	$2^{19} \cdot 7^{4}$	$1.89137$	$(a+1), (7)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	$2^{2}$	$0.643484354$	$2.125494405$	2.735444791	$\frac{694948}{49} a + \frac{30148}{7}$	$\bigl[0$ , $-i - 1$ , $0$ , $-10 i - 13$ , $31 i + 13\bigr]$	${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(-10i-13\right){x}+31i+13$
12544.1-d1	12544.1-d	$2$	$2$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	12544.1	$2^{8} \cdot 7^{2}$	$2^{12} \cdot 7^{2}$	$1.89137$	$(a+1), (7)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2$	$0.612005445$	$4.990559254$	3.054249441	$\frac{8000}{7}$	$\bigl[0$ , $-i$ , $0$ , $-2$ , $0\bigr]$	${y}^2={x}^{3}-i{x}^{2}-2{x}$
12544.1-d2	12544.1-d	$2$	$2$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	12544.1	$2^{8} \cdot 7^{2}$	$2^{18} \cdot 7^{4}$	$1.89137$	$(a+1), (7)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2^{3}$	$0.306002722$	$2.495279627$	3.054249441	$\frac{125000}{49}$	$\bigl[0$ , $-i$ , $0$ , $8$ , $-8 i\bigr]$	${y}^2={x}^{3}-i{x}^{2}+8{x}-8i$
12544.1-e1	12544.1-e	$6$	$18$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	12544.1	$2^{8} \cdot 7^{2}$	$2^{60} \cdot 7^{2}$	$1.89137$	$(a+1), (7)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B	$9$	$2^{2}$	$1$	$0.218854283$	1.969688554	$-\frac{548347731625}{1835008}$	$\bigl[0$ , $i$ , $0$ , $2728$ , $55920 i\bigr]$	${y}^2={x}^{3}+i{x}^{2}+2728{x}+55920i$
12544.1-e2	12544.1-e	$6$	$18$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	12544.1	$2^{8} \cdot 7^{2}$	$2^{28} \cdot 7^{2}$	$1.89137$	$(a+1), (7)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B	$1$	$2^{2}$	$1$	$1.969688554$	1.969688554	$-\frac{15625}{28}$	$\bigl[0$ , $i$ , $0$ , $8$ , $-16 i\bigr]$	${y}^2={x}^{3}+i{x}^{2}+8{x}-16i$
12544.1-e3	12544.1-e	$6$	$18$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	12544.1	$2^{8} \cdot 7^{2}$	$2^{36} \cdot 7^{6}$	$1.89137$	$(a+1), (7)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3Cs	$1$	$2^{2} \cdot 3$	$1$	$0.656562851$	1.969688554	$\frac{9938375}{21952}$	$\bigl[0$ , $i$ , $0$ , $-72$ , $368 i\bigr]$	${y}^2={x}^{3}+i{x}^{2}-72{x}+368i$
12544.1-e4	12544.1-e	$6$	$18$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	12544.1	$2^{8} \cdot 7^{2}$	$2^{30} \cdot 7^{12}$	$1.89137$	$(a+1), (7)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3Cs	$1$	$2^{3} \cdot 3$	$1$	$0.328281425$	1.969688554	$\frac{4956477625}{941192}$	$\bigl[0$ , $i$ , $0$ , $568$ , $4464 i\bigr]$	${y}^2={x}^{3}+i{x}^{2}+568{x}+4464i$
12544.1-e5	12544.1-e	$6$	$18$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	12544.1	$2^{8} \cdot 7^{2}$	$2^{26} \cdot 7^{4}$	$1.89137$	$(a+1), (7)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B	$1$	$2^{3}$	$1$	$0.984844277$	1.969688554	$\frac{128787625}{98}$	$\bigl[0$ , $i$ , $0$ , $168$ , $-784 i\bigr]$	${y}^2={x}^{3}+i{x}^{2}+168{x}-784i$
12544.1-e6	12544.1-e	$6$	$18$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	12544.1	$2^{8} \cdot 7^{2}$	$2^{42} \cdot 7^{4}$	$1.89137$	$(a+1), (7)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B	$9$	$2^{3}$	$1$	$0.109427141$	1.969688554	$\frac{2251439055699625}{25088}$	$\bigl[0$ , $i$ , $0$ , $43688$ , $3529328 i\bigr]$	${y}^2={x}^{3}+i{x}^{2}+43688{x}+3529328i$
12544.1-f1	12544.1-f	$2$	$2$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	12544.1	$2^{8} \cdot 7^{2}$	$2^{20} \cdot 7^{2}$	$1.89137$	$(a+1), (7)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2^{2}$	$1$	$3.197869643$	3.197869643	$-\frac{4}{7}$	$\bigl[0$ , $i$ , $0$ , $0$ , $-4 i\bigr]$	${y}^2={x}^{3}+i{x}^{2}-4i$
12544.1-f2	12544.1-f	$2$	$2$	$\Q(\sqrt{-1})$	$2$	$[0, 1]$	12544.1	$2^{8} \cdot 7^{2}$	$2^{22} \cdot 7^{4}$	$1.89137$	$(a+1), (7)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2^{3}$	$1$	$1.598934821$	3.197869643	$\frac{3543122}{49}$	$\bigl[0$ , $i$ , $0$ , $40$ , $-84 i\bigr]$	${y}^2={x}^{3}+i{x}^{2}+40{x}-84i$

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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.