Elliptic curves over \(\Q(\sqrt{-1}) \) of conductor 194.2

The results below are complete, since the LMFDB contains all elliptic curves with conductor norm at most 100000 over imaginary quadratic fields with absolute discriminant 4

Note: The completeness Only modular elliptic curves are included

Results (5 matches)

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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
194.2-a1	194.2-a	$3$	$9$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	194.2	\( 2 \cdot 97 \)	\( 2^{5} \cdot 97 \)	$0.66699$	$(a+1), (4a+9)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$3$	3B.1.1	$1$	\( 1 \)	$1$	$5.067207090$	0.563023010	\( \frac{8303035}{776} a - \frac{179274083}{776} \)	\( \bigl[1\) , \( -i - 1\) , \( i\) , \( 3 i - 4\) , \( 4 i\bigr] \)	${y}^2+{x}{y}+i{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(3i-4\right){x}+4i$
194.2-a2	194.2-a	$3$	$9$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	194.2	\( 2 \cdot 97 \)	\( 2^{15} \cdot 97^{3} \)	$0.66699$	$(a+1), (4a+9)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$3$	3Cs.1.1	$1$	\( 3 \)	$1$	$1.689069030$	0.563023010	\( -\frac{1486569367205}{233644288} a - \frac{1058154142429}{233644288} \)	\( \bigl[1\) , \( -i - 1\) , \( i\) , \( 23 i + 1\) , \( -33 i - 29\bigr] \)	${y}^2+{x}{y}+i{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(23i+1\right){x}-33i-29$
194.2-a3	194.2-a	$3$	$9$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	194.2	\( 2 \cdot 97 \)	\( 2^{45} \cdot 97 \)	$0.66699$	$(a+1), (4a+9)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$3$	3B.1.2	$1$	\( 1 \)	$1$	$0.563023010$	0.563023010	\( \frac{45722483399515}{813694976} a + \frac{8559354083197}{813694976} \)	\( \bigl[1\) , \( -i - 1\) , \( i\) , \( -57 i + 306\) , \( -2126 i - 640\bigr] \)	${y}^2+{x}{y}+i{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-57i+306\right){x}-2126i-640$
194.2-b1	194.2-b	$2$	$7$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	194.2	\( 2 \cdot 97 \)	\( 2 \cdot 97^{7} \)	$0.66699$	$(a+1), (4a+9)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$7$	7B.1.3	$1$	\( 1 \)	$1$	$0.902019052$	0.902019052	\( \frac{103211006703479285}{161596568956226} a + \frac{36131733240801619}{161596568956226} \)	\( \bigl[i\) , \( -i\) , \( i\) , \( -24 i - 35\) , \( 180 i - 19\bigr] \)	${y}^2+i{x}{y}+i{y}={x}^{3}-i{x}^{2}+\left(-24i-35\right){x}+180i-19$
194.2-b2	194.2-b	$2$	$7$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	194.2	\( 2 \cdot 97 \)	\( 2^{7} \cdot 97 \)	$0.66699$	$(a+1), (4a+9)$	0	$\Z/7\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$7$	7B.1.1	$1$	\( 7 \)	$1$	$6.314133367$	0.902019052	\( -\frac{493285}{1552} a + \frac{823523}{1552} \)	\( \bigl[1\) , \( i\) , \( 1\) , \( i - 1\) , \( -1\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}+i{x}^{2}+\left(i-1\right){x}-1$

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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.