Elliptic curves over \(\Q(\sqrt{-1}) \) of conductor 1690.6

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 (4 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
1690.6-a1	1690.6-a	$4$	$10$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	1690.6	\( 2 \cdot 5 \cdot 13^{2} \)	\( 2 \cdot 5^{10} \cdot 13^{3} \)	$1.14588$	$(a+1), (2a+1), (2a+3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 5$	2B, 5B	$1$	\( 2^{2} \cdot 5 \)	$0.074207181$	$1.607133521$	1.192608490	\( -\frac{80398914857}{19531250} a - \frac{197826917099}{19531250} \)	\( \bigl[1\) , \( -i\) , \( i + 1\) , \( -28 i - 2\) , \( 43 i - 47\bigr] \)	${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}-i{x}^{2}+\left(-28i-2\right){x}+43i-47$
1690.6-a2	1690.6-a	$4$	$10$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	1690.6	\( 2 \cdot 5 \cdot 13^{2} \)	\( 2^{2} \cdot 5^{5} \cdot 13^{3} \)	$1.14588$	$(a+1), (2a+1), (2a+3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 5$	2B, 5B	$1$	\( 2^{2} \cdot 5 \)	$0.037103590$	$3.214267043$	1.192608490	\( \frac{10462207}{6250} a - \frac{2706038}{3125} \)	\( \bigl[i\) , \( i\) , \( i + 1\) , \( -3 i + 4\) , \( -3 i - 2\bigr] \)	${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-3i+4\right){x}-3i-2$
1690.6-a3	1690.6-a	$4$	$10$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	1690.6	\( 2 \cdot 5 \cdot 13^{2} \)	\( 2^{10} \cdot 5 \cdot 13^{3} \)	$1.14588$	$(a+1), (2a+1), (2a+3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 5$	2B, 5B	$1$	\( 2^{2} \)	$0.185517953$	$3.214267043$	1.192608490	\( -\frac{523313}{160} a + \frac{424661}{40} \)	\( \bigl[i\) , \( -i\) , \( 0\) , \( 7 i + 1\) , \( 2 i + 8\bigr] \)	${y}^2+i{x}{y}={x}^{3}-i{x}^{2}+\left(7i+1\right){x}+2i+8$
1690.6-a4	1690.6-a	$4$	$10$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	1690.6	\( 2 \cdot 5 \cdot 13^{2} \)	\( 2^{5} \cdot 5^{2} \cdot 13^{3} \)	$1.14588$	$(a+1), (2a+1), (2a+3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 5$	2B, 5B	$1$	\( 2^{2} \)	$0.371035907$	$1.607133521$	1.192608490	\( -\frac{12916359143}{200} a + \frac{17274394699}{200} \)	\( \bigl[1\) , \( i\) , \( 0\) , \( 107 i + 21\) , \( -190 i - 420\bigr] \)	${y}^2+{x}{y}={x}^{3}+i{x}^{2}+\left(107i+21\right){x}-190i-420$

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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.