Elliptic curves over \(\Q(\sqrt{-1}) \) of conductor 340.1

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
340.1-a1	340.1-a	$4$	$6$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	340.1	\( 2^{2} \cdot 5 \cdot 17 \)	\( 2^{4} \cdot 5^{3} \cdot 17^{6} \)	$0.76743$	$(a+1), (-a-2), (a+4)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B.1.2	$1$	\( 2 \)	$1$	$1.693569039$	0.846784519	\( \frac{8285953568288}{3017196125} a + \frac{8530762181584}{3017196125} \)	\( \bigl[i + 1\) , \( i + 1\) , \( i + 1\) , \( 7 i - 19\) , \( -17 i + 18\bigr] \)	${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(7i-19\right){x}-17i+18$
340.1-a2	340.1-a	$4$	$6$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	340.1	\( 2^{2} \cdot 5 \cdot 17 \)	\( 2^{8} \cdot 5^{2} \cdot 17 \)	$0.76743$	$(a+1), (-a-2), (a+4)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B.1.1	$1$	\( 2 \cdot 3 \)	$1$	$5.080707118$	0.846784519	\( -\frac{274432}{425} a + \frac{1306624}{425} \)	\( \bigl[0\) , \( i\) , \( 0\) , \( 2 i - 1\) , \( -i - 1\bigr] \)	${y}^2={x}^{3}+i{x}^{2}+\left(2i-1\right){x}-i-1$
340.1-a3	340.1-a	$4$	$6$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	340.1	\( 2^{2} \cdot 5 \cdot 17 \)	\( 2^{8} \cdot 5^{6} \cdot 17^{3} \)	$0.76743$	$(a+1), (-a-2), (a+4)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B.1.2	$1$	\( 2 \)	$1$	$1.693569039$	0.846784519	\( -\frac{970218672128}{76765625} a + \frac{551994167296}{76765625} \)	\( \bigl[0\) , \( i\) , \( 0\) , \( -18 i + 19\) , \( -13 i - 41\bigr] \)	${y}^2={x}^{3}+i{x}^{2}+\left(-18i+19\right){x}-13i-41$
340.1-a4	340.1-a	$4$	$6$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	340.1	\( 2^{2} \cdot 5 \cdot 17 \)	\( 2^{4} \cdot 5 \cdot 17^{2} \)	$0.76743$	$(a+1), (-a-2), (a+4)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B.1.1	$1$	\( 2 \cdot 3 \)	$1$	$5.080707118$	0.846784519	\( \frac{13876192}{1445} a + \frac{35783056}{1445} \)	\( \bigl[i + 1\) , \( i + 1\) , \( i + 1\) , \( -3 i + 1\) , \( -i + 4\bigr] \)	${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-3i+1\right){x}-i+4$

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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.