Elliptic curves over \(\Q(\sqrt{-1}) \) of conductor 1010.4

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
1010.4-a1	1010.4-a	$4$	$6$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	1010.4	\( 2 \cdot 5 \cdot 101 \)	\( 2^{6} \cdot 5 \cdot 101^{3} \)	$1.00751$	$(a+1), (2a+1), (a-10)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.2	$1$	\( 2 \)	$1$	$1.763521018$	0.881760509	\( -\frac{2793559038081}{41212040} a - \frac{3305349252124}{5151505} \)	\( \bigl[i\) , \( i + 1\) , \( 1\) , \( 32 i - 35\) , \( 109 i - 75\bigr] \)	${y}^2+i{x}{y}+{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(32i-35\right){x}+109i-75$
1010.4-a2	1010.4-a	$4$	$6$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	1010.4	\( 2 \cdot 5 \cdot 101 \)	\( 2^{2} \cdot 5^{3} \cdot 101 \)	$1.00751$	$(a+1), (2a+1), (a-10)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.1	$1$	\( 2 \cdot 3 \)	$1$	$5.290563054$	0.881760509	\( -\frac{95771151}{25250} a - \frac{14736616}{12625} \)	\( \bigl[i\) , \( i + 1\) , \( 1\) , \( 2 i\) , \( -2\bigr] \)	${y}^2+i{x}{y}+{y}={x}^{3}+\left(i+1\right){x}^{2}+2i{x}-2$
1010.4-a3	1010.4-a	$4$	$6$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	1010.4	\( 2 \cdot 5 \cdot 101 \)	\( 2 \cdot 5^{6} \cdot 101^{2} \)	$1.00751$	$(a+1), (2a+1), (a-10)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.1	$1$	\( 2^{2} \cdot 3 \)	$1$	$2.645281527$	0.881760509	\( \frac{341466750407}{318781250} a - \frac{239857387801}{318781250} \)	\( \bigl[i\) , \( i + 1\) , \( 1\) , \( -3 i + 5\) , \( -6 i - 2\bigr] \)	${y}^2+i{x}{y}+{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-3i+5\right){x}-6i-2$
1010.4-a4	1010.4-a	$4$	$6$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	1010.4	\( 2 \cdot 5 \cdot 101 \)	\( 2^{3} \cdot 5^{2} \cdot 101^{6} \)	$1.00751$	$(a+1), (2a+1), (a-10)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.2	$1$	\( 2^{2} \)	$1$	$0.881760509$	0.881760509	\( -\frac{59033391128865961}{106152015060100} a + \frac{81290680662074473}{106152015060100} \)	\( \bigl[i\) , \( i + 1\) , \( 1\) , \( 22 i - 45\) , \( 137 i - 3\bigr] \)	${y}^2+i{x}{y}+{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(22i-45\right){x}+137i-3$

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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.