Elliptic curves over \(\Q(\sqrt{-7}) \) of conductor 896.4

The results below are complete, since the LMFDB contains all elliptic curves with conductor norm at most 50000 over imaginary quadratic fields with absolute discriminant 7

Note: The completeness Only modular elliptic curves are included

Results (6 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
896.4-a1	896.4-a	$6$	$8$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	896.4	\( 2^{7} \cdot 7 \)	\( 2^{25} \cdot 7 \)	$1.29349$	$(a), (-a+1), (-2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$4$	\( 2 \)	$1$	$0.978421342$	1.479234028	\( -\frac{4096655365}{28} a - \frac{1660660737}{28} \)	\( \bigl[0\) , \( a\) , \( 0\) , \( -213 a + 255\) , \( -80 a + 2380\bigr] \)	${y}^2={x}^{3}+a{x}^{2}+\left(-213a+255\right){x}-80a+2380$
896.4-a2	896.4-a	$6$	$8$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	896.4	\( 2^{7} \cdot 7 \)	\( 2^{17} \cdot 7^{2} \)	$1.29349$	$(a), (-a+1), (-2a+1)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{4} \)	$1$	$1.956842684$	1.479234028	\( \frac{13647889}{14} a - \frac{94721547}{14} \)	\( \bigl[0\) , \( -a\) , \( 0\) , \( 40 a - 15\) , \( -74 a - 60\bigr] \)	${y}^2={x}^{3}-a{x}^{2}+\left(40a-15\right){x}-74a-60$
896.4-a3	896.4-a	$6$	$8$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	896.4	\( 2^{7} \cdot 7 \)	\( 2^{26} \cdot 7^{2} \)	$1.29349$	$(a), (-a+1), (-2a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	\( 2^{4} \)	$1$	$1.956842684$	1.479234028	\( \frac{1145925}{112} a - \frac{1290439}{112} \)	\( \bigl[0\) , \( a\) , \( 0\) , \( -13 a + 15\) , \( 44\bigr] \)	${y}^2={x}^{3}+a{x}^{2}+\left(-13a+15\right){x}+44$
896.4-a4	896.4-a	$6$	$8$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	896.4	\( 2^{7} \cdot 7 \)	\( 2^{31} \cdot 7 \)	$1.29349$	$(a), (-a+1), (-2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{2} \)	$1$	$1.956842684$	1.479234028	\( \frac{138325}{1792} a - \frac{774199}{1792} \)	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 5 a - 6\) , \( -16 a + 4\bigr] \)	${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(5a-6\right){x}-16a+4$
896.4-a5	896.4-a	$6$	$8$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	896.4	\( 2^{7} \cdot 7 \)	\( 2^{23} \cdot 7^{8} \)	$1.29349$	$(a), (-a+1), (-2a+1)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{5} \)	$1$	$0.978421342$	1.479234028	\( \frac{5786513}{4802} a - \frac{2104499}{4802} \)	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 21 a + 26\) , \( 8 a - 128\bigr] \)	${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(21a+26\right){x}+8a-128$
896.4-a6	896.4-a	$6$	$8$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	896.4	\( 2^{7} \cdot 7 \)	\( 2^{22} \cdot 7^{4} \)	$1.29349$	$(a), (-a+1), (-2a+1)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	\( 2^{6} \)	$1$	$1.956842684$	1.479234028	\( -\frac{361845}{196} a + \frac{274391}{196} \)	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( a - 14\) , \( 12 a - 24\bigr] \)	${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(a-14\right){x}+12a-24$

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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.