Elliptic curves over \(\Q(\sqrt{-7}) \) of conductor 9072.5

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 (10 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
9072.5-a1	9072.5-a	$4$	$4$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	9072.5	\( 2^{4} \cdot 3^{4} \cdot 7 \)	\( 2^{10} \cdot 3^{20} \cdot 7 \)	$2.30735$	$(-a+1), (-2a+1), (3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{4} \)	$0.451069876$	$0.731790536$	1.996188624	\( \frac{48284377}{189} a - \frac{108521789}{567} \)	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 138 a - 238\) , \( -1076 a + 908\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(138a-238\right){x}-1076a+908$
9072.5-a2	9072.5-a	$4$	$4$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	9072.5	\( 2^{4} \cdot 3^{4} \cdot 7 \)	\( 2^{10} \cdot 3^{14} \cdot 7 \)	$2.30735$	$(-a+1), (-2a+1), (3)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{3} \)	$1.804279506$	$1.463581072$	1.996188624	\( -\frac{219127}{7} a - \frac{566221}{21} \)	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -33 a + 35\) , \( 8 a - 104\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-33a+35\right){x}+8a-104$
9072.5-a3	9072.5-a	$4$	$4$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	9072.5	\( 2^{4} \cdot 3^{4} \cdot 7 \)	\( 2^{8} \cdot 3^{16} \cdot 7^{2} \)	$2.30735$	$(-a+1), (-2a+1), (3)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	\( 2^{4} \)	$0.902139753$	$1.463581072$	1.996188624	\( -\frac{4009}{21} a + \frac{2191}{9} \)	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 3 a - 13\) , \( -32 a + 8\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(3a-13\right){x}-32a+8$
9072.5-a4	9072.5-a	$4$	$4$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	9072.5	\( 2^{4} \cdot 3^{4} \cdot 7 \)	\( 2^{4} \cdot 3^{14} \cdot 7^{4} \)	$2.30735$	$(-a+1), (-2a+1), (3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{3} \)	$0.451069876$	$1.463581072$	1.996188624	\( \frac{166231}{49} a + \frac{660025}{147} \)	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -24 a + 17\) , \( -28 a + 80\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-24a+17\right){x}-28a+80$
9072.5-b1	9072.5-b	$6$	$8$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	9072.5	\( 2^{4} \cdot 3^{4} \cdot 7 \)	\( 2^{4} \cdot 3^{16} \cdot 7 \)	$2.30735$	$(-a+1), (-2a+1), (3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$4$	\( 2^{2} \)	$1$	$0.934962333$	2.827060365	\( -\frac{863944673}{63} a - \frac{1616364293}{63} \)	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -27 a - 270\) , \( 187 a + 1639\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-27a-270\right){x}+187a+1639$
9072.5-b2	9072.5-b	$6$	$8$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	9072.5	\( 2^{4} \cdot 3^{4} \cdot 7 \)	\( 2^{11} \cdot 3^{14} \cdot 7^{8} \)	$2.30735$	$(-a+1), (-2a+1), (3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{5} \)	$1$	$0.467481166$	2.827060365	\( \frac{70011793}{7203} a - \frac{221078161}{7203} \)	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 117 a - 423\) , \( -1350 a + 3078\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(117a-423\right){x}-1350a+3078$
9072.5-b3	9072.5-b	$6$	$8$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	9072.5	\( 2^{4} \cdot 3^{4} \cdot 7 \)	\( 2^{10} \cdot 3^{16} \cdot 7^{4} \)	$2.30735$	$(-a+1), (-2a+1), (3)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	\( 2^{6} \)	$1$	$0.934962333$	2.827060365	\( \frac{172799}{441} a - \frac{2545}{9} \)	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -18 a - 18\) , \( -135 a + 81\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-18a-18\right){x}-135a+81$
9072.5-b4	9072.5-b	$6$	$8$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	9072.5	\( 2^{4} \cdot 3^{4} \cdot 7 \)	\( 2^{8} \cdot 3^{20} \cdot 7^{2} \)	$2.30735$	$(-a+1), (-2a+1), (3)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$4$	\( 2^{4} \)	$1$	$0.934962333$	2.827060365	\( -\frac{839201}{189} a + \frac{2555873}{567} \)	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -54 a + 30\) , \( -151 a + 249\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-54a+30\right){x}-151a+249$
9072.5-b5	9072.5-b	$6$	$8$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	9072.5	\( 2^{4} \cdot 3^{4} \cdot 7 \)	\( 2^{10} \cdot 3^{28} \cdot 7 \)	$2.30735$	$(-a+1), (-2a+1), (3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$4$	\( 2^{3} \)	$1$	$0.467481166$	2.827060365	\( \frac{78717967}{15309} a - \frac{9092939}{45927} \)	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -189 a + 255\) , \( -304 a - 1596\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-189a+255\right){x}-304a-1596$
9072.5-b6	9072.5-b	$6$	$8$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	9072.5	\( 2^{4} \cdot 3^{4} \cdot 7 \)	\( 2^{11} \cdot 3^{14} \cdot 7^{2} \)	$2.30735$	$(-a+1), (-2a+1), (3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{4} \)	$1$	$0.934962333$	2.827060365	\( -\frac{13784383}{21} a + \frac{8018911}{21} \)	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -90 a + 174\) , \( -295 a - 575\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-90a+174\right){x}-295a-575$

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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.