Elliptic curves over \(\Q(\sqrt{-1}) \) of conductor 8450.9

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 (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
8450.9-a1	8450.9-a	$6$	$18$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	8450.9	\( 2 \cdot 5^{2} \cdot 13^{2} \)	\( 2^{18} \cdot 5^{15} \cdot 13^{7} \)	$1.71349$	$(a+1), (2a+1), (2a+3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{4} \)	$2.048802786$	$0.119163442$	1.953139148	\( -\frac{276861163011391}{13000000000} a - \frac{33515586556057}{812500000} \)	\( \bigl[i\) , \( i\) , \( 0\) , \( 6444 i + 1740\) , \( -79392 i - 200320\bigr] \)	${y}^2+i{x}{y}={x}^{3}+i{x}^{2}+\left(6444i+1740\right){x}-79392i-200320$
8450.9-a2	8450.9-a	$6$	$18$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	8450.9	\( 2 \cdot 5^{2} \cdot 13^{2} \)	\( 2^{6} \cdot 5^{9} \cdot 13^{9} \)	$1.71349$	$(a+1), (2a+1), (2a+3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3Cs	$1$	\( 2^{4} \)	$0.682934262$	$0.357490328$	1.953139148	\( \frac{37525044319}{2197000} a - \frac{7169596274}{274625} \)	\( \bigl[i\) , \( i\) , \( 0\) , \( 524 i - 445\) , \( 6620 i - 2129\bigr] \)	${y}^2+i{x}{y}={x}^{3}+i{x}^{2}+\left(524i-445\right){x}+6620i-2129$
8450.9-a3	8450.9-a	$6$	$18$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	8450.9	\( 2 \cdot 5^{2} \cdot 13^{2} \)	\( 2^{3} \cdot 5^{12} \cdot 13^{12} \)	$1.71349$	$(a+1), (2a+1), (2a+3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3Cs	$1$	\( 2^{4} \)	$1.365868524$	$0.178745164$	1.953139148	\( \frac{133816114442969}{301675562500} a - \frac{19082395919017}{301675562500} \)	\( \bigl[i\) , \( i\) , \( 0\) , \( -266 i - 915\) , \( 19254 i + 12233\bigr] \)	${y}^2+i{x}{y}={x}^{3}+i{x}^{2}+\left(-266i-915\right){x}+19254i+12233$
8450.9-a4	8450.9-a	$6$	$18$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	8450.9	\( 2 \cdot 5^{2} \cdot 13^{2} \)	\( 2^{9} \cdot 5^{24} \cdot 13^{8} \)	$1.71349$	$(a+1), (2a+1), (2a+3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{4} \)	$4.097605573$	$0.059581721$	1.953139148	\( -\frac{8418015312387897223}{20629882812500000} a + \frac{2783266907131437289}{20629882812500000} \)	\( \bigl[i\) , \( i\) , \( 0\) , \( 2684 i + 8060\) , \( -553840 i - 196784\bigr] \)	${y}^2+i{x}{y}={x}^{3}+i{x}^{2}+\left(2684i+8060\right){x}-553840i-196784$
8450.9-a5	8450.9-a	$6$	$18$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	8450.9	\( 2 \cdot 5^{2} \cdot 13^{2} \)	\( 2^{2} \cdot 5^{7} \cdot 13^{7} \)	$1.71349$	$(a+1), (2a+1), (2a+3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{4} \)	$0.227644754$	$1.072470984$	1.953139148	\( \frac{31409}{130} a + \frac{101344}{65} \)	\( \bigl[i\) , \( i\) , \( 0\) , \( -26 i + 30\) , \( 54 i + 8\bigr] \)	${y}^2+i{x}{y}={x}^{3}+i{x}^{2}+\left(-26i+30\right){x}+54i+8$
8450.9-a6	8450.9-a	$6$	$18$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	8450.9	\( 2 \cdot 5^{2} \cdot 13^{2} \)	\( 2 \cdot 5^{8} \cdot 13^{8} \)	$1.71349$	$(a+1), (2a+1), (2a+3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{4} \)	$0.455289508$	$0.536235492$	1.953139148	\( \frac{4406742137}{8450} a + \frac{1310300809}{8450} \)	\( \bigl[i\) , \( i\) , \( 0\) , \( -261 i + 425\) , \( 3077 i + 3197\bigr] \)	${y}^2+i{x}{y}={x}^{3}+i{x}^{2}+\left(-261i+425\right){x}+3077i+3197$
8450.9-b1	8450.9-b	$4$	$10$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	8450.9	\( 2 \cdot 5^{2} \cdot 13^{2} \)	\( 2 \cdot 5^{16} \cdot 13^{9} \)	$1.71349$	$(a+1), (2a+1), (2a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 5$	2B, 5B	$4$	\( 2^{3} \)	$1$	$0.199340379$	1.594723038	\( -\frac{80398914857}{19531250} a - \frac{197826917099}{19531250} \)	\( \bigl[i\) , \( -1\) , \( 0\) , \( 1741 i - 362\) , \( 26365 i + 15070\bigr] \)	${y}^2+i{x}{y}={x}^{3}-{x}^{2}+\left(1741i-362\right){x}+26365i+15070$
8450.9-b2	8450.9-b	$4$	$10$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	8450.9	\( 2 \cdot 5^{2} \cdot 13^{2} \)	\( 2^{2} \cdot 5^{11} \cdot 13^{9} \)	$1.71349$	$(a+1), (2a+1), (2a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 5$	2B, 5B	$1$	\( 2^{4} \)	$1$	$0.398680759$	1.594723038	\( \frac{10462207}{6250} a - \frac{2706038}{3125} \)	\( \bigl[1\) , \( 1\) , \( 0\) , \( 86 i - 277\) , \( 498 i - 2511\bigr] \)	${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(86i-277\right){x}+498i-2511$
8450.9-b3	8450.9-b	$4$	$10$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	8450.9	\( 2 \cdot 5^{2} \cdot 13^{2} \)	\( 2^{10} \cdot 5^{7} \cdot 13^{9} \)	$1.71349$	$(a+1), (2a+1), (2a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 5$	2B, 5B	$1$	\( 2^{4} \)	$1$	$0.398680759$	1.594723038	\( -\frac{523313}{160} a + \frac{424661}{40} \)	\( \bigl[1\) , \( -i - 1\) , \( 1\) , \( -451 i + 26\) , \( -2160 i + 2404\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-451i+26\right){x}-2160i+2404$
8450.9-b4	8450.9-b	$4$	$10$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	8450.9	\( 2 \cdot 5^{2} \cdot 13^{2} \)	\( 2^{5} \cdot 5^{8} \cdot 13^{9} \)	$1.71349$	$(a+1), (2a+1), (2a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 5$	2B, 5B	$4$	\( 2^{3} \)	$1$	$0.199340379$	1.594723038	\( -\frac{12916359143}{200} a + \frac{17274394699}{200} \)	\( \bigl[i\) , \( i + 1\) , \( i\) , \( -7071 i + 367\) , \( 147448 i - 171820\bigr] \)	${y}^2+i{x}{y}+i{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-7071i+367\right){x}+147448i-171820$

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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.