Elliptic curves over \(\Q(\sqrt{-55}) \) of conductor 220.2

The results below are complete, since the LMFDB contains all elliptic curves with conductor norm at most 1000 over imaginary quadratic fields with absolute discriminant 55

Note: The completeness Only modular elliptic curves are included

Results (12 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
220.2-a1	220.2-a	$2$	$3$	\(\Q(\sqrt{-55}) \)	$2$	$[0, 1]$	220.2	\( 2^{2} \cdot 5 \cdot 11 \)	\( 2^{6} \cdot 5^{14} \cdot 11^{2} \)	$2.55226$	$(2,a), (2,a+1), (5,a+2), (11,a+5)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3B	$1$	\( 2^{2} \)	$0.165868134$	$5.023922189$	1.797812943	\( -\frac{117649}{440} \)	\( \bigl[1\) , \( 1\) , \( 0\) , \( -25\) , \( 125\bigr] \)	${y}^2+{x}{y}={x}^3+{x}^2-25{x}+125$
220.2-a2	220.2-a	$2$	$3$	\(\Q(\sqrt{-55}) \)	$2$	$[0, 1]$	220.2	\( 2^{2} \cdot 5 \cdot 11 \)	\( 2^{2} \cdot 5^{18} \cdot 11^{6} \)	$2.55226$	$(2,a), (2,a+1), (5,a+2), (11,a+5)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3B	$1$	\( 2^{2} \)	$0.497604403$	$1.674640729$	1.797812943	\( \frac{80062991}{332750} \)	\( \bigl[1\) , \( 1\) , \( 0\) , \( 225\) , \( -3125\bigr] \)	${y}^2+{x}{y}={x}^3+{x}^2+225{x}-3125$
220.2-b1	220.2-b	$2$	$3$	\(\Q(\sqrt{-55}) \)	$2$	$[0, 1]$	220.2	\( 2^{2} \cdot 5 \cdot 11 \)	\( 2^{14} \cdot 5^{2} \cdot 11^{6} \)	$2.55226$	$(2,a), (2,a+1), (5,a+2), (11,a+5)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3B.1.1	$4$	\( 2^{2} \cdot 3 \)	$1$	$1.098979844$	1.580655060	\( -\frac{76711450249}{851840} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( -89\) , \( 316\bigr] \)	${y}^2+{x}{y}+{y}={x}^3-89{x}+316$
220.2-b2	220.2-b	$2$	$3$	\(\Q(\sqrt{-55}) \)	$2$	$[0, 1]$	220.2	\( 2^{2} \cdot 5 \cdot 11 \)	\( 2^{42} \cdot 5^{6} \cdot 11^{2} \)	$2.55226$	$(2,a), (2,a+1), (5,a+2), (11,a+5)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3B.1.1	$4$	\( 2^{2} \)	$1$	$0.366326614$	1.580655060	\( \frac{2882081488391}{2883584000} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( 296\) , \( 1702\bigr] \)	${y}^2+{x}{y}+{y}={x}^3+296{x}+1702$
220.2-c1	220.2-c	$2$	$5$	\(\Q(\sqrt{-55}) \)	$2$	$[0, 1]$	220.2	\( 2^{2} \cdot 5 \cdot 11 \)	\( 2^{2} \cdot 5^{14} \cdot 11^{10} \)	$2.55226$	$(2,a), (2,a+1), (5,a+2), (11,a+5)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$5$	5B.1.4	$1$	\( 2^{2} \cdot 5 \)	$0.690524660$	$0.275229175$	2.050134267	\( -\frac{23178622194826561}{1610510} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( -148501\) , \( -22038602\bigr] \)	${y}^2+{x}{y}+{y}={x}^3-148501{x}-22038602$
220.2-c2	220.2-c	$2$	$5$	\(\Q(\sqrt{-55}) \)	$2$	$[0, 1]$	220.2	\( 2^{2} \cdot 5 \cdot 11 \)	\( 2^{10} \cdot 5^{22} \cdot 11^{2} \)	$2.55226$	$(2,a), (2,a+1), (5,a+2), (11,a+5)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$5$	5B.1.4	$1$	\( 2^{2} \cdot 5 \)	$0.138104932$	$1.376145879$	2.050134267	\( \frac{109902239}{1100000} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( 249\) , \( -6102\bigr] \)	${y}^2+{x}{y}+{y}={x}^3+249{x}-6102$
220.2-d1	220.2-d	$2$	$3$	\(\Q(\sqrt{-55}) \)	$2$	$[0, 1]$	220.2	\( 2^{2} \cdot 5 \cdot 11 \)	\( 2^{14} \cdot 5^{14} \cdot 11^{6} \)	$2.55226$	$(2,a), (2,a+1), (5,a+2), (11,a+5)$	$2$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3B	$1$	\( 2^{2} \cdot 3 \cdot 7^{2} \)	$0.011773960$	$1.098979844$	8.207261610	\( -\frac{76711450249}{851840} \)	\( \bigl[1\) , \( 1\) , \( 1\) , \( -2213\) , \( 39531\bigr] \)	${y}^2+{x}{y}+{y}={x}^3+{x}^2-2213{x}+39531$
220.2-d2	220.2-d	$2$	$3$	\(\Q(\sqrt{-55}) \)	$2$	$[0, 1]$	220.2	\( 2^{2} \cdot 5 \cdot 11 \)	\( 2^{42} \cdot 5^{18} \cdot 11^{2} \)	$2.55226$	$(2,a), (2,a+1), (5,a+2), (11,a+5)$	$2$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3B	$1$	\( 2^{2} \cdot 3^{2} \cdot 7^{2} \)	$0.011773960$	$0.366326614$	8.207261610	\( \frac{2882081488391}{2883584000} \)	\( \bigl[1\) , \( 1\) , \( 1\) , \( 7412\) , \( 212781\bigr] \)	${y}^2+{x}{y}+{y}={x}^3+{x}^2+7412{x}+212781$
220.2-e1	220.2-e	$2$	$3$	\(\Q(\sqrt{-55}) \)	$2$	$[0, 1]$	220.2	\( 2^{2} \cdot 5 \cdot 11 \)	\( 2^{6} \cdot 5^{2} \cdot 11^{2} \)	$2.55226$	$(2,a), (2,a+1), (5,a+2), (11,a+5)$	$1$	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3B.1.1	$1$	\( 2^{2} \cdot 3^{2} \)	$0.672977302$	$5.023922189$	7.294272090	\( -\frac{117649}{440} \)	\( \bigl[1\) , \( 0\) , \( 0\) , \( -1\) , \( 1\bigr] \)	${y}^2+{x}{y}={x}^3-{x}+1$
220.2-e2	220.2-e	$2$	$3$	\(\Q(\sqrt{-55}) \)	$2$	$[0, 1]$	220.2	\( 2^{2} \cdot 5 \cdot 11 \)	\( 2^{2} \cdot 5^{6} \cdot 11^{6} \)	$2.55226$	$(2,a), (2,a+1), (5,a+2), (11,a+5)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3B.1.1	$1$	\( 2^{2} \)	$2.018931907$	$1.674640729$	7.294272090	\( \frac{80062991}{332750} \)	\( \bigl[1\) , \( 0\) , \( 0\) , \( 9\) , \( -25\bigr] \)	${y}^2+{x}{y}={x}^3+9{x}-25$
220.2-f1	220.2-f	$2$	$5$	\(\Q(\sqrt{-55}) \)	$2$	$[0, 1]$	220.2	\( 2^{2} \cdot 5 \cdot 11 \)	\( 2^{2} \cdot 5^{2} \cdot 11^{10} \)	$2.55226$	$(2,a), (2,a+1), (5,a+2), (11,a+5)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$5$	5B.1.1	$1$	\( 2^{2} \cdot 5 \)	$3.160732306$	$0.275229175$	9.384061113	\( -\frac{23178622194826561}{1610510} \)	\( \bigl[1\) , \( 1\) , \( 1\) , \( -5940\) , \( -178685\bigr] \)	${y}^2+{x}{y}+{y}={x}^3+{x}^2-5940{x}-178685$
220.2-f2	220.2-f	$2$	$5$	\(\Q(\sqrt{-55}) \)	$2$	$[0, 1]$	220.2	\( 2^{2} \cdot 5 \cdot 11 \)	\( 2^{10} \cdot 5^{10} \cdot 11^{2} \)	$2.55226$	$(2,a), (2,a+1), (5,a+2), (11,a+5)$	$1$	$\Z/5\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$5$	5B.1.1	$1$	\( 2^{2} \cdot 5^{3} \)	$0.632146461$	$1.376145879$	9.384061113	\( \frac{109902239}{1100000} \)	\( \bigl[1\) , \( 1\) , \( 1\) , \( 10\) , \( -45\bigr] \)	${y}^2+{x}{y}+{y}={x}^3+{x}^2+10{x}-45$

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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.