Cremona's table of elliptic curves

2772 = 2² · 3² · 7 · 11

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 11-	Signs for the Atkin-Lehner involutions
Class	2772b	Isogeny class
Conductor	2772	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	2880	Modular degree for the optimal curve
Δ	-91493197488 = -1 · 24 · 39 · 74 · 112	Discriminant
Eigenvalues	2- 3+ -4 7+ 11-  2  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,648,-13095]	[a1,a2,a3,a4,a6]
Generators	[42:297:1]	Generators of the group modulo torsion
j	95551488/290521	j-invariant
L	2.5962310479364	L(r)(E,1)/r!
Ω	0.54881946201294	Real period
R	0.78842899096363	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	11088bc1 44352c1 2772a1 69300k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2772b1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	+	-4	+	-	2	0	4	4	-4	-4	6	0	-4	-8	-8	-8	-2	8	-4	-2	-8	-8	4	-18

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Quadratic twists for elliptic curve 2772b1

-4	8	-3	5	-7	-11
11088bc1	44352c1	2772a1	69300k1	19404h1	30492h1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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