Cremona's table of elliptic curves

61152 = 2⁵ · 3 · 7² · 13

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 13+	Signs for the Atkin-Lehner involutions
Class	61152r	Isogeny class
Conductor	61152	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	19968	Modular degree for the optimal curve
Δ	7705152 = 26 · 33 · 73 · 13	Discriminant
Eigenvalues	2+ 3- -2 7-  0 13+  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-814,8672]	[a1,a2,a3,a4,a6]
Generators	[2:84:1]	Generators of the group modulo torsion
j	2720547136/351	j-invariant
L	6.6589328702057	L(r)(E,1)/r!
Ω	2.2563878394078	Real period
R	0.9837157651852	Regulator
r	1	Rank of the group of rational points
S	1.000000000032	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	61152d1 122304gc1 61152k1	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 61152r1

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
+	-	-2	-	0	+	6	-4	8	0	-4	-8	-4	4	6	12	4	-2	-10	0	-10	-8	0	12	-2

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Quadratic twists for elliptic curve 61152r1

-4	8	-7
61152d1	122304gc1	61152k1

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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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