Cremona's table of elliptic curves

52 = 2² · 13

Field	Data	Notes
Atkin-Lehner	2- 13+	Signs for the Atkin-Lehner involutions
Class	52a	Isogeny class
Conductor	52	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	3	Modular degree for the optimal curve
Δ	-43264 = -1 · 28 · 132	Discriminant
Eigenvalues	2-  0  2 -2 -2 13+  6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,1,-10]	[a1,a2,a3,a4,a6]
j	432/169	j-invariant
L	0.84548320864565	L(r)(E,1)/r!
Ω	1.6909664172913	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	208c1 832d2 468c2 1300b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 52a1

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

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Quadratic twists for elliptic curve 52a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47
208c1	832d2	468c2	1300b2	2548i2	6292g2	676a2	15028a2	18772e2	27508b2	43732a2	49972c2	71188d2	87412c2	96148c2	114868a2

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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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