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	1	Product of Tamagawa factors cp
Δ	208 = 24 · 13	Discriminant
Eigenvalues	2-  0  2 -2 -2 13+  6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-4,-3]	[a1,a2,a3,a4,a6]
j	442368/13	j-invariant
L	0.84548320864565	L(r)(E,1)/r!
Ω	3.3819328345826	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	208c2 832d1 468c1 1300b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 52a2

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

---

Quadratic twists for elliptic curve 52a2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47
208c2	832d1	468c1	1300b1	2548i1	6292g1	676a1	15028a1	18772e1	27508b1	43732a1	49972c1	71188d1	87412c1	96148c1	114868a1

---

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

Part of Computational Number Theory
Back to Tables and computations