Cremona's table of elliptic curves

1222 = 2 · 13 · 47

Field	Data	Notes
Atkin-Lehner	2- 13+ 47+	Signs for the Atkin-Lehner involutions
Class	1222b	Isogeny class
Conductor	1222	Conductor
∏ cp	7	Product of Tamagawa factors cp
deg	364	Modular degree for the optimal curve
Δ	-78208 = -1 · 27 · 13 · 47	Discriminant
Eigenvalues	2-  2  0  4  4 13+ -7  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-248,-1607]	[a1,a2,a3,a4,a6]
j	-1687284042625/78208	j-invariant
L	4.2106035342818	L(r)(E,1)/r!
Ω	0.60151479061169	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	9776b1 39104e1 10998g1 30550h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1222b1

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	4	4	+	-7	2	-4	1	-7	3	9	-11	+	14	-3	-2	2	0	2	-1	15	2	-4

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Quadratic twists for elliptic curve 1222b1

-4	8	-3	5	-7	13	-47
9776b1	39104e1	10998g1	30550h1	59878y1	15886b1	57434g1

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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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