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	1222a	Isogeny class
Conductor	1222	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	140	Modular degree for the optimal curve
Δ	-19552 = -1 · 25 · 13 · 47	Discriminant
Eigenvalues	2+  2  4  0  0 13-  1 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,7,5]	[a1,a2,a3,a4,a6]
j	30080231/19552	j-invariant
L	2.4087023127434	L(r)(E,1)/r!
Ω	2.4087023127434	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	9776c1 39104a1 10998u1 30550t1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1222a1

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	4	0	0	-	1	-2	-4	7	1	5	9	11	+	-6	-13	-10	2	-12	-14	-1	9	10	12

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Quadratic twists for elliptic curve 1222a1

-4	8	-3	5	-7	13	-47
9776c1	39104a1	10998u1	30550t1	59878m1	15886e1	57434c1

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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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