Cremona's table of elliptic curves

1196 = 2² · 13 · 23

Field	Data	Notes
Atkin-Lehner	2- 13+ 23-	Signs for the Atkin-Lehner involutions
Class	1196a	Isogeny class
Conductor	1196	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	432	Modular degree for the optimal curve
Δ	9836970832 = 24 · 133 · 234	Discriminant
Eigenvalues	2-  0 -2  2  2 13+ -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-556,1641]	[a1,a2,a3,a4,a6]
Generators	[-20:69:1]	Generators of the group modulo torsion
j	1188031905792/614810677	j-invariant
L	2.433909008603	L(r)(E,1)/r!
Ω	1.1365370800976	Real period
R	0.71383768913023	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4784b1 19136m1 10764f1 29900d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1196a1

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	+	-2	-2	-	2	-6	-10	-6	4	6	-10	6	-2	-10	-6	-6	-12	-10	6	6

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Quadratic twists for elliptic curve 1196a1

-4	8	-3	5	-7	13	-23
4784b1	19136m1	10764f1	29900d1	58604k1	15548b1	27508a1

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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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