Cremona's table of elliptic curves

11856 = 2⁴ · 3 · 13 · 19

Field	Data	Notes
Atkin-Lehner	2- 3+ 13- 19+	Signs for the Atkin-Lehner involutions
Class	11856s	Isogeny class
Conductor	11856	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	12096	Modular degree for the optimal curve
Δ	-1262228078592 = -1 · 219 · 33 · 13 · 193	Discriminant
Eigenvalues	2- 3+  0  1 -3 13-  6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2488,-71312]	[a1,a2,a3,a4,a6]
Generators	[252:3904:1]	Generators of the group modulo torsion
j	-415996269625/308161152	j-invariant
L	3.9891287883149	L(r)(E,1)/r!
Ω	0.3274050552806	Real period
R	3.0460195436629	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1482e1 47424dc1 35568bx1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 11856s1

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	1	-3	-	6	+	3	-6	-2	2	12	-5	-6	6	-6	-4	1	-3	-4	1	-12	12	2

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Quadratic twists for elliptic curve 11856s1

-4	8	-3
1482e1	47424dc1	35568bx1

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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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