Cremona's table of elliptic curves

11424 = 2⁵ · 3 · 7 · 17

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 17-	Signs for the Atkin-Lehner involutions
Class	11424m	Isogeny class
Conductor	11424	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	5632	Modular degree for the optimal curve
Δ	399680064 = 26 · 32 · 74 · 172	Discriminant
Eigenvalues	2- 3+ -2 7+  4 -2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-834,9504]	[a1,a2,a3,a4,a6]
Generators	[-16:136:1]	Generators of the group modulo torsion
j	1003604321728/6245001	j-invariant
L	3.1887744536636	L(r)(E,1)/r!
Ω	1.6947338462289	Real period
R	1.8815783143525	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	11424k1 22848bd2 34272i1 79968cl1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 11424m1

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	-2	-	-4	4	6	-8	10	-6	-4	0	-14	4	2	4	12	2	8	4	-14	-14

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Quadratic twists for elliptic curve 11424m1

-4	8	-3	-7
11424k1	22848bd2	34272i1	79968cl1

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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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