Cremona's table of elliptic curves

17424 = 2⁴ · 3² · 11²

Field	Data	Notes
Atkin-Lehner	2- 3+ 11-	Signs for the Atkin-Lehner involutions
Class	17424bh	Isogeny class
Conductor	17424	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	17281949100945408 = 212 · 39 · 118	Discriminant
Eigenvalues	2- 3+  4 -2 11-  2  2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-290763,-60014790]	[a1,a2,a3,a4,a6]
Generators	[-37045:44486:125]	Generators of the group modulo torsion
j	19034163/121	j-invariant
L	6.3779732980346	L(r)(E,1)/r!
Ω	0.20567480223548	Real period
R	7.7524971808803	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	1089d2 69696ew2 17424bi2 1584i2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 17424bh2

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

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Quadratic twists for elliptic curve 17424bh2

-4	8	-3	-11
1089d2	69696ew2	17424bi2	1584i2

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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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