Cremona's table of elliptic curves

2394 = 2 · 3² · 7 · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 19+	Signs for the Atkin-Lehner involutions
Class	2394k	Isogeny class
Conductor	2394	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	111724714584 = 23 · 37 · 72 · 194	Discriminant
Eigenvalues	2- 3- -2 7+  0  2 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-56516,-5157169]	[a1,a2,a3,a4,a6]
Generators	[-137:73:1]	Generators of the group modulo torsion
j	27384399945278713/153257496	j-invariant
L	4.0767646535074	L(r)(E,1)/r!
Ω	0.30964027660617	Real period
R	2.1943552790736	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	19152bz3 76608bt4 798b3 59850bu4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2394k3

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

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Quadratic twists for elliptic curve 2394k3

-4	8	-3	5	-7	-19
19152bz3	76608bt4	798b3	59850bu4	16758bo3	45486l4

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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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