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	96	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	8339853312 = 212 · 37 · 72 · 19	Discriminant
Eigenvalues	2- 3- -2 7+  0  2 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-716,6095]	[a1,a2,a3,a4,a6]
Generators	[-27:85:1]	Generators of the group modulo torsion
j	55611739513/11440128	j-invariant
L	4.0767646535074	L(r)(E,1)/r!
Ω	1.2385611064247	Real period
R	0.5485888197684	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	19152bz1 76608bt1 798b1 59850bu1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2394k1

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 2394k1

-4	8	-3	5	-7	-19
19152bz1	76608bt1	798b1	59850bu1	16758bo1	45486l1

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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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