Cremona's table of elliptic curves

2397 = 3 · 17 · 47

Field	Data	Notes
Atkin-Lehner	3+ 17+ 47-	Signs for the Atkin-Lehner involutions
Class	2397a	Isogeny class
Conductor	2397	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	5400	Modular degree for the optimal curve
Δ	-213615997011 = -1 · 39 · 173 · 472	Discriminant
Eigenvalues	2 3+ -3 -2  3 -3 17+  5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-3652,89037]	[a1,a2,a3,a4,a6]
j	-5388091135971328/213615997011	j-invariant
L	1.9823324816566	L(r)(E,1)/r!
Ω	0.99116624082828	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	38352p1 7191h1 59925s1 117453y1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2397a1

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	+	-3	-2	3	-3	+	5	7	2	0	12	7	3	-	2	-12	8	4	-12	8	8	-2	14	6

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Quadratic twists for elliptic curve 2397a1

-4	-3	5	-7	17	-47
38352p1	7191h1	59925s1	117453y1	40749n1	112659c1

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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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