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	2397c	Isogeny class
Conductor	2397	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	864	Modular degree for the optimal curve
Δ	810130869 = 33 · 172 · 473	Discriminant
Eigenvalues	0 3- -3 -1  3  2 17+  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-237,245]	[a1,a2,a3,a4,a6]
Generators	[-15:25:1]	Generators of the group modulo torsion
j	1478427148288/810130869	j-invariant
L	2.6742267338541	L(r)(E,1)/r!
Ω	1.3825579703021	Real period
R	0.96713005577254	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	38352h1 7191g1 59925d1 117453i1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2397c1

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
0	-	-3	-1	3	2	+	2	-3	9	-10	-1	-6	-4	-	12	-12	2	2	-12	2	-1	-6	0	-13

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Quadratic twists for elliptic curve 2397c1

-4	-3	5	-7	17	-47
38352h1	7191g1	59925d1	117453i1	40749f1	112659f1

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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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