Cremona's table of elliptic curves

2378 = 2 · 29 · 41

Field	Data	Notes
Atkin-Lehner	2+ 29+ 41+	Signs for the Atkin-Lehner involutions
Class	2378a	Isogeny class
Conductor	2378	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2496	Modular degree for the optimal curve
Δ	-275669940116 = -1 · 22 · 293 · 414	Discriminant
Eigenvalues	2+  1  1  2 -5 -5  4  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,802,23764]	[a1,a2,a3,a4,a6]
Generators	[139:1611:1]	Generators of the group modulo torsion
j	57151154952359/275669940116	j-invariant
L	2.8639424365224	L(r)(E,1)/r!
Ω	0.70216913705388	Real period
R	1.0196768432955	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	19024a1 76096c1 21402h1 59450k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2378a1

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
+	1	1	2	-5	-5	4	0	4	+	7	-4	+	-9	-5	-7	-4	-8	4	-10	4	1	12	-2	-6

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Quadratic twists for elliptic curve 2378a1

-4	8	-3	5	-7	29	41
19024a1	76096c1	21402h1	59450k1	116522g1	68962i1	97498c1

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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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