Cremona's table of elliptic curves

7378 = 2 · 7 · 17 · 31

Field	Data	Notes
Atkin-Lehner	2+ 7+ 17- 31-	Signs for the Atkin-Lehner involutions
Class	7378g	Isogeny class
Conductor	7378	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2496	Modular degree for the optimal curve
Δ	-501704 = -1 · 23 · 7 · 172 · 31	Discriminant
Eigenvalues	2+ -3 -1 7+ -6  6 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,20,-8]	[a1,a2,a3,a4,a6]
Generators	[3:7:1]	Generators of the group modulo torsion
j	860085351/501704	j-invariant
L	1.3563951589208	L(r)(E,1)/r!
Ω	1.7359942944892	Real period
R	0.39066809240864	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	59024x1 66402x1 51646f1 125426f1	Quadratic twists by: -4 -3 -7 17

Hecke Eigenvalues for elliptic curve 7378g1

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
+	-3	-1	+	-6	6	-	-4	3	-1	-	2	-10	10	-9	-6	0	14	9	-8	-7	1	-3	15	-8

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Quadratic twists for elliptic curve 7378g1

-4	-3	-7	17
59024x1	66402x1	51646f1	125426f1

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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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