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	7378m	Isogeny class
Conductor	7378	Conductor
∏ cp	104	Product of Tamagawa factors cp
deg	19968	Modular degree for the optimal curve
Δ	53721518047232 = 226 · 72 · 17 · 312	Discriminant
Eigenvalues	2- -2  0 7+  2  2 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-19408,-980736]	[a1,a2,a3,a4,a6]
Generators	[-80:288:1]	Generators of the group modulo torsion
j	808476612589626625/53721518047232	j-invariant
L	4.3281433700711	L(r)(E,1)/r!
Ω	0.40617531654958	Real period
R	0.40984039628297	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	59024r1 66402d1 51646be1 125426s1	Quadratic twists by: -4 -3 -7 17

Hecke Eigenvalues for elliptic curve 7378m1

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	+	0	-4	0	-	4	-10	4	-8	6	-4	8	-8	12	-14	4	0	10	-2

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Quadratic twists for elliptic curve 7378m1

-4	-3	-7	17
59024r1	66402d1	51646be1	125426s1

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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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