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	7378r	Isogeny class
Conductor	7378	Conductor
∏ cp	368	Product of Tamagawa factors cp
Δ	1616594636267061248 = 223 · 74 · 174 · 312	Discriminant
Eigenvalues	2- -2  2 7- -2  0 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-44730097,-115149450903]	[a1,a2,a3,a4,a6]
Generators	[-3862:2043:1]	Generators of the group modulo torsion
j	9897448089772377164326261393/1616594636267061248	j-invariant
L	5.0386012371326	L(r)(E,1)/r!
Ω	0.058378051978812	Real period
R	0.9381506044655	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	59024m2 66402m2 51646bj2 125426p2	Quadratic twists by: -4 -3 -7 17

Hecke Eigenvalues for elliptic curve 7378r2

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

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Quadratic twists for elliptic curve 7378r2

-4	-3	-7	17
59024m2	66402m2	51646bj2	125426p2

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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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