Cremona's table of elliptic curves

7315 = 5 · 7 · 11 · 19

Field	Data	Notes
Atkin-Lehner	5- 7- 11+ 19+	Signs for the Atkin-Lehner involutions
Class	7315d	Isogeny class
Conductor	7315	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	588601475 = 52 · 72 · 113 · 192	Discriminant
Eigenvalues	1  2 5- 7- 11+ -4  6 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-7112,-233839]	[a1,a2,a3,a4,a6]
Generators	[34680:1223417:27]	Generators of the group modulo torsion
j	39791871606904201/588601475	j-invariant
L	7.2237395202988	L(r)(E,1)/r!
Ω	0.51986915705552	Real period
R	6.9476515602631	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	117040ce2 65835w2 36575c2 51205g2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 7315d2

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

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Quadratic twists for elliptic curve 7315d2

-4	-3	5	-7	-11
117040ce2	65835w2	36575c2	51205g2	80465n2

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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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