Cremona's table of elliptic curves

5635 = 5 · 7² · 23

Field	Data	Notes
Atkin-Lehner	5- 7- 23+	Signs for the Atkin-Lehner involutions
Class	5635f	Isogeny class
Conductor	5635	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	40320	Modular degree for the optimal curve
Δ	-35289355426521875 = -1 · 55 · 79 · 234	Discriminant
Eigenvalues	2  1 5- 7- -3  1 -5 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,78090,3363931]	[a1,a2,a3,a4,a6]
Generators	[18650:907231:8]	Generators of the group modulo torsion
j	1305034698752/874503125	j-invariant
L	8.5717877065023	L(r)(E,1)/r!
Ω	0.23059932272493	Real period
R	1.8585890897709	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	90160da1 50715bf1 28175m1 5635c1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5635f1

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	1	-	-	-3	1	-5	-2	+	-1	-2	4	2	-6	-3	2	-6	-4	2	8	-6	3	12	-16	-1

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Quadratic twists for elliptic curve 5635f1

-4	-3	5	-7	-23
90160da1	50715bf1	28175m1	5635c1	129605p1

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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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