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	5635h	Isogeny class
Conductor	5635	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	7224	Modular degree for the optimal curve
Δ	-32484653635 = -1 · 5 · 710 · 23	Discriminant
Eigenvalues	2 -2 5- 7- -2  0  2  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-800,-12561]	[a1,a2,a3,a4,a6]
Generators	[19612646:165971671:238328]	Generators of the group modulo torsion
j	-200704/115	j-invariant
L	5.6233746644554	L(r)(E,1)/r!
Ω	0.43723345542967	Real period
R	12.861263461482	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	90160dc1 50715be1 28175o1 5635a1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5635h1

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	2	6	+	-9	3	11	3	-11	-6	-6	0	-10	13	-8	-16	0	-15	-14	-1

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Quadratic twists for elliptic curve 5635h1

-4	-3	5	-7	-23
90160dc1	50715be1	28175o1	5635a1	129605r1

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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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