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	5635g	Isogeny class
Conductor	5635	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	274560	Modular degree for the optimal curve
Δ	-3.845673184351E+20	Discriminant
Eigenvalues	2  1 5- 7- -5 -3  5  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,1127180,-823053801]	[a1,a2,a3,a4,a6]
Generators	[25818:1527081:8]	Generators of the group modulo torsion
j	1346216501445963776/3268768272021875	j-invariant
L	8.4835028353461	L(r)(E,1)/r!
Ω	0.08739756182479	Real period
R	4.8533978856031	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	90160db1 50715bh1 28175n1 805a1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5635g1

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	-	-	-5	-3	5	0	+	3	-6	-4	0	-2	9	-6	6	-10	4	-8	-10	-15	-12	10	-7

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Quadratic twists for elliptic curve 5635g1

-4	-3	5	-7	-23
90160db1	50715bh1	28175n1	805a1	129605q1

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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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