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	5635d	Isogeny class
Conductor	5635	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	13440	Modular degree for the optimal curve
Δ	-13341911314375 = -1 · 54 · 79 · 232	Discriminant
Eigenvalues	1 -2 5+ 7-  0  4  2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,1836,173261]	[a1,a2,a3,a4,a6]
Generators	[54:3419:8]	Generators of the group modulo torsion
j	16974593/330625	j-invariant
L	2.8615927843598	L(r)(E,1)/r!
Ω	0.52837860560523	Real period
R	2.7078999357686	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	90160bu1 50715bo1 28175e1 5635i1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5635d1

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	+	-	0	4	2	-8	-	-2	-2	10	-8	12	-6	-2	-6	14	8	16	-12	12	12	-14	14

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Quadratic twists for elliptic curve 5635d1

-4	-3	5	-7	-23
90160bu1	50715bo1	28175e1	5635i1	129605y1

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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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