Cremona's table of elliptic curves

2635 = 5 · 17 · 31

Field	Data	Notes
Atkin-Lehner	5+ 17- 31-	Signs for the Atkin-Lehner involutions
Class	2635c	Isogeny class
Conductor	2635	Conductor
∏ cp	7	Product of Tamagawa factors cp
deg	9240	Modular degree for the optimal curve
Δ	-2338572199435 = -1 · 5 · 17 · 317	Discriminant
Eigenvalues	1  2 5+  5 -5 -5 17- -7	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-7403,252908]	[a1,a2,a3,a4,a6]
Generators	[328:5602:1]	Generators of the group modulo torsion
j	-44878529736708409/2338572199435	j-invariant
L	5.1522363276795	L(r)(E,1)/r!
Ω	0.80847717895185	Real period
R	0.91039522235038	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	42160q1 23715k1 13175d1 129115s1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2635c1

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	+	5	-5	-5	-	-7	-8	-6	-	2	-4	4	12	-3	1	7	-6	12	0	-7	11	-8	-5

---

Quadratic twists for elliptic curve 2635c1

-4	-3	5	-7	17	-31
42160q1	23715k1	13175d1	129115s1	44795f1	81685c1

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations