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	2635a	Isogeny class
Conductor	2635	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	1368	Modular degree for the optimal curve
Δ	1029296875 = 59 · 17 · 31	Discriminant
Eigenvalues	-1  1 5+  2 -6 -1 17-  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-901,-10370]	[a1,a2,a3,a4,a6]
j	80896216567249/1029296875	j-invariant
L	0.87206749438955	L(r)(E,1)/r!
Ω	0.87206749438955	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	42160r1 23715h1 13175a1 129115u1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2635a1

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	1	+	2	-6	-1	-	2	-1	7	+	-2	6	-12	3	9	6	14	15	3	-2	-10	8	8	6

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Quadratic twists for elliptic curve 2635a1

-4	-3	5	-7	17	-31
42160r1	23715h1	13175a1	129115u1	44795i1	81685d1

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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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