Cremona's table of elliptic curves

5096 = 2³ · 7² · 13

Field	Data	Notes
Atkin-Lehner	2+ 7- 13-	Signs for the Atkin-Lehner involutions
Class	5096c	Isogeny class
Conductor	5096	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	-21926008832 = -1 · 211 · 77 · 13	Discriminant
Eigenvalues	2+  1  0 7-  3 13- -4 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-408,7664]	[a1,a2,a3,a4,a6]
Generators	[-5:98:1]	Generators of the group modulo torsion
j	-31250/91	j-invariant
L	4.4741063752254	L(r)(E,1)/r!
Ω	1.0629237938519	Real period
R	1.0523111819267	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	10192g1 40768s1 45864bp1 127400bj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5096c1

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	0	-	3	-	-4	-2	1	4	-9	3	5	4	-9	-4	-10	-5	11	-16	-11	-5	4	2	7

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Quadratic twists for elliptic curve 5096c1

-4	8	-3	5	-7	13
10192g1	40768s1	45864bp1	127400bj1	728a1	66248q1

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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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