Cremona's table of elliptic curves

2678 = 2 · 13 · 103

Field	Data	Notes
Atkin-Lehner	2+ 13- 103-	Signs for the Atkin-Lehner involutions
Class	2678d	Isogeny class
Conductor	2678	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	144	Modular degree for the optimal curve
Δ	5356 = 22 · 13 · 103	Discriminant
Eigenvalues	2+ -1  3  0 -2 13- -1 -1	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-6,-8]	[a1,a2,a3,a4,a6]
Generators	[-2:2:1]	Generators of the group modulo torsion
j	30664297/5356	j-invariant
L	2.3827850600174	L(r)(E,1)/r!
Ω	3.0233133193288	Real period
R	0.39406849511488	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	21424l1 85696n1 24102bi1 66950u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2678d1

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	3	0	-2	-	-1	-1	4	-9	2	-7	-2	-4	6	2	-13	1	-10	10	-3	-10	-1	3	14

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Quadratic twists for elliptic curve 2678d1

-4	8	-3	5	13
21424l1	85696n1	24102bi1	66950u1	34814p1

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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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