Cremona's table of elliptic curves

2680 = 2³ · 5 · 67

Field	Data	Notes
Atkin-Lehner	2+ 5- 67-	Signs for the Atkin-Lehner involutions
Class	2680b	Isogeny class
Conductor	2680	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	432	Modular degree for the optimal curve
Δ	-134000 = -1 · 24 · 53 · 67	Discriminant
Eigenvalues	2+ -3 5-  1  2 -2 -4  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-7,19]	[a1,a2,a3,a4,a6]
Generators	[3:-5:1]	Generators of the group modulo torsion
j	-2370816/8375	j-invariant
L	2.2273389374653	L(r)(E,1)/r!
Ω	2.8745973994231	Real period
R	0.12913918182725	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	5360e1 21440e1 24120s1 13400m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2680b1

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
+	-3	-	1	2	-2	-4	0	-8	5	-8	6	12	-7	12	-7	3	8	-	-12	10	-10	-12	-15	-5

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Quadratic twists for elliptic curve 2680b1

-4	8	-3	5
5360e1	21440e1	24120s1	13400m1

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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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