Cremona's table of elliptic curves

2345 = 5 · 7 · 67

Field	Data	Notes
Atkin-Lehner	5- 7+ 67+	Signs for the Atkin-Lehner involutions
Class	2345a	Isogeny class
Conductor	2345	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	1440	Modular degree for the optimal curve
Δ	-51296875 = -1 · 56 · 72 · 67	Discriminant
Eigenvalues	-2 -2 5- 7+ -6 -4 -5 -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-50,354]	[a1,a2,a3,a4,a6]
Generators	[-22:171:8] [-4:22:1]	Generators of the group modulo torsion
j	-14102327296/51296875	j-invariant
L	1.6283639983322	L(r)(E,1)/r!
Ω	1.7497274263736	Real period
R	0.077553222185251	Regulator
r	2	Rank of the group of rational points
S	0.99999999999884	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	37520n1 21105c1 11725d1 16415a1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2345a1

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
-2	-2	-	+	-6	-4	-5	-7	3	-9	-4	-3	-6	4	7	-12	-5	6	+	0	-11	-10	4	-3	-14

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Quadratic twists for elliptic curve 2345a1

-4	-3	5	-7
37520n1	21105c1	11725d1	16415a1

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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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