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	2345b	Isogeny class
Conductor	2345	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	816	Modular degree for the optimal curve
Δ	-7698635 = -1 · 5 · 73 · 672	Discriminant
Eigenvalues	0 -3 5- 7+ -5  1 -3  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-262,-1638]	[a1,a2,a3,a4,a6]
Generators	[20:33:1]	Generators of the group modulo torsion
j	-1988967038976/7698635	j-invariant
L	1.5150269711859	L(r)(E,1)/r!
Ω	0.59318972776018	Real period
R	1.2770172006404	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	37520m1 21105d1 11725a1 16415c1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2345b1

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

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Quadratic twists for elliptic curve 2345b1

-4	-3	5	-7
37520m1	21105d1	11725a1	16415c1

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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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