Cremona's table of elliptic curves

2350 = 2 · 5² · 47

Field	Data	Notes
Atkin-Lehner	2+ 5+ 47+	Signs for the Atkin-Lehner involutions
Class	2350a	Isogeny class
Conductor	2350	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	58750000 = 24 · 57 · 47	Discriminant
Eigenvalues	2+  1 5+  3 -5  1 -2 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-276,1698]	[a1,a2,a3,a4,a6]
Generators	[-3:51:1]	Generators of the group modulo torsion
j	148035889/3760	j-invariant
L	2.8100328345074	L(r)(E,1)/r!
Ω	1.9727986122184	Real period
R	0.17804863716851	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	18800bd1 75200i1 21150ce1 470e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2350a1

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	-5	1	-2	-1	0	2	-7	0	-8	4	+	-12	6	-7	0	-16	-11	10	9	6	16

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Quadratic twists for elliptic curve 2350a1

-4	8	-3	5	-7	-47
18800bd1	75200i1	21150ce1	470e1	115150o1	110450f1

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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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