Cremona's table of elliptic curves

2850 = 2 · 3 · 5² · 19

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 19+	Signs for the Atkin-Lehner involutions
Class	2850a	Isogeny class
Conductor	2850	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	57600	Modular degree for the optimal curve
Δ	-4491417600000000000 = -1 · 220 · 35 · 511 · 192	Discriminant
Eigenvalues	2+ 3+ 5+  2  2 -4  2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,233375,-92172875]	[a1,a2,a3,a4,a6]
Generators	[35421:6649418:1]	Generators of the group modulo torsion
j	89962967236397039/287450726400000	j-invariant
L	2.2566318158248	L(r)(E,1)/r!
Ω	0.12522120436829	Real period
R	9.0105818228185	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	22800dh1 91200dv1 8550y1 570l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2850a1

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	-4	2	+	-4	0	-8	-8	-8	6	12	6	0	2	-8	-8	-14	0	-4	0	12

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Quadratic twists for elliptic curve 2850a1

-4	8	-3	5	-19
22800dh1	91200dv1	8550y1	570l1	54150cn1

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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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