Cremona's table of elliptic curves

2800 = 2⁴ · 5² · 7

Field	Data	Notes
Atkin-Lehner	2+ 5+ 7+	Signs for the Atkin-Lehner involutions
Class	2800b	Isogeny class
Conductor	2800	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	-2508800 = -1 · 211 · 52 · 72	Discriminant
Eigenvalues	2+  1 5+ 7+  1  6 -7 -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-168,788]	[a1,a2,a3,a4,a6]
Generators	[4:14:1]	Generators of the group modulo torsion
j	-10303010/49	j-invariant
L	3.7340376939084	L(r)(E,1)/r!
Ω	2.5854242329515	Real period
R	0.36106624652907	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	1400b1 11200bz1 25200z1 2800l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2800b1

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	+	+	1	6	-7	-1	-8	-6	-4	8	-5	0	-6	4	4	6	5	-14	15	-14	-1	-3	-6

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Quadratic twists for elliptic curve 2800b1

-4	8	-3	5	-7
1400b1	11200bz1	25200z1	2800l1	19600o1

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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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