Cremona's table of elliptic curves

5628 = 2² · 3 · 7 · 67

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 67-	Signs for the Atkin-Lehner involutions
Class	5628b	Isogeny class
Conductor	5628	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	1508304 = 24 · 3 · 7 · 672	Discriminant
Eigenvalues	2- 3+ -2 7-  0  0  2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-29,-6]	[a1,a2,a3,a4,a6]
j	174456832/94269	j-invariant
L	1.0928529112863	L(r)(E,1)/r!
Ω	2.1857058225727	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	22512q1 90048v1 16884k1 39396p1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 5628b1

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	-	0	0	2	-2	-2	2	0	-6	-2	4	12	4	4	4	-	-6	6	-16	-12	-6	-8

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Quadratic twists for elliptic curve 5628b1

-4	8	-3	-7
22512q1	90048v1	16884k1	39396p1

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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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