Cremona's table of elliptic curves

5070 = 2 · 3 · 5 · 13²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 13+	Signs for the Atkin-Lehner involutions
Class	5070a	Isogeny class
Conductor	5070	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	73415764890000 = 24 · 32 · 54 · 138	Discriminant
Eigenvalues	2+ 3+ 5+  0 -4 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-10988,158592]	[a1,a2,a3,a4,a6]
Generators	[-73:797:1]	Generators of the group modulo torsion
j	30400540561/15210000	j-invariant
L	2.0246361312266	L(r)(E,1)/r!
Ω	0.54355837265042	Real period
R	1.8623907137649	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	40560bz2 15210bn2 25350cs2 390b2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5070a2

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	-4	+	-6	-4	8	6	8	10	6	4	0	-10	-4	-2	12	-16	-2	-16	12	-10	6

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Quadratic twists for elliptic curve 5070a2

-4	-3	5	13
40560bz2	15210bn2	25350cs2	390b2

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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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