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	1116653783976900 = 22 · 34 · 52 · 1310	Discriminant
Eigenvalues	2+ 3+ 5+  0 -4 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-95488,-11282708]	[a1,a2,a3,a4,a6]
Generators	[-173:397:1]	Generators of the group modulo torsion
j	19948814692561/231344100	j-invariant
L	2.0246361312266	L(r)(E,1)/r!
Ω	0.27177918632521	Real period
R	3.7247814275298	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	40560bz3 15210bn4 25350cs3 390b3	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5070a3

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 5070a3

-4	-3	5	13
40560bz3	15210bn4	25350cs3	390b3

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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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