Cremona's table of elliptic curves

6930 = 2 · 3² · 5 · 7 · 11

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 7+ 11+	Signs for the Atkin-Lehner involutions
Class	6930k	Isogeny class
Conductor	6930	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	122880	Modular degree for the optimal curve
Δ	-440675340779520000 = -1 · 220 · 38 · 54 · 7 · 114	Discriminant
Eigenvalues	2+ 3- 5- 7+ 11+ -2 -6  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-364329,90559053]	[a1,a2,a3,a4,a6]
Generators	[322:2399:1]	Generators of the group modulo torsion
j	-7336316844655213969/604492922880000	j-invariant
L	3.0609813201506	L(r)(E,1)/r!
Ω	0.29127197751259	Real period
R	1.3136267631591	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	55440ev1 2310r1 34650dk1 48510r1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6930k1

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	-6	8	0	2	-4	-2	2	4	4	-14	-4	14	12	8	-2	-8	-16	-2	2

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Quadratic twists for elliptic curve 6930k1

-4	-3	5	-7	-11
55440ev1	2310r1	34650dk1	48510r1	76230ez1

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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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