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	6930bi	Isogeny class
Conductor	6930	Conductor
∏ cp	192	Product of Tamagawa factors cp
deg	12288	Modular degree for the optimal curve
Δ	120708403200 = 212 · 37 · 52 · 72 · 11	Discriminant
Eigenvalues	2- 3- 5- 7- 11+ -6 -6  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-7772,265119]	[a1,a2,a3,a4,a6]
Generators	[-43:741:1]	Generators of the group modulo torsion
j	71210194441849/165580800	j-invariant
L	6.3797181674195	L(r)(E,1)/r!
Ω	1.049759934268	Real period
R	0.50644262870349	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	55440ej1 2310c1 34650m1 48510da1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6930bi1

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

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Quadratic twists for elliptic curve 6930bi1

-4	-3	5	-7	-11
55440ej1	2310c1	34650m1	48510da1	76230by1

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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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