Cremona's table of elliptic curves

4680 = 2³ · 3² · 5 · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 13-	Signs for the Atkin-Lehner involutions
Class	4680k	Isogeny class
Conductor	4680	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	-6550502400 = -1 · 210 · 39 · 52 · 13	Discriminant
Eigenvalues	2- 3+ 5+  0  0 13-  6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-243,4158]	[a1,a2,a3,a4,a6]
Generators	[6:54:1]	Generators of the group modulo torsion
j	-78732/325	j-invariant
L	3.5699238874628	L(r)(E,1)/r!
Ω	1.1639481545524	Real period
R	1.5335407653255	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	9360c1 37440o1 4680c1 23400a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4680k1

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	0	-	6	-8	-6	-2	6	-2	10	-4	4	-4	-4	-2	-10	0	-12	0	-4	14	-4

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Quadratic twists for elliptic curve 4680k1

-4	8	-3	5	13
9360c1	37440o1	4680c1	23400a1	60840b1

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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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