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	4680c	Isogeny class
Conductor	4680	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-8985600 = -1 · 210 · 33 · 52 · 13	Discriminant
Eigenvalues	2+ 3+ 5-  0  0 13- -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-27,-154]	[a1,a2,a3,a4,a6]
Generators	[10:24:1]	Generators of the group modulo torsion
j	-78732/325	j-invariant
L	3.9750182809631	L(r)(E,1)/r!
Ω	0.95417356892492	Real period
R	2.0829639440976	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	9360g1 37440a1 4680k1 23400z1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4680c1

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 4680c1

-4	8	-3	5	13
9360g1	37440a1	4680k1	23400z1	60840be1

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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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