Cremona's table of elliptic curves

3914 = 2 · 19 · 103

Field	Data	Notes
Atkin-Lehner	2+ 19- 103+	Signs for the Atkin-Lehner involutions
Class	3914b	Isogeny class
Conductor	3914	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	832	Modular degree for the optimal curve
Δ	31312 = 24 · 19 · 103	Discriminant
Eigenvalues	2+ -3 -2 -3  0  0 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-28,64]	[a1,a2,a3,a4,a6]
Generators	[-1:10:1] [0:8:1]	Generators of the group modulo torsion
j	2476813977/31312	j-invariant
L	2.0116631234226	L(r)(E,1)/r!
Ω	3.7189728824831	Real period
R	0.27045950414166	Regulator
r	2	Rank of the group of rational points
S	0.99999999999865	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	31312q1 125248f1 35226d1 97850r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3914b1

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
+	-3	-2	-3	0	0	-6	-	-3	-8	9	3	0	-6	-6	-5	-6	-7	-5	-5	-16	-14	7	-13	12

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Quadratic twists for elliptic curve 3914b1

-4	8	-3	5	-19
31312q1	125248f1	35226d1	97850r1	74366l1

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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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