Cremona's table of elliptic curves

3102 = 2 · 3 · 11 · 47

Field	Data	Notes
Atkin-Lehner	2+ 3- 11+ 47-	Signs for the Atkin-Lehner involutions
Class	3102f	Isogeny class
Conductor	3102	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-27918 = -1 · 2 · 33 · 11 · 47	Discriminant
Eigenvalues	2+ 3- -4 -2 11+  4  3  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,7,2]	[a1,a2,a3,a4,a6]
Generators	[0:1:1]	Generators of the group modulo torsion
j	46268279/27918	j-invariant
L	2.251609290283	L(r)(E,1)/r!
Ω	2.2959872708391	Real period
R	0.32689050136591	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	24816o1 99264o1 9306p1 77550bc1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3102f1

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
+	-	-4	-2	+	4	3	0	1	-3	-2	4	-8	0	-	-1	3	15	-7	4	-13	14	0	-18	-3

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Quadratic twists for elliptic curve 3102f1

-4	8	-3	5	-11
24816o1	99264o1	9306p1	77550bc1	34122z1

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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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