Cremona's table of elliptic curves

7462 = 2 · 7 · 13 · 41

Field	Data	Notes
Atkin-Lehner	2+ 7- 13- 41+	Signs for the Atkin-Lehner involutions
Class	7462g	Isogeny class
Conductor	7462	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	2045513526784 = 29 · 73 · 132 · 413	Discriminant
Eigenvalues	2+  1 -3 7- -6 13-  3  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-17165,-864248]	[a1,a2,a3,a4,a6]
Generators	[-74:82:1]	Generators of the group modulo torsion
j	559266446640355273/2045513526784	j-invariant
L	2.7484581153404	L(r)(E,1)/r!
Ω	0.41719314213252	Real period
R	1.0979958831903	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	59696o2 67158cd2 52234k2 97006j2	Quadratic twists by: -4 -3 -7 13

Hecke Eigenvalues for elliptic curve 7462g2

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
+	1	-3	-	-6	-	3	8	-6	9	5	8	+	-7	-12	-3	12	-7	8	15	-10	5	0	3	-13

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Quadratic twists for elliptic curve 7462g2

-4	-3	-7	13
59696o2	67158cd2	52234k2	97006j2

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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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