Cremona's table of elliptic curves

7400 = 2³ · 5² · 37

Field	Data	Notes
Atkin-Lehner	2+ 5- 37-	Signs for the Atkin-Lehner involutions
Class	7400d	Isogeny class
Conductor	7400	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1408	Modular degree for the optimal curve
Δ	4736000 = 210 · 53 · 37	Discriminant
Eigenvalues	2+  2 5- -4  4  2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-48,92]	[a1,a2,a3,a4,a6]
Generators	[-7:6:1]	Generators of the group modulo torsion
j	97556/37	j-invariant
L	5.3583000902073	L(r)(E,1)/r!
Ω	2.2257578703675	Real period
R	2.4074047593158	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	14800j1 59200bq1 66600bw1 7400j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 7400d1

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
+	2	-	-4	4	2	-2	-4	0	0	-2	-	-10	4	12	6	4	-8	-10	-12	0	-10	-6	-18	2

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Quadratic twists for elliptic curve 7400d1

-4	8	-3	5
14800j1	59200bq1	66600bw1	7400j1

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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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