Cremona's table of elliptic curves

40425 = 3 · 5² · 7² · 11

Field	Data	Notes
Atkin-Lehner	3+ 5+ 7- 11+	Signs for the Atkin-Lehner involutions
Class	40425m	Isogeny class
Conductor	40425	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	1327104	Modular degree for the optimal curve
Δ	1433157837890625 = 34 · 59 · 77 · 11	Discriminant
Eigenvalues	-1 3+ 5+ 7- 11+ -2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-19897088,34152852656]	[a1,a2,a3,a4,a6]
j	473897054735271721/779625	j-invariant
L	0.61738104123794	L(r)(E,1)/r!
Ω	0.30869052060741	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	121275ed1 8085n1 5775o1	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 40425m1

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	+	+	-	+	-2	-6	-4	4	-2	4	2	2	12	0	2	0	14	8	-16	10	16	-4	6	2

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Quadratic twists for elliptic curve 40425m1

-3	5	-7
121275ed1	8085n1	5775o1

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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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