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	40425w	Isogeny class
Conductor	40425	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	294912	Modular degree for the optimal curve
Δ	23355164765625 = 3 · 57 · 77 · 112	Discriminant
Eigenvalues	1 3+ 5+ 7- 11- -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-324650,-71333625]	[a1,a2,a3,a4,a6]
Generators	[-1350896:617775:4096]	Generators of the group modulo torsion
j	2058561081361/12705	j-invariant
L	4.7646288012476	L(r)(E,1)/r!
Ω	0.20000722741624	Real period
R	5.9555707846167	Regulator
r	1	Rank of the group of rational points
S	0.9999999999996	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	121275dh1 8085p1 5775u1	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 40425w1

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	-8	6	-8	-6	6	4	-8	10	12	10	12	-8	-6	8	-4	-10	-14

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Quadratic twists for elliptic curve 40425w1

-3	5	-7
121275dh1	8085p1	5775u1

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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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