Cremona's table of elliptic curves

7540 = 2² · 5 · 13 · 29

Field	Data	Notes
Atkin-Lehner	2- 5- 13+ 29+	Signs for the Atkin-Lehner involutions
Class	7540d	Isogeny class
Conductor	7540	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-5300921600 = -1 · 28 · 52 · 134 · 29	Discriminant
Eigenvalues	2-  0 5-  2 -4 13+  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-127,-3546]	[a1,a2,a3,a4,a6]
Generators	[19:30:1]	Generators of the group modulo torsion
j	-884901456/20706725	j-invariant
L	4.3712794965041	L(r)(E,1)/r!
Ω	0.58797775573829	Real period
R	2.4781433502901	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	30160x2 120640o2 67860l2 37700c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 7540d2

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

---

Quadratic twists for elliptic curve 7540d2

-4	8	-3	5	13
30160x2	120640o2	67860l2	37700c2	98020b2

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations