Cremona's table of elliptic curves

7504 = 2⁴ · 7 · 67

Field	Data	Notes
Atkin-Lehner	2- 7+ 67-	Signs for the Atkin-Lehner involutions
Class	7504r	Isogeny class
Conductor	7504	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	24097325056 = 220 · 73 · 67	Discriminant
Eigenvalues	2-  1 -1 7+  4 -3  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-896,6836]	[a1,a2,a3,a4,a6]
Generators	[-22:128:1]	Generators of the group modulo torsion
j	19443408769/5883136	j-invariant
L	4.4398105837498	L(r)(E,1)/r!
Ω	1.1107423281252	Real period
R	0.99928905006342	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	938c1 30016bf1 67536br1 52528bp1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 7504r1

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	-1	+	4	-3	0	-4	9	5	7	-11	5	8	-6	6	-10	-10	-	5	-6	2	6	-12	-2

---

Quadratic twists for elliptic curve 7504r1

-4	8	-3	-7
938c1	30016bf1	67536br1	52528bp1

---

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