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	7504o	Isogeny class
Conductor	7504	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	33685456 = 24 · 7 · 673	Discriminant
Eigenvalues	2- -1  3 7+  0  5  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-589,5696]	[a1,a2,a3,a4,a6]
j	1414772948992/2105341	j-invariant
L	2.0692846470239	L(r)(E,1)/r!
Ω	2.0692846470239	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1876b2 30016bm2 67536bm2 52528ba2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 7504o2

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	3	+	0	5	0	-2	3	9	1	-7	9	-2	-6	-12	-6	14	+	15	-4	10	-12	-18	2

---

Quadratic twists for elliptic curve 7504o2

-4	8	-3	-7
1876b2	30016bm2	67536bm2	52528ba2

---

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