Cremona's table of elliptic curves

7752 = 2³ · 3 · 17 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3+ 17+ 19+	Signs for the Atkin-Lehner involutions
Class	7752a	Isogeny class
Conductor	7752	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	9216	Modular degree for the optimal curve
Δ	1653829788672 = 210 · 36 · 17 · 194	Discriminant
Eigenvalues	2+ 3+  0 -2  4  2 17+ 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3168,30780]	[a1,a2,a3,a4,a6]
Generators	[9:54:1]	Generators of the group modulo torsion
j	3434917850500/1615068153	j-invariant
L	3.5297285701408	L(r)(E,1)/r!
Ω	0.75202861885274	Real period
R	2.3468046837935	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	15504e1 62016ba1 23256k1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 7752a1

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	2	+	+	6	-4	-2	-4	2	-12	-12	6	12	-8	4	6	10	6	-4	6	10

---

Quadratic twists for elliptic curve 7752a1

-4	8	-3
15504e1	62016ba1	23256k1

---

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