Cremona's table of elliptic curves

5775 = 3 · 5² · 7 · 11

Field	Data	Notes
Atkin-Lehner	3+ 5+ 7+ 11+	Signs for the Atkin-Lehner involutions
Class	5775d	Isogeny class
Conductor	5775	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	46080	Modular degree for the optimal curve
Δ	31333304652890625 = 316 · 57 · 7 · 113	Discriminant
Eigenvalues	-1 3+ 5+ 7+ 11+ -6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-78938,550406]	[a1,a2,a3,a4,a6]
Generators	[4:482:1]	Generators of the group modulo torsion
j	3481467828171481/2005331497785	j-invariant
L	1.7817210601578	L(r)(E,1)/r!
Ω	0.31578676125366	Real period
R	5.6421651531067	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	92400hp1 17325r1 1155l1 40425ck1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5775d1

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	+	+	+	+	-6	-2	4	4	-2	4	2	6	-4	-8	2	-8	10	8	0	14	-16	4	-6	-18

---

Quadratic twists for elliptic curve 5775d1

-4	-3	5	-7	-11
92400hp1	17325r1	1155l1	40425ck1	63525p1

---

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