Cremona's table of elliptic curves

4278 = 2 · 3 · 23 · 31

Field	Data	Notes
Atkin-Lehner	2- 3- 23- 31-	Signs for the Atkin-Lehner involutions
Class	4278o	Isogeny class
Conductor	4278	Conductor
∏ cp	810	Product of Tamagawa factors cp
deg	38880	Modular degree for the optimal curve
Δ	-152624900793014784 = -1 · 29 · 39 · 232 · 315	Discriminant
Eigenvalues	2- 3- -1  0 -3 -5  1 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-139696,-27528448]	[a1,a2,a3,a4,a6]
Generators	[752:-17488:1]	Generators of the group modulo torsion
j	-301492018259600732929/152624900793014784	j-invariant
L	5.7649952015762	L(r)(E,1)/r!
Ω	0.12058550259453	Real period
R	0.059022667513931	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	34224p1 12834d1 106950c1 98394bo1	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 4278o1

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	0	-3	-5	1	-1	-	0	-	-6	-12	8	-1	-2	0	-7	13	-5	0	-5	-9	-6	-9

---

Quadratic twists for elliptic curve 4278o1

-4	-3	5	-23
34224p1	12834d1	106950c1	98394bo1

---

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