Cremona's table of elliptic curves

3978 = 2 · 3² · 13 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 13+ 17-	Signs for the Atkin-Lehner involutions
Class	3978c	Isogeny class
Conductor	3978	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	8377668 = 22 · 36 · 132 · 17	Discriminant
Eigenvalues	2+ 3-  2  2 -4 13+ 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-81,265]	[a1,a2,a3,a4,a6]
Generators	[3:5:1]	Generators of the group modulo torsion
j	81182737/11492	j-invariant
L	3.097960489522	L(r)(E,1)/r!
Ω	2.2348705047573	Real period
R	0.69309619571413	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	31824be1 127296bs1 442d1 99450db1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3978c1

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
+	-	2	2	-4	+	-	-4	-8	8	10	-10	8	-12	-8	-2	-12	0	-4	6	-4	-4	-12	2	12

---

Quadratic twists for elliptic curve 3978c1

-4	8	-3	5	13	17
31824be1	127296bs1	442d1	99450db1	51714u1	67626j1

---

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