Cremona's table of elliptic curves

12152 = 2³ · 7² · 31

Field	Data	Notes
Atkin-Lehner	2- 7- 31-	Signs for the Atkin-Lehner involutions
Class	12152f	Isogeny class
Conductor	12152	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	7680	Modular degree for the optimal curve
Δ	-45749460736 = -1 · 28 · 78 · 31	Discriminant
Eigenvalues	2-  0 -2 7- -6  0 -4  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,49,10290]	[a1,a2,a3,a4,a6]
Generators	[-19:50:1] [-7:98:1]	Generators of the group modulo torsion
j	432/1519	j-invariant
L	5.5862982779655	L(r)(E,1)/r!
Ω	0.89237890867474	Real period
R	1.5650017676521	Regulator
r	2	Rank of the group of rational points
S	0.99999999999999	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	24304b1 97216r1 109368w1 1736c1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12152f1

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	-	-6	0	-4	4	-6	-6	-	-6	-2	-2	0	-2	-12	0	-8	8	-12	-14	4	-4	2

---

Quadratic twists for elliptic curve 12152f1

-4	8	-3	-7
24304b1	97216r1	109368w1	1736c1

---

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