Cremona's table of elliptic curves

12480 = 2⁶ · 3 · 5 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 13+	Signs for the Atkin-Lehner involutions
Class	12480a	Isogeny class
Conductor	12480	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	155750400000000 = 218 · 32 · 58 · 132	Discriminant
Eigenvalues	2+ 3+ 5+  0 -4 13+  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-520001,-144154815]	[a1,a2,a3,a4,a6]
Generators	[-2047888:96761:4913]	Generators of the group modulo torsion
j	59319456301170001/594140625	j-invariant
L	3.4058133531174	L(r)(E,1)/r!
Ω	0.17778646770203	Real period
R	9.5783818564456	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	12480cj5 195a5 37440ca6 62400cs6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12480a5

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	-4	+	2	4	8	2	-8	-6	-6	4	-8	-6	12	2	4	0	-6	16	4	10	18

---

Quadratic twists for elliptic curve 12480a5

-4	8	-3	5
12480cj5	195a5	37440ca6	62400cs6

---

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