Cremona's table of elliptic curves

10296 = 2³ · 3² · 11 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3+ 11+ 13+	Signs for the Atkin-Lehner involutions
Class	10296a	Isogeny class
Conductor	10296	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	5120	Modular degree for the optimal curve
Δ	12849408 = 28 · 33 · 11 · 132	Discriminant
Eigenvalues	2+ 3+  4 -2 11+ 13+  2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1863,-30950]	[a1,a2,a3,a4,a6]
Generators	[50:30:1]	Generators of the group modulo torsion
j	103456682352/1859	j-invariant
L	5.4750151156715	L(r)(E,1)/r!
Ω	0.7266860264899	Real period
R	3.7671118723153	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	20592b1 82368p1 10296h1 113256bi1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 10296a1

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

---

Quadratic twists for elliptic curve 10296a1

-4	8	-3	-11
20592b1	82368p1	10296h1	113256bi1

---

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