Cremona's table of elliptic curves

10815 = 3 · 5 · 7 · 103

Field	Data	Notes
Atkin-Lehner	3+ 5- 7- 103+	Signs for the Atkin-Lehner involutions
Class	10815f	Isogeny class
Conductor	10815	Conductor
∏ cp	22	Product of Tamagawa factors cp
deg	97152	Modular degree for the optimal curve
Δ	230980517578125 = 38 · 511 · 7 · 103	Discriminant
Eigenvalues	2 3+ 5- 7- -2 -1 -3 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-346780,-78482319]	[a1,a2,a3,a4,a6]
Generators	[-2710:401:8]	Generators of the group modulo torsion
j	4611976559150578978816/230980517578125	j-invariant
L	7.9506520019697	L(r)(E,1)/r!
Ω	0.19673754369089	Real period
R	1.8369308980732	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	32445j1 54075t1 75705u1	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 10815f1

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	-1	-3	-4	4	9	5	-2	-2	1	-2	1	4	-8	-8	-14	-4	3	-7	-9	2

---

Quadratic twists for elliptic curve 10815f1

-3	5	-7
32445j1	54075t1	75705u1

---

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