Cremona's table of elliptic curves

12495 = 3 · 5 · 7² · 17

Field	Data	Notes
Atkin-Lehner	3+ 5- 7- 17+	Signs for the Atkin-Lehner involutions
Class	12495d	Isogeny class
Conductor	12495	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-771762733875 = -1 · 32 · 53 · 79 · 17	Discriminant
Eigenvalues	0 3+ 5- 7- -6  1 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-606685,182085756]	[a1,a2,a3,a4,a6]
Generators	[460:367:1]	Generators of the group modulo torsion
j	-209906535145406464/6559875	j-invariant
L	2.9312209889513	L(r)(E,1)/r!
Ω	0.65856090890614	Real period
R	0.37091241287259	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	37485bb2 62475ca2 1785l2	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 12495d2

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	+	-	-	-6	1	+	-2	3	0	-5	5	-9	8	9	0	0	-5	8	6	16	2	-3	-6	-2

---

Quadratic twists for elliptic curve 12495d2

-3	5	-7
37485bb2	62475ca2	1785l2

---

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