Cremona's table of elliptic curves

12810 = 2 · 3 · 5 · 7 · 61

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 7+ 61+	Signs for the Atkin-Lehner involutions
Class	12810f	Isogeny class
Conductor	12810	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	11520	Modular degree for the optimal curve
Δ	-11863341000 = -1 · 23 · 34 · 53 · 74 · 61	Discriminant
Eigenvalues	2+ 3- 5- 7+  2 -1 -1  3	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-323,-5722]	[a1,a2,a3,a4,a6]
Generators	[54:340:1]	Generators of the group modulo torsion
j	-3710197529641/11863341000	j-invariant
L	4.5100160108275	L(r)(E,1)/r!
Ω	0.51924472814992	Real period
R	0.36190513566509	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	102480bp1 38430bf1 64050bw1 89670g1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 12810f1

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	-1	-1	3	6	-9	-5	-12	-7	7	9	-10	-4	+	5	0	-16	-3	-14	-10	0

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Quadratic twists for elliptic curve 12810f1

-4	-3	5	-7
102480bp1	38430bf1	64050bw1	89670g1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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