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	12810c	Isogeny class
Conductor	12810	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	76800	Modular degree for the optimal curve
Δ	559782659358720 = 220 · 36 · 5 · 74 · 61	Discriminant
Eigenvalues	2+ 3+ 5- 7+ -4  6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-21357,-392931]	[a1,a2,a3,a4,a6]
Generators	[-135:297:1]	Generators of the group modulo torsion
j	1077398156586248281/559782659358720	j-invariant
L	2.984806551614	L(r)(E,1)/r!
Ω	0.41804356577504	Real period
R	3.569970687242	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	102480ck1 38430bh1 64050cp1 89670r1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 12810c1

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	6	-2	4	0	-6	0	10	2	-4	-12	-6	0	-	-4	4	6	-12	-12	6	14

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Quadratic twists for elliptic curve 12810c1

-4	-3	5	-7
102480ck1	38430bh1	64050cp1	89670r1

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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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