Cremona's table of elliptic curves

12950 = 2 · 5² · 7 · 37

Field	Data	Notes
Atkin-Lehner	2+ 5- 7+ 37-	Signs for the Atkin-Lehner involutions
Class	12950i	Isogeny class
Conductor	12950	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	31360	Modular degree for the optimal curve
Δ	181938176000 = 214 · 53 · 74 · 37	Discriminant
Eigenvalues	2+ -2 5- 7+  4  2  6  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-9041,-330972]	[a1,a2,a3,a4,a6]
Generators	[2507:124186:1]	Generators of the group modulo torsion
j	653723433587069/1455505408	j-invariant
L	2.6167177093964	L(r)(E,1)/r!
Ω	0.48967653207304	Real period
R	2.6718839254135	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	103600ch1 116550fp1 12950r1 90650bp1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 12950i1

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	-	+	4	2	6	8	0	-8	2	-	6	-12	-8	-10	0	-8	-14	-12	-8	2	-2	14	2

---

Quadratic twists for elliptic curve 12950i1

-4	-3	5	-7
103600ch1	116550fp1	12950r1	90650bp1

---

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