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Properties

Label 139650.jn
Number of curves $1$
Conductor $139650$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("jn1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 139650.jn1 has rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(3\)\(1 - T\)
\(5\)\(1\)
\(7\)\(1\)
\(19\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 - 5 T + 11 T^{2}\) 1.11.af
\(13\) \( 1 - T + 13 T^{2}\) 1.13.ab
\(17\) \( 1 + 6 T + 17 T^{2}\) 1.17.g
\(23\) \( 1 + T + 23 T^{2}\) 1.23.b
\(29\) \( 1 - 4 T + 29 T^{2}\) 1.29.ae
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 139650.jn do not have complex multiplication.

Modular form 139650.2.a.jn

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + q^{8} + q^{9} + 5 q^{11} + q^{12} + q^{13} + q^{16} - 6 q^{17} + q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 139650.jn

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139650.jn1 139650co1 \([1, 0, 0, -92397628056938, 341972087775214851492]\) \(-138357846491853121383730987168838623/55816105091607428996184145920\) \(-35193455767772268562381555063848960000000\) \([]\) \(22983367680\) \(6.7434\) \(\Gamma_0(N)\)-optimal