Properties

Label 139650dc
Number of curves $1$
Conductor $139650$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("dc1")
 
E.isogeny_class()
 

Elliptic curves in class 139650dc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139650.fj1 139650dc1 \([1, 1, 1, -403402938, 7235492143431]\) \(-98735339854432038328225/250451215107692352768\) \(-18415834378878061006751520000\) \([]\) \(100638720\) \(4.1114\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 139650dc1 has rank \(1\).

Complex multiplication

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

Modular form 139650.2.a.dc

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