Properties

Label 19950.cx
Number of curves $1$
Conductor $19950$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("cx1")
 
E.isogeny_class()
 

Elliptic curves in class 19950.cx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19950.cx1 19950da1 \([1, 0, 0, 29687, -1517383]\) \(185183253170999/171032148000\) \(-2672377312500000\) \([]\) \(138240\) \(1.6474\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 19950.cx1 has rank \(1\).

Complex multiplication

The elliptic curves in class 19950.cx do not have complex multiplication.

Modular form 19950.2.a.cx

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + q^{7} + q^{8} + q^{9} - 5 q^{11} + q^{12} - 3 q^{13} + q^{14} + q^{16} + 5 q^{17} + q^{18} + q^{19} + O(q^{20})\) Copy content Toggle raw display