Properties

Label 19950p
Number of curves $1$
Conductor $19950$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 19950p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19950.e1 19950p1 \([1, 1, 0, -12105, -3294675]\) \(-1569510182075597/36491419872936\) \(-4561427484117000\) \([]\) \(153216\) \(1.6854\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 19950p1 has rank \(1\).

Complex multiplication

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

Modular form 19950.2.a.p

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