Properties

Label 42050.a
Number of curves $1$
Conductor $42050$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 42050.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
42050.a1 42050j1 \([1, -1, 0, -24967, 2197441]\) \(-185193/116\) \(-1078117269312500\) \([]\) \(362880\) \(1.5861\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 42050.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 42050.a do not have complex multiplication.

Modular form 42050.2.a.a

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