Properties

Label 141570ex
Number of curves $1$
Conductor $141570$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("ex1")
 
E.isogeny_class()
 

Elliptic curves in class 141570ex

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141570.l1 141570ex1 \([1, -1, 0, 20850, 1777870]\) \(20956092093/40842230\) \(-1953571549167810\) \([]\) \(806400\) \(1.6186\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 141570ex1 has rank \(1\).

Complex multiplication

The elliptic curves in class 141570ex do not have complex multiplication.

Modular form 141570.2.a.ex

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