Properties

Label 1785.f
Number of curves 1
Conductor 1785
CM no
Rank 1

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Show commands for: SageMath
sage: E = EllipticCurve("1785.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1785.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1785.f1 1785d1 [0, -1, 1, -4759851, 3999274382] [] 42000 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1785.f1 has rank \(1\).

Modular form 1785.2.a.f

sage: E.q_eigenform(10)
 
\( q - q^{3} - 2q^{4} - q^{5} + q^{7} + q^{9} + 2q^{11} + 2q^{12} - 5q^{13} + q^{15} + 4q^{16} + q^{17} + 2q^{19} + O(q^{20}) \)