Properties

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

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

Elliptic curves in class 1785f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1785.g1 1785f1 \([0, -1, 1, -35, 131]\) \(-4878401536/3346875\) \(-3346875\) \([]\) \(240\) \(-0.047669\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 1785f do not have complex multiplication.

Modular form 1785.2.a.f

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