Properties

Label 349830.f
Number of curves $1$
Conductor $349830$
CM no
Rank $1$

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

Elliptic curves in class 349830.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
349830.f1 349830f1 \([1, -1, 0, 3789540, 4985635266]\) \(289056138613409999/683205566406250\) \(-14225001918771972656250\) \([]\) \(27555840\) \(2.9348\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 349830.f1 has rank \(1\).

Complex multiplication

The elliptic curves in class 349830.f do not have complex multiplication.

Modular form 349830.2.a.f

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