Properties

Label 3381.f
Number of curves $1$
Conductor $3381$
CM no
Rank $1$

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

Elliptic curves in class 3381.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3381.f1 3381e1 \([0, -1, 1, -1143, 15476]\) \(-4096000/69\) \(-2784398883\) \([]\) \(2016\) \(0.61117\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3381.f1 has rank \(1\).

Complex multiplication

The elliptic curves in class 3381.f do not have complex multiplication.

Modular form 3381.2.a.f

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