Properties

Label 338130.df
Number of curves $1$
Conductor $338130$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("df1")
 
E.isogeny_class()
 

Elliptic curves in class 338130.df

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
338130.df1 338130df1 \([1, -1, 1, -9668, -500633]\) \(-1033364331/532480\) \(-51492189265920\) \([]\) \(1437696\) \(1.3356\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 338130.df1 has rank \(1\).

Complex multiplication

The elliptic curves in class 338130.df do not have complex multiplication.

Modular form 338130.2.a.df

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} + 4 q^{7} + q^{8} - q^{10} + 3 q^{11} + q^{13} + 4 q^{14} + q^{16} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display