Properties

Label 84672en
Number of curves $1$
Conductor $84672$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("en1")
 
E.isogeny_class()
 

Elliptic curves in class 84672en

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
84672.cd1 84672en1 \([0, 0, 0, 294, -686]\) \(1536\) \(-1829677248\) \([]\) \(36288\) \(0.46615\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 84672en1 has rank \(1\).

Complex multiplication

The elliptic curves in class 84672en do not have complex multiplication.

Modular form 84672.2.a.en

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} - 2 q^{11} + q^{13} + 6 q^{17} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display