Properties

Label 6672.k
Number of curves $1$
Conductor $6672$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 6672.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6672.k1 6672p1 \([0, 1, 0, -16432, -817324]\) \(-119801283921073/184467456\) \(-755578699776\) \([]\) \(16128\) \(1.1786\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 6672.k1 has rank \(1\).

Complex multiplication

The elliptic curves in class 6672.k do not have complex multiplication.

Modular form 6672.2.a.k

sage: E.q_eigenform(10)
 
\(q + q^{3} - 3 q^{5} - q^{7} + q^{9} - q^{11} - 5 q^{13} - 3 q^{15} + 8 q^{19} + O(q^{20})\) Copy content Toggle raw display