Properties

Label 84672kr
Number of curves $1$
Conductor $84672$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("kr1")
 
E.isogeny_class()
 

Elliptic curves in class 84672kr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
84672.bi1 84672kr1 \([0, 0, 0, -294, -686]\) \(13824/7\) \(1423082304\) \([]\) \(36864\) \(0.44887\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 84672kr1 has rank \(2\).

Complex multiplication

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

Modular form 84672.2.a.kr

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