Properties

Label 272832.k
Number of curves $1$
Conductor $272832$
CM no
Rank $1$

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

Elliptic curves in class 272832.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
272832.k1 272832k1 \([0, -1, 0, -7317, 33741]\) \(458752/261\) \(24651580391424\) \([]\) \(709632\) \(1.2595\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 272832.k1 has rank \(1\).

Complex multiplication

The elliptic curves in class 272832.k do not have complex multiplication.

Modular form 272832.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{3} - 3 q^{5} + q^{9} - 3 q^{13} + 3 q^{15} + 4 q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display