Properties

Label 67600k
Number of curves $1$
Conductor $67600$
CM no
Rank $1$

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

Elliptic curves in class 67600k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
67600.bd1 67600k1 \([0, -1, 0, -1408, -313]\) \(43264/25\) \(178506250000\) \([]\) \(55296\) \(0.84849\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 67600k1 has rank \(1\).

Complex multiplication

The elliptic curves in class 67600k do not have complex multiplication.

Modular form 67600.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{3} - 3 q^{7} - 2 q^{9} + 3 q^{11} + 3 q^{17} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display