Properties

Label 644a
Number of curves $1$
Conductor $644$
CM no
Rank $1$

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Show commands: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 644a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
644.b1 644a1 \([0, 1, 0, 6, -43]\) \(1257728/55223\) \(-883568\) \([]\) \(48\) \(-0.17923\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 644a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 644a do not have complex multiplication.

Modular form 644.2.a.a

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{5} - q^{7} - 2 q^{9} - 2 q^{11} - q^{13} - 2 q^{15} - 6 q^{19} + O(q^{20})\)  Toggle raw display