Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 644b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
644.a1 644b1 \([0, -1, 0, 2, -7]\) \(32000/1127\) \(-18032\) \([]\) \(24\) \(-0.50341\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 644b1 has rank \(1\).

Complex multiplication

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

Modular form 644.2.a.b

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