Properties

Label 648.a
Number of curves $1$
Conductor $648$
CM no
Rank $1$

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

Elliptic curves in class 648.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
648.a1 648b1 \([0, 0, 0, -3, -1]\) \(2304\) \(1296\) \([]\) \(24\) \(-0.70659\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 648.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 648.a do not have complex multiplication.

Modular form 648.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{5} - 3q^{7} + 5q^{11} - 5q^{13} - 2q^{17} - 4q^{19} + O(q^{20})\)  Toggle raw display