Properties

Label 784.a
Number of curves $1$
Conductor $784$
CM no
Rank $1$

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

Elliptic curves in class 784.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
784.a1 784b1 [0, 0, 0, -343, 2401] [] 336 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 784.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 784.a do not have complex multiplication.

Modular form 784.2.a.a

sage: E.q_eigenform(10)
 
\(q - 3q^{3} - q^{5} + 6q^{9} + q^{11} + 2q^{13} + 3q^{15} + 3q^{17} - 5q^{19} + O(q^{20})\)  Toggle raw display