Properties

Label 4704b
Number of curves $1$
Conductor $4704$
CM no
Rank $1$

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

Elliptic curves in class 4704b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4704.h1 4704b1 \([0, -1, 0, -653, 6693]\) \(-3136000/27\) \(-265531392\) \([]\) \(1728\) \(0.44143\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4704b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 4704b do not have complex multiplication.

Modular form 4704.2.a.b

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