Properties

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

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 4704z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4704.bc1 4704z1 \([0, 1, 0, 3120, 7272]\) \(2731405432/1594323\) \(-1959920395776\) \([]\) \(6240\) \(1.0481\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4704z1 has rank \(1\).

Complex multiplication

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

Modular form 4704.2.a.z

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{9} - q^{11} + q^{15} - 8 q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display