Properties

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

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 4704c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4704.o1 4704c1 \([0, -1, 0, -3544, -81164]\) \(-1668296/27\) \(-79692609024\) \([]\) \(6048\) \(0.89218\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4704c1 has rank \(1\).

Complex multiplication

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

Modular form 4704.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{3} + 3 q^{5} + q^{9} + q^{11} - 4 q^{13} - 3 q^{15} + 4 q^{17} + O(q^{20})\) Copy content Toggle raw display