Properties

Label 5184.s
Number of curves $1$
Conductor $5184$
CM no
Rank $1$

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Show commands: SageMath
sage: E = EllipticCurve("s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5184.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5184.s1 5184e1 \([0, 0, 0, -12, -8]\) \(2304\) \(82944\) \([]\) \(384\) \(-0.36001\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5184.s1 has rank \(1\).

Complex multiplication

The elliptic curves in class 5184.s do not have complex multiplication.

Modular form 5184.2.a.s

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