Properties

Label 7728.n
Number of curves $1$
Conductor $7728$
CM no
Rank $1$

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Show commands: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7728.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7728.n1 7728f1 \([0, 1, 0, -392, 4116]\) \(-3261064466/1917027\) \(-3926071296\) \([]\) \(4800\) \(0.54347\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 7728.n1 has rank \(1\).

Complex multiplication

The elliptic curves in class 7728.n do not have complex multiplication.

Modular form 7728.2.a.n

sage: E.q_eigenform(10)
 
\(q + q^{3} - 3 q^{5} + q^{7} + q^{9} - q^{13} - 3 q^{15} - 4 q^{17} + O(q^{20})\) Copy content Toggle raw display