Properties

Label 7728.u
Number of curves $1$
Conductor $7728$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 7728.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7728.u1 7728s1 \([0, 1, 0, -82104, 9072468]\) \(-14943832855786297/85501108224\) \(-350212539285504\) \([]\) \(37440\) \(1.6325\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 7728.u1 has rank \(0\).

Complex multiplication

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

Modular form 7728.2.a.u

sage: E.q_eigenform(10)
 
\(q + q^{3} + 3 q^{5} - q^{7} + q^{9} - 4 q^{11} + 3 q^{13} + 3 q^{15} + O(q^{20})\) Copy content Toggle raw display