Properties

Label 7728m
Number of curves $1$
Conductor $7728$
CM no
Rank $1$

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Show commands for: SageMath
sage: E = EllipticCurve("m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7728m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7728.j1 7728m1 \([0, -1, 0, 145536, -14389248]\) \(83228502970940543/69854999176704\) \(-286126076627779584\) \([]\) \(95040\) \(2.0373\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 7728m1 has rank \(1\).

Complex multiplication

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

Modular form 7728.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{3} + 3q^{5} + q^{7} + q^{9} - 4q^{11} - 3q^{13} - 3q^{15} - 4q^{17} + O(q^{20})\)  Toggle raw display