Properties

Label 28224.z
Number of curves $1$
Conductor $28224$
CM no
Rank $1$

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Show commands: SageMath
sage: E = EllipticCurve("z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 28224.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28224.z1 28224ed1 \([0, 0, 0, 756, 3024]\) \(1512\) \(-31603654656\) \([]\) \(23040\) \(0.70350\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 28224.z1 has rank \(1\).

Complex multiplication

The elliptic curves in class 28224.z do not have complex multiplication.

Modular form 28224.2.a.z

sage: E.q_eigenform(10)
 
\(q - 3q^{5} + 5q^{11} + 2q^{13} + 2q^{17} + 6q^{19} + O(q^{20})\)  Toggle raw display