Properties

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

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Show commands: SageMath
E = EllipticCurve("ef1")
 
E.isogeny_class()
 

Elliptic curves in class 28224.ef

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28224.ef1 28224em1 \([0, 0, 0, 112308, -1346128]\) \(2731405432/1594323\) \(-91442045985325056\) \([]\) \(199680\) \(1.9440\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 28224.ef1 has rank \(1\).

Complex multiplication

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

Modular form 28224.2.a.ef

sage: E.q_eigenform(10)
 
\(q + q^{5} - q^{11} + 8 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display