Properties

Label 445280.f
Number of curves $1$
Conductor $445280$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 445280.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
445280.f1 445280f1 \([0, 0, 0, 49973, -4437554]\) \(15216119352/18184375\) \(-16493941534400000\) \([]\) \(4377600\) \(1.7980\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 445280.f1 has rank \(2\).

Complex multiplication

The elliptic curves in class 445280.f do not have complex multiplication.

Modular form 445280.2.a.f

sage: E.q_eigenform(10)
 
\(q - 3 q^{3} + q^{5} + q^{7} + 6 q^{9} - 3 q^{15} - 3 q^{17} + 3 q^{19} + O(q^{20})\) Copy content Toggle raw display