Properties

Label 445280.f
Number of curves 11
Conductor 445280445280
CM no
Rank 22

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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][0, 0, 0, 49973, -4437554] 15216119352/1818437515216119352/18184375 16493941534400000-16493941534400000 [][] 43776004377600 1.79801.7980 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 445280.f1 has rank 22.

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)
 
q3q3+q5+q7+6q93q153q17+3q19+O(q20)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