Properties

Label 2240.f
Number of curves $1$
Conductor $2240$
CM no
Rank $1$

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

Elliptic curves in class 2240.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2240.f1 2240a1 \([0, -1, 0, 9, -59]\) \(1124864/21875\) \(-1400000\) \([]\) \(320\) \(-0.14028\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 2240.f1 has rank \(1\).

Complex multiplication

The elliptic curves in class 2240.f do not have complex multiplication.

Modular form 2240.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - q^{7} - 2 q^{9} + 3 q^{11} + 7 q^{13} + q^{15} - 5 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display