Properties

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

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 2240.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2240.b1 2240v1 \([0, 0, 0, 2, -2]\) \(13824/35\) \(-2240\) \([]\) \(192\) \(-0.67336\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 2240.b1 has rank \(1\).

Complex multiplication

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

Modular form 2240.2.a.b

sage: E.q_eigenform(10)
 
\(q - 3 q^{3} - q^{5} + q^{7} + 6 q^{9} - 3 q^{11} - q^{13} + 3 q^{15} - q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display