Properties

Label 1840.b
Number of curves $1$
Conductor $1840$
CM no
Rank $1$

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

Elliptic curves in class 1840.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1840.b1 1840a1 \([0, -1, 0, 4, -5]\) \(340736/575\) \(-9200\) \([]\) \(64\) \(-0.55442\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1840.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1840.b do not have complex multiplication.

Modular form 1840.2.a.b

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