Properties

Label 5040.bd
Number of curves $1$
Conductor $5040$
CM no
Rank $1$

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Show commands for: SageMath
sage: E = EllipticCurve("bd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5040.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5040.bd1 5040bp1 [0, 0, 0, 288, 5724] [] 3360 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5040.bd1 has rank \(1\).

Complex multiplication

The elliptic curves in class 5040.bd do not have complex multiplication.

Modular form 5040.2.a.bd

sage: E.q_eigenform(10)
 
\( q + q^{5} + q^{7} - 5q^{11} - 3q^{13} + q^{17} - 6q^{19} + O(q^{20}) \)