Properties

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

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

Elliptic curves in class 5040.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5040.bd1 5040bp1 \([0, 0, 0, 288, 5724]\) \(14155776/84035\) \(-15682947840\) \([]\) \(3360\) \(0.63824\) \(\Gamma_0(N)\)-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)
 
\(q + q^{5} + q^{7} - 5 q^{11} - 3 q^{13} + q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display