# Properties

 Label 5040bp Number of curves $1$ Conductor $5040$ CM no Rank $1$

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bp1")

sage: E.isogeny_class()

## Elliptic curves in class 5040bp

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 5040bp1 has rank $$1$$.

## Complex multiplication

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

## Modular form5040.2.a.bp

sage: E.q_eigenform(10)

$$q + q^{5} + q^{7} - 5q^{11} - 3q^{13} + q^{17} - 6q^{19} + O(q^{20})$$