# Properties

 Label 139650.bt Number of curves $1$ Conductor $139650$ CM no Rank $1$

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bt1")

sage: E.isogeny_class()

## Elliptic curves in class 139650.bt

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139650.bt1 139650ic1 $$[1, 1, 0, -294515, 360089325]$$ $$-560087524907/10788274176$$ $$-54418222038319104000$$ $$[]$$ $$4290048$$ $$2.4679$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 139650.bt1 has rank $$1$$.

## Complex multiplication

The elliptic curves in class 139650.bt do not have complex multiplication.

## Modular form 139650.2.a.bt

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} + 3 q^{11} - q^{12} + 5 q^{13} + q^{16} - 4 q^{17} - q^{18} - q^{19} + O(q^{20})$$