# Properties

 Label 405600bc Number of curves $1$ Conductor $405600$ CM no Rank $1$

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bc1")

sage: E.isogeny_class()

## Elliptic curves in class 405600bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
405600.bc1 405600bc1 $$[0, -1, 0, -140833, 8918239537]$$ $$-1600/177957$$ $$-34358577968520000000000$$ $$[]$$ $$38707200$$ $$3.0032$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 405600bc1 has rank $$1$$.

## Complex multiplication

The elliptic curves in class 405600bc do not have complex multiplication.

## Modular form 405600.2.a.bc

sage: E.q_eigenform(10)

$$q - q^{3} - 3q^{7} + q^{9} + 5q^{11} + 5q^{17} + 4q^{19} + O(q^{20})$$