# Properties

 Label 182070dm Number of curves $1$ Conductor $182070$ CM no Rank $1$

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("dm1")

sage: E.isogeny_class()

## Elliptic curves in class 182070dm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
182070.q1 182070dm1 $$[1, -1, 0, -236745, -50160425]$$ $$-288568081/47250$$ $$-240281708994605250$$ $$[]$$ $$2643840$$ $$2.0625$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 182070dm1 has rank $$1$$.

## Complex multiplication

The elliptic curves in class 182070dm do not have complex multiplication.

## Modular form 182070.2.a.dm

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{5} - q^{7} - q^{8} + q^{10} + 2q^{11} + 4q^{13} + q^{14} + q^{16} + 6q^{19} + O(q^{20})$$