# Properties

 Label 303450.hb Number of curves $1$ Conductor $303450$ CM no Rank $1$

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("hb1")

sage: E.isogeny_class()

## Elliptic curves in class 303450.hb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
303450.hb1 303450hb1 $$[1, 0, 0, -22581888, -24991420608]$$ $$18694465225/6858432$$ $$467214434156176875000000$$ $$[]$$ $$67858560$$ $$3.2420$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 303450.hb1 has rank $$1$$.

## Complex multiplication

The elliptic curves in class 303450.hb do not have complex multiplication.

## Modular form 303450.2.a.hb

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} + q^{7} + q^{8} + q^{9} + 4q^{11} + q^{12} - 3q^{13} + q^{14} + q^{16} + q^{18} - 2q^{19} + O(q^{20})$$