# Properties

 Label 379050.hv Number of curves $2$ Conductor $379050$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("hv1")

sage: E.isogeny_class()

## Elliptic curves in class 379050.hv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
379050.hv1 379050hv2 $$[1, 1, 1, -126538, 18278231]$$ $$-7620530425/526848$$ $$-15491267695680000$$ $$[]$$ $$4478976$$ $$1.8575$$
379050.hv2 379050hv1 $$[1, 1, 1, 8837, 29681]$$ $$2595575/1512$$ $$-44458357545000$$ $$[]$$ $$1492992$$ $$1.3082$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 379050.hv have rank $$1$$.

## Complex multiplication

The elliptic curves in class 379050.hv do not have complex multiplication.

## Modular form 379050.2.a.hv

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - q^{6} + q^{7} + q^{8} + q^{9} + 6q^{11} - q^{12} + q^{13} + q^{14} + q^{16} + 3q^{17} + q^{18} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.