# Properties

 Label 490.h Number of curves $4$ Conductor $490$ CM no Rank $0$ Graph # Learn more

Show commands for: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

## Elliptic curves in class 490.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
490.h1 490h4 $$[1, -1, 1, -13117, 581459]$$ $$2121328796049/120050$$ $$14123762450$$ $$$$ $$768$$ $$1.0119$$
490.h2 490h3 $$[1, -1, 1, -4297, -100229]$$ $$74565301329/5468750$$ $$643392968750$$ $$$$ $$768$$ $$1.0119$$
490.h3 490h2 $$[1, -1, 1, -867, 8159]$$ $$611960049/122500$$ $$14412002500$$ $$[2, 2]$$ $$384$$ $$0.66537$$
490.h4 490h1 $$[1, -1, 1, 113, 711]$$ $$1367631/2800$$ $$-329417200$$ $$$$ $$192$$ $$0.31880$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 490.h have rank $$0$$.

## Complex multiplication

The elliptic curves in class 490.h do not have complex multiplication.

## Modular form490.2.a.h

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{5} + q^{8} - 3q^{9} + q^{10} + 4q^{11} + 6q^{13} + q^{16} - 2q^{17} - 3q^{18} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 