# Properties

 Label 62.a Number of curves $4$ Conductor $62$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 62.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62.a1 62a4 $$[1, -1, 1, -331, 2397]$$ $$3999236143617/62$$ $$62$$ $$$$ $$8$$ $$-0.10808$$
62.a2 62a3 $$[1, -1, 1, -31, 5]$$ $$3196010817/1847042$$ $$1847042$$ $$$$ $$8$$ $$-0.10808$$
62.a3 62a2 $$[1, -1, 1, -21, 41]$$ $$979146657/3844$$ $$3844$$ $$[2, 2]$$ $$4$$ $$-0.45465$$
62.a4 62a1 $$[1, -1, 1, -1, 1]$$ $$-35937/496$$ $$-496$$ $$$$ $$2$$ $$-0.80122$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 62.a have rank $$0$$.

## Complex multiplication

The elliptic curves in class 62.a do not have complex multiplication.

## Modular form62.2.a.a

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - 2q^{5} + q^{8} - 3q^{9} - 2q^{10} + 2q^{13} + q^{16} - 6q^{17} - 3q^{18} + 4q^{19} + O(q^{20})$$ ## 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. 