# Properties

 Label 58604.g Number of curves $2$ Conductor $58604$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 58604.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58604.g1 58604i2 $$[0, 0, 0, -16415, -67914]$$ $$16241202000/9332687$$ $$281083210972928$$ $$$$ $$138240$$ $$1.4621$$
58604.g2 58604i1 $$[0, 0, 0, -10780, 429093]$$ $$73598976000/336973$$ $$634312583632$$ $$$$ $$69120$$ $$1.1155$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 58604.g have rank $$0$$.

## Complex multiplication

The elliptic curves in class 58604.g do not have complex multiplication.

## Modular form 58604.2.a.g

sage: E.q_eigenform(10)

$$q - 3q^{9} + q^{13} - 6q^{17} + 4q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 