# Properties

 Label 46800fr Number of curves $2$ Conductor $46800$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("fr1")

sage: E.isogeny_class()

## Elliptic curves in class 46800fr

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.a2 46800fr1 $$[0, 0, 0, -469875, -156748750]$$ $$-9836106385/3407872$$ $$-3974941900800000000$$ $$[]$$ $$1036800$$ $$2.2803$$ $$\Gamma_0(N)$$-optimal
46800.a1 46800fr2 $$[0, 0, 0, -40789875, -100271308750]$$ $$-6434774386429585/140608$$ $$-164005171200000000$$ $$[]$$ $$3110400$$ $$2.8296$$

## Rank

sage: E.rank()

The elliptic curves in class 46800fr have rank $$1$$.

## Complex multiplication

The elliptic curves in class 46800fr do not have complex multiplication.

## Modular form 46800.2.a.fr

sage: E.q_eigenform(10)

$$q - 5q^{7} - 3q^{11} + q^{13} - 3q^{17} + 4q^{19} + O(q^{20})$$ ## 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 Cremona 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 Cremona labels. 