# Properties

 Label 265200fm Number of curves $2$ Conductor $265200$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("fm1")

sage: E.isogeny_class()

## Elliptic curves in class 265200fm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
265200.fm1 265200fm1 $$[0, 1, 0, -7025408, -7158898812]$$ $$2396726313900986596/4154072495625$$ $$66465159930000000000$$ $$$$ $$8847360$$ $$2.6975$$ $$\Gamma_0(N)$$-optimal
265200.fm2 265200fm2 $$[0, 1, 0, -4828408, -11715476812]$$ $$-389032340685029858/1627263833203125$$ $$-52072442662500000000000$$ $$$$ $$17694720$$ $$3.0441$$

## Rank

sage: E.rank()

The elliptic curves in class 265200fm have rank $$0$$.

## Complex multiplication

The elliptic curves in class 265200fm do not have complex multiplication.

## Modular form 265200.2.a.fm

sage: E.q_eigenform(10)

$$q + q^{3} + q^{9} - 2 q^{11} + q^{13} + q^{17} + 8 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 