# Properties

 Label 7220.f Number of curves $4$ Conductor $7220$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 7220.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7220.f1 7220c3 $$[0, -1, 0, -14921, 706370]$$ $$488095744/125$$ $$94091762000$$ $$$$ $$10368$$ $$1.0916$$
7220.f2 7220c4 $$[0, -1, 0, -13116, 881816]$$ $$-20720464/15625$$ $$-188183524000000$$ $$$$ $$20736$$ $$1.4381$$
7220.f3 7220c1 $$[0, -1, 0, -481, -2634]$$ $$16384/5$$ $$3763670480$$ $$$$ $$3456$$ $$0.54227$$ $$\Gamma_0(N)$$-optimal
7220.f4 7220c2 $$[0, -1, 0, 1324, -19240]$$ $$21296/25$$ $$-301093638400$$ $$$$ $$6912$$ $$0.88884$$

## Rank

sage: E.rank()

The elliptic curves in class 7220.f have rank $$1$$.

## Complex multiplication

The elliptic curves in class 7220.f do not have complex multiplication.

## Modular form7220.2.a.f

sage: E.q_eigenform(10)

$$q + 2q^{3} - q^{5} + 2q^{7} + q^{9} - 2q^{13} - 2q^{15} - 6q^{17} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 