# Properties

 Label 7220.b Number of curves $2$ Conductor $7220$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 7220.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7220.b1 7220d1 $$[0, 1, 0, -332601, -68967860]$$ $$5405726654464/407253125$$ $$306553312890050000$$ $$$$ $$86400$$ $$2.1006$$ $$\Gamma_0(N)$$-optimal
7220.b2 7220d2 $$[0, 1, 0, 319004, -305630796]$$ $$298091207216/3525390625$$ $$-42458907602500000000$$ $$$$ $$172800$$ $$2.4472$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form7220.2.a.b

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 