# Properties

 Label 97020bz Number of curves $2$ Conductor $97020$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bz1")

sage: E.isogeny_class()

## Elliptic curves in class 97020bz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
97020.u1 97020bz1 [0, 0, 0, -273, 1757] [] 31104 $$\Gamma_0(N)$$-optimal
97020.u2 97020bz2 [0, 0, 0, 987, 8813] [] 93312

## Rank

sage: E.rank()

The elliptic curves in class 97020bz have rank $$1$$.

## Complex multiplication

The elliptic curves in class 97020bz do not have complex multiplication.

## Modular form 97020.2.a.bz

sage: E.q_eigenform(10)

$$q - q^{5} + q^{11} - 5q^{13} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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 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.