# Properties

 Label 42320z Number of curves 4 Conductor 42320 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("42320.ba1")

sage: E.isogeny_class()

## Elliptic curves in class 42320z

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
42320.ba3 42320z1 [0, -1, 0, -705, 5192]  23760 $$\Gamma_0(N)$$-optimal
42320.ba4 42320z2 [0, -1, 0, 1940, 32700]  47520
42320.ba1 42320z3 [0, -1, 0, -21865, -1236900]  71280
42320.ba2 42320z4 [0, -1, 0, -19220, -1550068]  142560

## Rank

sage: E.rank()

The elliptic curves in class 42320z have rank $$0$$.

## Modular form 42320.2.a.ba

sage: E.q_eigenform(10)

$$q + 2q^{3} + q^{5} + 2q^{7} + q^{9} + 2q^{13} + 2q^{15} + 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 