# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("42320.l1")

sage: E.isogeny_class()

## Elliptic curves in class 42320.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
42320.l1 42320c4 [0, 0, 0, -56603, -5183142]  98560
42320.l2 42320c2 [0, 0, 0, -3703, -73002] [2, 2] 49280
42320.l3 42320c1 [0, 0, 0, -1058, 12167]  24640 $$\Gamma_0(N)$$-optimal
42320.l4 42320c3 [0, 0, 0, 6877, -413678]  98560

## Rank

sage: E.rank()

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

## Modular form 42320.2.a.l

sage: E.q_eigenform(10)

$$q - q^{5} - 4q^{7} - 3q^{9} + 4q^{11} - 2q^{13} - 2q^{17} + 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 