# Properties

 Label 60840.cb Number of curves 4 Conductor 60840 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("60840.cb1")

sage: E.isogeny_class()

## Elliptic curves in class 60840.cb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
60840.cb1 60840y4 [0, 0, 0, -162747, 25269894] [2] 294912
60840.cb2 60840y2 [0, 0, 0, -10647, 355914] [2, 2] 147456
60840.cb3 60840y1 [0, 0, 0, -3042, -59319] [2] 73728 $$\Gamma_0(N)$$-optimal
60840.cb4 60840y3 [0, 0, 0, 19773, 2016846] [2] 294912

## Rank

sage: E.rank()

The elliptic curves in class 60840.cb have rank $$1$$.

## Modular form 60840.2.a.cb

sage: E.q_eigenform(10)

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

## 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.