# Properties

 Label 39600.bl Number of curves 3 Conductor 39600 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("39600.bl1")

sage: E.isogeny_class()

## Elliptic curves in class 39600.bl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
39600.bl1 39600dy3 [0, 0, 0, -28153200, -57496282000] [] 840000
39600.bl2 39600dy2 [0, 0, 0, -37200, -5002000] [] 168000
39600.bl3 39600dy1 [0, 0, 0, -1200, 38000] [] 33600 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 39600.bl have rank $$0$$.

## Modular form 39600.2.a.bl

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 