# Properties

 Label 39600.fb Number of curves 4 Conductor 39600 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("39600.fb1")

sage: E.isogeny_class()

## Elliptic curves in class 39600.fb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
39600.fb1 39600ed4 [0, 0, 0, -527475, 147307250]  393216
39600.fb2 39600ed2 [0, 0, 0, -41475, 1021250] [2, 2] 196608
39600.fb3 39600ed1 [0, 0, 0, -23475, -1372750]  98304 $$\Gamma_0(N)$$-optimal
39600.fb4 39600ed3 [0, 0, 0, 156525, 7951250]  393216

## Rank

sage: E.rank()

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

## Modular form 39600.2.a.fb

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 