# Properties

 Label 19600.bj Number of curves 2 Conductor 19600 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("19600.bj1")

sage: E.isogeny_class()

## Elliptic curves in class 19600.bj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19600.bj1 19600dv2 [0, -1, 0, -83233208, 292303684912] [] 568320
19600.bj2 19600dv1 [0, -1, 0, -3208, -75088] [] 15360 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 19600.bj have rank $$0$$.

## Modular form 19600.2.a.bj

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 37 \\ 37 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 