# Properties

 Label 388080.dj Number of curves 4 Conductor 388080 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("388080.dj1")

sage: E.isogeny_class()

## Elliptic curves in class 388080.dj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
388080.dj1 388080dj4 [0, 0, 0, -184274643, 935540391058]  95551488
388080.dj2 388080dj2 [0, 0, 0, -25232403, -48351607598]  31850496
388080.dj3 388080dj1 [0, 0, 0, -395283, -1861486382]  15925248 $$\Gamma_0(N)$$-optimal
388080.dj4 388080dj3 [0, 0, 0, 3556077, 50143943122]  47775744

## Rank

sage: E.rank()

The elliptic curves in class 388080.dj have rank $$0$$.

## Modular form 388080.2.a.dj

sage: E.q_eigenform(10)

$$q - q^{5} - q^{11} + 4q^{13} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 