# Properties

 Label 283920.gm Number of curves $4$ Conductor $283920$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("gm1")

sage: E.isogeny_class()

## Elliptic curves in class 283920.gm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
283920.gm1 283920gm4 [0, 1, 0, -1010000, -391024620]  3538944
283920.gm2 283920gm2 [0, 1, 0, -63600, -6029100] [2, 2] 1769472
283920.gm3 283920gm1 [0, 1, 0, -9520, 222548]  884736 $$\Gamma_0(N)$$-optimal
283920.gm4 283920gm3 [0, 1, 0, 17520, -20273772]  3538944

## Rank

sage: E.rank()

The elliptic curves in class 283920.gm have rank $$0$$.

## Complex multiplication

The elliptic curves in class 283920.gm do not have complex multiplication.

## Modular form 283920.2.a.gm

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} - q^{7} + q^{9} - 4q^{11} + q^{15} - 6q^{17} + O(q^{20})$$

## 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. 