# Properties

 Label 72600n Number of curves 4 Conductor 72600 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("72600.ce1")

sage: E.isogeny_class()

## Elliptic curves in class 72600n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
72600.ce4 72600n1 [0, -1, 0, 2017, -955788]  368640 $$\Gamma_0(N)$$-optimal
72600.ce3 72600n2 [0, -1, 0, -134108, -18379788] [2, 2] 737280
72600.ce2 72600n3 [0, -1, 0, -315608, 42241212]  1474560
72600.ce1 72600n4 [0, -1, 0, -2130608, -1196314788]  1474560

## Rank

sage: E.rank()

The elliptic curves in class 72600n have rank $$0$$.

## Modular form 72600.2.a.ce

sage: E.q_eigenform(10)

$$q - q^{3} + 4q^{7} + q^{9} + 6q^{13} + 6q^{17} + 8q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels. 