# Properties

 Label 91200x Number of curves $4$ Conductor $91200$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("91200.cf1")

sage: E.isogeny_class()

## Elliptic curves in class 91200x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
91200.cf3 91200x1 [0, -1, 0, -49633, 4247137]  294912 $$\Gamma_0(N)$$-optimal
91200.cf2 91200x2 [0, -1, 0, -81633, -1864863] [2, 2] 589824
91200.cf4 91200x3 [0, -1, 0, 318367, -15064863]  1179648
91200.cf1 91200x4 [0, -1, 0, -993633, -380344863]  1179648

## Rank

sage: E.rank()

The elliptic curves in class 91200x have rank $$0$$.

## Modular form 91200.2.a.cf

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} - 4q^{11} + 2q^{13} - 2q^{17} + q^{19} + O(q^{20})$$

## 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. 