# Properties

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

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

sage: E.isogeny_class()

## Elliptic curves in class 91200.cf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
91200.cf1 91200x4 $$[0, -1, 0, -993633, -380344863]$$ $$26487576322129/44531250$$ $$182400000000000000$$ $$$$ $$1179648$$ $$2.2074$$
91200.cf2 91200x2 $$[0, -1, 0, -81633, -1864863]$$ $$14688124849/8122500$$ $$33269760000000000$$ $$[2, 2]$$ $$589824$$ $$1.8608$$
91200.cf3 91200x1 $$[0, -1, 0, -49633, 4247137]$$ $$3301293169/22800$$ $$93388800000000$$ $$$$ $$294912$$ $$1.5142$$ $$\Gamma_0(N)$$-optimal
91200.cf4 91200x3 $$[0, -1, 0, 318367, -15064863]$$ $$871257511151/527800050$$ $$-2161869004800000000$$ $$$$ $$1179648$$ $$2.2074$$

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 91200.cf do not have complex multiplication.

## 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 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. 