# Properties

 Label 91200fm Number of curves $4$ Conductor $91200$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("91200.ef1")

sage: E.isogeny_class()

## Elliptic curves in class 91200fm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
91200.ef4 91200fm1 [0, -1, 0, -16033, -1328063] [2] 442368 $$\Gamma_0(N)$$-optimal
91200.ef3 91200fm2 [0, -1, 0, -304033, -64400063] [2, 2] 884736
91200.ef2 91200fm3 [0, -1, 0, -352033, -42656063] [2] 1769472
91200.ef1 91200fm4 [0, -1, 0, -4864033, -4127360063] [2] 1769472

## Rank

sage: E.rank()

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

## Modular form 91200.2.a.ef

sage: E.q_eigenform(10)

$$q - q^{3} + 4q^{7} + q^{9} - 4q^{11} - 2q^{13} + 2q^{17} - q^{19} + O(q^{20})$$

## 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.