# Properties

 Label 91200ed Number of curves $4$ Conductor $91200$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("91200.ff1")

sage: E.isogeny_class()

## Elliptic curves in class 91200ed

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
91200.ff4 91200ed1 [0, 1, 0, -16033, 1328063] [2] 442368 $$\Gamma_0(N)$$-optimal
91200.ff3 91200ed2 [0, 1, 0, -304033, 64400063] [2, 2] 884736
91200.ff2 91200ed3 [0, 1, 0, -352033, 42656063] [2] 1769472
91200.ff1 91200ed4 [0, 1, 0, -4864033, 4127360063] [2] 1769472

## Rank

sage: E.rank()

The elliptic curves in class 91200ed have rank $$1$$.

## Modular form 91200.2.a.ff

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.