# Properties

 Label 11550z Number of curves 4 Conductor 11550 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("11550.bd1")

sage: E.isogeny_class()

## Elliptic curves in class 11550z

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11550.bd3 11550z1 [1, 0, 1, -12526, -469552]  36864 $$\Gamma_0(N)$$-optimal
11550.bd2 11550z2 [1, 0, 1, -53026, 4228448] [2, 2] 73728
11550.bd1 11550z3 [1, 0, 1, -824776, 288232448]  147456
11550.bd4 11550z4 [1, 0, 1, 70724, 21058448]  147456

## Rank

sage: E.rank()

The elliptic curves in class 11550z have rank $$1$$.

## Modular form 11550.2.a.bd

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{6} + q^{7} - q^{8} + q^{9} - q^{11} + q^{12} - 2q^{13} - q^{14} + q^{16} - 2q^{17} - q^{18} + 4q^{19} + O(q^{20})$$

## 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. 