# Properties

 Label 11550m Number of curves $2$ Conductor $11550$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 11550m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11550.g2 11550m1 $$[1, 1, 0, 70, 0]$$ $$296740963/174636$$ $$-21829500$$ $$$$ $$3072$$ $$0.097611$$ $$\Gamma_0(N)$$-optimal
11550.g1 11550m2 $$[1, 1, 0, -280, -350]$$ $$19530306557/11114334$$ $$1389291750$$ $$$$ $$6144$$ $$0.44418$$

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 11550m do not have complex multiplication.

## Modular form 11550.2.a.m

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels. 