# Properties

 Label 102550.t Number of curves 2 Conductor 102550 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("102550.t1")

sage: E.isogeny_class()

## Elliptic curves in class 102550.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
102550.t1 102550w2 [1, -1, 1, -4779430, 4022918197]  1971200
102550.t2 102550w1 [1, -1, 1, -299430, 62598197]  985600 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 102550.t have rank $$1$$.

## Modular form 102550.2.a.t

sage: E.q_eigenform(10)

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

## 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 LMFDB 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 LMFDB labels. 