# Properties

 Label 25050.t Number of curves 2 Conductor 25050 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("25050.t1")
sage: E.isogeny_class()

## Elliptic curves in class 25050.t

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
25050.t1 25050p2 [1, 1, 1, -3113, -67969] 2 36864
25050.t2 25050p1 [1, 1, 1, -113, -1969] 2 18432 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 25050.t have rank $$0$$.

## Modular form None

sage: E.q_eigenform(10)
$$q + q^{2} - q^{3} + q^{4} - q^{6} + 4q^{7} + q^{8} + q^{9} - 4q^{11} - q^{12} + 4q^{14} + q^{16} + 4q^{17} + q^{18} - 4q^{19} + O(q^{20})$$

## 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 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.