# Properties

 Label 50025g Number of curves 2 Conductor 50025 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("50025.c1")
sage: E.isogeny_class()

## Elliptic curves in class 50025g

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
50025.c1 50025g1 [1, 1, 1, -9338, 343406] 2 41472 $$\Gamma_0(N)$$-optimal
50025.c2 50025g2 [1, 1, 1, -8713, 392156] 2 82944

## Rank

sage: E.rank()

The elliptic curves in class 50025g have rank $$1$$.

## Modular form 50025.2.a.c

sage: E.q_eigenform(10)
$$q - q^{2} - q^{3} - q^{4} + q^{6} + 3q^{8} + q^{9} + 2q^{11} + q^{12} - 2q^{13} - q^{16} + 4q^{17} - q^{18} + O(q^{20})$$

## 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. 