# Properties

 Label 25200j Number of curves $2$ Conductor $25200$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("25200.k1")

sage: E.isogeny_class()

## Elliptic curves in class 25200j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
25200.k1 25200j1 [0, 0, 0, -675, 3250]  18432 $$\Gamma_0(N)$$-optimal
25200.k2 25200j2 [0, 0, 0, 2325, 24250]  36864

## Rank

sage: E.rank()

The elliptic curves in class 25200j have rank $$1$$.

## Modular form 25200.2.a.k

sage: E.q_eigenform(10)

$$q - q^{7} - 4q^{11} - 6q^{13} + 4q^{17} + 2q^{19} + O(q^{20})$$

## 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. 