# Properties

 Label 25200fi Number of curves $2$ Conductor $25200$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("25200.b1")

sage: E.isogeny_class()

## Elliptic curves in class 25200fi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
25200.b1 25200fi1 [0, 0, 0, -64875, 6156250] [2] 122880 $$\Gamma_0(N)$$-optimal
25200.b2 25200fi2 [0, 0, 0, 25125, 21906250] [2] 245760

## Rank

sage: E.rank()

The elliptic curves in class 25200fi have rank $$0$$.

## Modular form 25200.2.a.b

sage: E.q_eigenform(10)

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

## 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.