# Properties

 Label 25200es Number of curves $2$ Conductor $25200$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("es1")

sage: E.isogeny_class()

## Elliptic curves in class 25200es

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25200.ft2 25200es1 $$[0, 0, 0, 88125, -818750]$$ $$2595575/1512$$ $$-44089920000000000$$ $$[]$$ $$207360$$ $$1.8832$$ $$\Gamma_0(N)$$-optimal
25200.ft1 25200es2 $$[0, 0, 0, -1261875, -577268750]$$ $$-7620530425/526848$$ $$-15362887680000000000$$ $$[]$$ $$622080$$ $$2.4325$$

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 25200es do not have complex multiplication.

## Modular form 25200.2.a.es

sage: E.q_eigenform(10)

$$q + q^{7} + 6q^{11} + q^{13} + 3q^{17} + 4q^{19} + O(q^{20})$$ ## 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 Cremona numbering.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels. 