# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("fh1")

sage: E.isogeny_class()

## Elliptic curves in class 25200fh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25200.da2 25200fh1 $$[0, 0, 0, 3525, -6550]$$ $$2595575/1512$$ $$-2821754880000$$ $$[]$$ $$41472$$ $$1.0785$$ $$\Gamma_0(N)$$-optimal
25200.da1 25200fh2 $$[0, 0, 0, -50475, -4618150]$$ $$-7620530425/526848$$ $$-983224811520000$$ $$[]$$ $$124416$$ $$1.6278$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 25200.2.a.fh

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.