# Properties

 Label 25200bf Number of curves $4$ Conductor $25200$ CM no Rank $2$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bf1")

sage: E.isogeny_class()

## Elliptic curves in class 25200bf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25200.l4 25200bf1 $$[0, 0, 0, 225, 6750]$$ $$432/7$$ $$-20412000000$$ $$[2]$$ $$16384$$ $$0.65884$$ $$\Gamma_0(N)$$-optimal
25200.l3 25200bf2 $$[0, 0, 0, -4275, 101250]$$ $$740772/49$$ $$571536000000$$ $$[2, 2]$$ $$32768$$ $$1.0054$$
25200.l2 25200bf3 $$[0, 0, 0, -13275, -465750]$$ $$11090466/2401$$ $$56010528000000$$ $$[2]$$ $$65536$$ $$1.3520$$
25200.l1 25200bf4 $$[0, 0, 0, -67275, 6716250]$$ $$1443468546/7$$ $$163296000000$$ $$[2]$$ $$65536$$ $$1.3520$$

## Rank

sage: E.rank()

The elliptic curves in class 25200bf have rank $$2$$.

## Complex multiplication

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

## Modular form 25200.2.a.bf

sage: E.q_eigenform(10)

$$q - q^{7} - 4q^{11} - 2q^{13} - 6q^{17} - 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.