# Properties

 Label 116025.bh Number of curves $2$ Conductor $116025$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bh1")

sage: E.isogeny_class()

## Elliptic curves in class 116025.bh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116025.bh1 116025c1 $$[1, 1, 0, -11375, 462000]$$ $$10418796526321/6390657$$ $$99854015625$$ $$$$ $$179200$$ $$1.0534$$ $$\Gamma_0(N)$$-optimal
116025.bh2 116025c2 $$[1, 1, 0, -9250, 642625]$$ $$-5602762882081/8312741073$$ $$-129886579265625$$ $$$$ $$358400$$ $$1.3999$$

## Rank

sage: E.rank()

The elliptic curves in class 116025.bh have rank $$1$$.

## Complex multiplication

The elliptic curves in class 116025.bh do not have complex multiplication.

## Modular form 116025.2.a.bh

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} - q^{4} - q^{6} - q^{7} - 3q^{8} + q^{9} - 4q^{11} + q^{12} - q^{13} - q^{14} - q^{16} - q^{17} + q^{18} + O(q^{20})$$ ## 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 LMFDB 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 LMFDB labels. 