# Properties

 Label 115920.bh Number of curves $2$ Conductor $115920$ CM no Rank $2$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 115920.bh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.bh1 115920dl2 $$[0, 0, 0, -573123, 166896322]$$ $$6972359126281921/5071500000$$ $$15143417856000000$$ $$$$ $$1474560$$ $$2.0393$$
115920.bh2 115920dl1 $$[0, 0, 0, -43203, 1455298]$$ $$2986606123201/1421952000$$ $$4245925920768000$$ $$$$ $$737280$$ $$1.6927$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 115920.bh have rank $$2$$.

## Complex multiplication

The elliptic curves in class 115920.bh do not have complex multiplication.

## Modular form 115920.2.a.bh

sage: E.q_eigenform(10)

$$q - q^{5} + q^{7} - 2q^{11} - 6q^{13} - 4q^{17} + 2q^{19} + O(q^{20})$$ ## 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 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. 