# Properties

 Label 115920.dh Number of curves $2$ Conductor $115920$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("dh1")

sage: E.isogeny_class()

## Elliptic curves in class 115920.dh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.dh1 115920ei1 $$[0, 0, 0, -496992, -134856601]$$ $$1163923388486385664/4141725$$ $$48309080400$$ $$$$ $$540672$$ $$1.6920$$ $$\Gamma_0(N)$$-optimal
115920.dh2 115920ei2 $$[0, 0, 0, -496767, -134984806]$$ $$-72646456083703504/137231087805$$ $$-25610614530520320$$ $$$$ $$1081344$$ $$2.0386$$

## Rank

sage: E.rank()

The elliptic curves in class 115920.dh have rank $$1$$.

## Complex multiplication

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

## Modular form 115920.2.a.dh

sage: E.q_eigenform(10)

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