# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("du1")

sage: E.isogeny_class()

## Elliptic curves in class 115920.du

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.du1 115920bl1 $$[0, 0, 0, -20658567, 36140450726]$$ $$5224645130090610708304/67370009765625$$ $$12572860702500000000$$ $$$$ $$6881280$$ $$2.8100$$ $$\Gamma_0(N)$$-optimal
115920.du2 115920bl2 $$[0, 0, 0, -20096067, 38201338226]$$ $$-1202345928696155427076/148724718496003125$$ $$-111022407458392348800000$$ $$$$ $$13762560$$ $$3.1566$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 115920.2.a.du

sage: E.q_eigenform(10)

$$q + q^{5} - q^{7} + 6 q^{11} - 4 q^{13} - 2 q^{17} + 8 q^{19} + O(q^{20})$$ ## 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. 