# Properties

 Label 115920p Number of curves $4$ Conductor $115920$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("p1")

sage: E.isogeny_class()

## Elliptic curves in class 115920p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.g4 115920p1 $$[0, 0, 0, -9183, -21922]$$ $$458891455696/264449745$$ $$49352669210880$$ $$$$ $$245760$$ $$1.3171$$ $$\Gamma_0(N)$$-optimal
115920.g2 115920p2 $$[0, 0, 0, -104403, -12952798]$$ $$168591300897604/472410225$$ $$352652343321600$$ $$[2, 2]$$ $$491520$$ $$1.6636$$
115920.g3 115920p3 $$[0, 0, 0, -63003, -23327638]$$ $$-18524646126002/146738831715$$ $$-219079901839841280$$ $$$$ $$983040$$ $$2.0102$$
115920.g1 115920p4 $$[0, 0, 0, -1669323, -830154022]$$ $$344577854816148242/2716875$$ $$4056272640000$$ $$$$ $$983040$$ $$2.0102$$

## Rank

sage: E.rank()

The elliptic curves in class 115920p have rank $$0$$.

## Complex multiplication

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

## Modular form 115920.2.a.p

sage: E.q_eigenform(10)

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