# Properties

 Label 115920cz Number of curves $4$ Conductor $115920$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("cz1")

sage: E.isogeny_class()

## Elliptic curves in class 115920cz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.q4 115920cz1 $$[0, 0, 0, 41526717, 187202684482]$$ $$2652277923951208297919/6605028468326400000$$ $$-19722509325967137177600000$$ $$[2]$$ $$29491200$$ $$3.5375$$ $$\Gamma_0(N)$$-optimal
115920.q3 115920cz2 $$[0, 0, 0, -348494403, 2091207788098]$$ $$1567558142704512417614401/274462175610000000000$$ $$819539664976650240000000000$$ $$[2, 2]$$ $$58982400$$ $$3.8841$$
115920.q2 115920cz3 $$[0, 0, 0, -1620832323, -23161900780478]$$ $$157706830105239346386477121/13650704956054687500000$$ $$40760786587500000000000000000$$ $$[2]$$ $$117964800$$ $$4.2306$$
115920.q1 115920cz4 $$[0, 0, 0, -5316494403, 149200642988098]$$ $$5565604209893236690185614401/229307220930246900000$$ $$684707692782182359449600000$$ $$[2]$$ $$117964800$$ $$4.2306$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 115920.2.a.cz

sage: E.q_eigenform(10)

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

## 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.