# Properties

 Label 369600.oc Number of curves $4$ Conductor $369600$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("oc1")

sage: E.isogeny_class()

## Elliptic curves in class 369600.oc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.oc1 369600oc4 $$[0, 1, 0, -8132033, -8928503937]$$ $$116158555210501448/4764375$$ $$2439360000000000$$ $$[2]$$ $$9437184$$ $$2.4394$$
369600.oc2 369600oc3 $$[0, 1, 0, -824033, 53280063]$$ $$120861530858888/67523047515$$ $$34571800327680000000$$ $$[2]$$ $$9437184$$ $$2.4394$$
369600.oc3 369600oc2 $$[0, 1, 0, -509033, -139184937]$$ $$227919983840704/1452753225$$ $$92976206400000000$$ $$[2, 2]$$ $$4718592$$ $$2.0928$$
369600.oc4 369600oc1 $$[0, 1, 0, -12908, -4735062]$$ $$-237867017536/9530541405$$ $$-9530541405000000$$ $$[2]$$ $$2359296$$ $$1.7462$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 369600.oc have rank $$0$$.

## Complex multiplication

The elliptic curves in class 369600.oc do not have complex multiplication.

## Modular form 369600.2.a.oc

sage: E.q_eigenform(10)

$$q + q^{3} - q^{7} + q^{9} - q^{11} + 6 q^{13} - 6 q^{17} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.