# Properties

 Label 369600ov Number of curves $4$ Conductor $369600$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("ov1")

sage: E.isogeny_class()

## Elliptic curves in class 369600ov

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.ov4 369600ov1 $$[0, 1, 0, -7516993, 7930071743]$$ $$1433528304665250149/162339408$$ $$5319537721344000$$ $$[2]$$ $$7372800$$ $$2.4414$$ $$\Gamma_0(N)$$-optimal
369600.ov3 369600ov2 $$[0, 1, 0, -7536193, 7887505343]$$ $$1444540994277943589/15251205665388$$ $$499751507243433984000$$ $$[2]$$ $$14745600$$ $$2.7880$$
369600.ov2 369600ov3 $$[0, 1, 0, -27774593, -48029603457]$$ $$72313087342699809269/11447096545640448$$ $$375098459607546200064000$$ $$[2]$$ $$36864000$$ $$3.2462$$
369600.ov1 369600ov4 $$[0, 1, 0, -425905793, -3383174665857]$$ $$260744057755293612689909/8504954620259328$$ $$278690352996657659904000$$ $$[2]$$ $$73728000$$ $$3.5927$$

## Rank

sage: E.rank()

The elliptic curves in class 369600ov have rank $$1$$.

## Complex multiplication

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

## Modular form 369600.2.a.ov

sage: E.q_eigenform(10)

$$q + q^{3} - q^{7} + q^{9} + q^{11} - 4 q^{13} - 2 q^{17} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.