# Properties

 Label 235200co Number of curves $4$ Conductor $235200$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("co1")

sage: E.isogeny_class()

## Elliptic curves in class 235200co

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235200.co4 235200co1 $$[0, -1, 0, -1960191508, 32993938276762]$$ $$7079962908642659949376/100085966990454375$$ $$11775013930459966764375000000$$ $$[2]$$ $$247726080$$ $$4.1911$$ $$\Gamma_0(N)$$-optimal
235200.co2 235200co2 $$[0, -1, 0, -31255876633, 2126903032586137]$$ $$448487713888272974160064/91549016015625$$ $$689321611854225000000000000$$ $$[2, 2]$$ $$495452160$$ $$4.5377$$
235200.co1 235200co3 $$[0, -1, 0, -500094001633, 136121307995711137]$$ $$229625675762164624948320008/9568125$$ $$576348333120000000000$$ $$[2]$$ $$990904320$$ $$4.8842$$
235200.co3 235200co4 $$[0, -1, 0, -31148713633, 2142211374299137]$$ $$-55486311952875723077768/801237030029296875$$ $$-48263544497109375000000000000000$$ $$[2]$$ $$990904320$$ $$4.8842$$

## Rank

sage: E.rank()

The elliptic curves in class 235200co have rank $$1$$.

## Complex multiplication

The elliptic curves in class 235200co do not have complex multiplication.

## Modular form 235200.2.a.co

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} - 4q^{11} + 6q^{13} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.