# Properties

 Label 14400co Number of curves $2$ Conductor $14400$ CM no Rank $1$ Graph # Learn more

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

sage: E.isogeny_class()

## Elliptic curves in class 14400co

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14400.h1 14400co1 $$[0, 0, 0, -480, -3800]$$ $$131072/9$$ $$839808000$$ $$$$ $$6144$$ $$0.46063$$ $$\Gamma_0(N)$$-optimal
14400.h2 14400co2 $$[0, 0, 0, 420, -16400]$$ $$5488/81$$ $$-120932352000$$ $$$$ $$12288$$ $$0.80720$$

## Rank

sage: E.rank()

The elliptic curves in class 14400co have rank $$1$$.

## Complex multiplication

The elliptic curves in class 14400co do not have complex multiplication.

## Modular form 14400.2.a.co

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 