# Properties

 Label 14400s Number of curves $2$ Conductor $14400$ CM no Rank $0$ Graph # Learn more

Show commands: SageMath
sage: E = EllipticCurve("s1")

sage: E.isogeny_class()

## Elliptic curves in class 14400s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14400.q2 14400s1 $$[0, 0, 0, -540, -10800]$$ $$-432$$ $$-40310784000$$ $$$$ $$12288$$ $$0.72338$$ $$\Gamma_0(N)$$-optimal
14400.q1 14400s2 $$[0, 0, 0, -11340, -464400]$$ $$1000188$$ $$161243136000$$ $$$$ $$24576$$ $$1.0699$$

## Rank

sage: E.rank()

The elliptic curves in class 14400s have rank $$0$$.

## Complex multiplication

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

## Modular form 14400.2.a.s

sage: E.q_eigenform(10)

$$q - 4q^{7} + 4q^{11} - 4q^{13} + 6q^{17} + 4q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 