# Properties

 Label 14400eg Number of curves $4$ Conductor $14400$ CM no Rank $1$ Graph # Learn more

Show commands: SageMath
sage: E = EllipticCurve("eg1")

sage: E.isogeny_class()

## Elliptic curves in class 14400eg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14400.m4 14400eg1 $$[0, 0, 0, 825, 97000]$$ $$85184/5625$$ $$-4100625000000$$ $$$$ $$24576$$ $$1.0998$$ $$\Gamma_0(N)$$-optimal
14400.m3 14400eg2 $$[0, 0, 0, -27300, 1672000]$$ $$48228544/2025$$ $$94478400000000$$ $$[2, 2]$$ $$49152$$ $$1.4463$$
14400.m2 14400eg3 $$[0, 0, 0, -72300, -5258000]$$ $$111980168/32805$$ $$12244400640000000$$ $$$$ $$98304$$ $$1.7929$$
14400.m1 14400eg4 $$[0, 0, 0, -432300, 109402000]$$ $$23937672968/45$$ $$16796160000000$$ $$$$ $$98304$$ $$1.7929$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 14400.2.a.eg

sage: E.q_eigenform(10)

$$q - 4q^{7} - 2q^{13} - 6q^{17} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 