# Properties

 Label 14400bt Number of curves $4$ Conductor $14400$ CM no Rank $2$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bt1")

sage: E.isogeny_class()

## Elliptic curves in class 14400bt

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14400.f3 14400bt1 $$[0, 0, 0, -975, -11500]$$ $$140608/3$$ $$2187000000$$ $$[2]$$ $$8192$$ $$0.58123$$ $$\Gamma_0(N)$$-optimal
14400.f2 14400bt2 $$[0, 0, 0, -2100, 20000]$$ $$21952/9$$ $$419904000000$$ $$[2, 2]$$ $$16384$$ $$0.92780$$
14400.f1 14400bt3 $$[0, 0, 0, -29100, 1910000]$$ $$7301384/3$$ $$1119744000000$$ $$[2]$$ $$32768$$ $$1.2744$$
14400.f4 14400bt4 $$[0, 0, 0, 6900, 146000]$$ $$97336/81$$ $$-30233088000000$$ $$[2]$$ $$32768$$ $$1.2744$$

## Rank

sage: E.rank()

The elliptic curves in class 14400bt have rank $$2$$.

## Complex multiplication

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

## Modular form 14400.2.a.bt

sage: E.q_eigenform(10)

$$q - 4q^{7} - 4q^{11} - 2q^{13} - 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.