# Properties

 Label 14400.j Number of curves $4$ Conductor $14400$ CM no Rank $0$ Graph # Learn more

Show commands for: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

## Elliptic curves in class 14400.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14400.j1 14400bu3 $$[0, 0, 0, -446700, -63974000]$$ $$26410345352/10546875$$ $$3936600000000000000$$ $$$$ $$294912$$ $$2.2662$$
14400.j2 14400bu2 $$[0, 0, 0, -203700, 34684000]$$ $$20034997696/455625$$ $$21257640000000000$$ $$[2, 2]$$ $$147456$$ $$1.9197$$
14400.j3 14400bu1 $$[0, 0, 0, -202575, 35093500]$$ $$1261112198464/675$$ $$492075000000$$ $$$$ $$73728$$ $$1.5731$$ $$\Gamma_0(N)$$-optimal
14400.j4 14400bu4 $$[0, 0, 0, 21300, 107134000]$$ $$2863288/13286025$$ $$-4958982259200000000$$ $$$$ $$294912$$ $$2.2662$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 14400.2.a.j

sage: E.q_eigenform(10)

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