# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("dl1")

sage: E.isogeny_class()

## Elliptic curves in class 14400dl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14400.i2 14400dl1 $$[0, 0, 0, -13500, 1350000]$$ $$-432$$ $$-629856000000000$$ $$$$ $$61440$$ $$1.5281$$ $$\Gamma_0(N)$$-optimal
14400.i1 14400dl2 $$[0, 0, 0, -283500, 58050000]$$ $$1000188$$ $$2519424000000000$$ $$$$ $$122880$$ $$1.8747$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 14400.2.a.dl

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. 