# Properties

 Label 1440.l Number of curves $2$ Conductor $1440$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

## Elliptic curves in class 1440.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1440.l1 1440f1 $$[0, 0, 0, -57, 164]$$ $$438976/5$$ $$233280$$ $$[2]$$ $$192$$ $$-0.15674$$ $$\Gamma_0(N)$$-optimal
1440.l2 1440f2 $$[0, 0, 0, -12, 416]$$ $$-64/25$$ $$-74649600$$ $$[2]$$ $$384$$ $$0.18983$$

## Rank

sage: E.rank()

The elliptic curves in class 1440.l have rank $$1$$.

## Complex multiplication

The elliptic curves in class 1440.l do not have complex multiplication.

## Modular form1440.2.a.l

sage: E.q_eigenform(10)

$$q + q^{5} + 2 q^{7} - 4 q^{11} - 6 q^{13} - 2 q^{17} - 8 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.