# Properties

 Label 6240.l Number of curves $2$ Conductor $6240$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 6240.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6240.l1 6240g2 $$[0, -1, 0, -40, 40]$$ $$14172488/7605$$ $$3893760$$ $$$$ $$768$$ $$-0.044240$$
6240.l2 6240g1 $$[0, -1, 0, 10, 0]$$ $$1560896/975$$ $$-62400$$ $$$$ $$384$$ $$-0.39081$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 6240.l have rank $$0$$.

## Complex multiplication

The elliptic curves in class 6240.l do not have complex multiplication.

## Modular form6240.2.a.l

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + 2 q^{7} + q^{9} - q^{13} - q^{15} + 4 q^{17} + 2 q^{19} + O(q^{20})$$

## 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. 