# Properties

 Label 6240.v Number of curves $4$ Conductor $6240$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("v1")

sage: E.isogeny_class()

## Elliptic curves in class 6240.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6240.v1 6240l2 $$[0, 1, 0, -25625841, -49938972705]$$ $$454357982636417669333824/3003024375$$ $$12300387840000$$ $$[2]$$ $$215040$$ $$2.5707$$
6240.v2 6240l3 $$[0, 1, 0, -1711496, -667563336]$$ $$1082883335268084577352/251301565117746585$$ $$128666401340286251520$$ $$[2]$$ $$215040$$ $$2.5707$$
6240.v3 6240l1 $$[0, 1, 0, -1601646, -780664896]$$ $$7099759044484031233216/577161945398025$$ $$36938364505473600$$ $$[2, 2]$$ $$107520$$ $$2.2241$$ $$\Gamma_0(N)$$-optimal
6240.v4 6240l4 $$[0, 1, 0, -1492296, -891720756]$$ $$-717825640026599866952/254764560814329735$$ $$-130439455136936824320$$ $$[2]$$ $$215040$$ $$2.5707$$

## Rank

sage: E.rank()

The elliptic curves in class 6240.v have rank $$1$$.

## Complex multiplication

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

## Modular form6240.2.a.v

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + q^{9} + 4 q^{11} + q^{13} - q^{15} - 2 q^{17} - 4 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.