# Properties

 Label 2240.q Number of curves $4$ Conductor $2240$ CM no Rank $0$ Graph # Learn more

Show commands: SageMath
sage: E = EllipticCurve("q1")

sage: E.isogeny_class()

## Elliptic curves in class 2240.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2240.q1 2240y4 $$[0, 0, 0, -17132, 863056]$$ $$2121328796049/120050$$ $$31470387200$$ $$$$ $$3072$$ $$1.0787$$
2240.q2 2240y3 $$[0, 0, 0, -5612, -151216]$$ $$74565301329/5468750$$ $$1433600000000$$ $$$$ $$3072$$ $$1.0787$$
2240.q3 2240y2 $$[0, 0, 0, -1132, 11856]$$ $$611960049/122500$$ $$32112640000$$ $$[2, 2]$$ $$1536$$ $$0.73213$$
2240.q4 2240y1 $$[0, 0, 0, 148, 1104]$$ $$1367631/2800$$ $$-734003200$$ $$$$ $$768$$ $$0.38556$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 2240.q have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2240.q do not have complex multiplication.

## Modular form2240.2.a.q

sage: E.q_eigenform(10)

$$q + q^{5} + q^{7} - 3q^{9} + 4q^{11} + 6q^{13} + 2q^{17} + O(q^{20})$$ ## 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. 