# Properties

 Label 38640.a Number of curves $2$ Conductor $38640$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 38640.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38640.a1 38640e1 $$[0, -1, 0, -2295396, -1337770080]$$ $$5224645130090610708304/67370009765625$$ $$17246722500000000$$ $$$$ $$860160$$ $$2.2607$$ $$\Gamma_0(N)$$-optimal
38640.a2 38640e2 $$[0, -1, 0, -2232896, -1414120080]$$ $$-1202345928696155427076/148724718496003125$$ $$-152294111739907200000$$ $$$$ $$1720320$$ $$2.6073$$

## Rank

sage: E.rank()

The elliptic curves in class 38640.a have rank $$0$$.

## Complex multiplication

The elliptic curves in class 38640.a do not have complex multiplication.

## Modular form 38640.2.a.a

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} - q^{7} + q^{9} - 6q^{11} - 4q^{13} + q^{15} + 2q^{17} + 8q^{19} + O(q^{20})$$ ## 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. 