# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("cv1")

sage: E.isogeny_class()

## Elliptic curves in class 38640cv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38640.cv1 38640cv1 $$[0, 1, 0, -3920, -91500]$$ $$1626794704081/83462400$$ $$341861990400$$ $$$$ $$73728$$ $$0.97102$$ $$\Gamma_0(N)$$-optimal
38640.cv2 38640cv2 $$[0, 1, 0, 2480, -355180]$$ $$411664745519/13605414480$$ $$-55727777710080$$ $$$$ $$147456$$ $$1.3176$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 38640.2.a.cv

sage: E.q_eigenform(10)

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