# Properties

 Label 39600dv Number of curves $4$ Conductor $39600$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("dv1")

sage: E.isogeny_class()

## Elliptic curves in class 39600dv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
39600.ea4 39600dv1 $$[0, 0, 0, 49200, -15433625]$$ $$72268906496/606436875$$ $$-110523120468750000$$ $$$$ $$221184$$ $$1.9517$$ $$\Gamma_0(N)$$-optimal
39600.ea3 39600dv2 $$[0, 0, 0, -710175, -212111750]$$ $$13584145739344/1195803675$$ $$3486963516300000000$$ $$$$ $$442368$$ $$2.2983$$
39600.ea2 39600dv3 $$[0, 0, 0, -3514800, -2538300125]$$ $$-26348629355659264/24169921875$$ $$-4404968261718750000$$ $$$$ $$663552$$ $$2.5010$$
39600.ea1 39600dv4 $$[0, 0, 0, -56249175, -162376190750]$$ $$6749703004355978704/5671875$$ $$16539187500000000$$ $$$$ $$1327104$$ $$2.8476$$

## Rank

sage: E.rank()

The elliptic curves in class 39600dv have rank $$0$$.

## Complex multiplication

The elliptic curves in class 39600dv do not have complex multiplication.

## Modular form 39600.2.a.dv

sage: E.q_eigenform(10)

$$q + 2q^{7} + q^{11} - 2q^{13} - 2q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 