# Properties

 Label 51600.cv Number of curves $4$ Conductor $51600$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 51600.cv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51600.cv1 51600db4 $$[0, 1, 0, -26549408, -52658476812]$$ $$32337636827233520089/3023437500000$$ $$193500000000000000000$$ $$[2]$$ $$4423680$$ $$2.9304$$
51600.cv2 51600db3 $$[0, 1, 0, -9781408, 11192787188]$$ $$1617141066657115609/89723013444000$$ $$5742272860416000000000$$ $$[4]$$ $$4423680$$ $$2.9304$$
51600.cv3 51600db2 $$[0, 1, 0, -1781408, -695212812]$$ $$9768641617435609/2396304000000$$ $$153363456000000000000$$ $$[2, 2]$$ $$2211840$$ $$2.5839$$
51600.cv4 51600db1 $$[0, 1, 0, 266592, -68524812]$$ $$32740359775271/50724864000$$ $$-3246391296000000000$$ $$[2]$$ $$1105920$$ $$2.2373$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 51600.cv have rank $$0$$.

## Complex multiplication

The elliptic curves in class 51600.cv do not have complex multiplication.

## Modular form 51600.2.a.cv

sage: E.q_eigenform(10)

$$q + q^{3} + q^{9} - 4q^{11} + 6q^{13} + 6q^{17} + 8q^{19} + O(q^{20})$$

## 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 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.