# Properties

 Label 2496v Number of curves $2$ Conductor $2496$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("v1")

sage: E.isogeny_class()

## Elliptic curves in class 2496v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2496.o2 2496v1 $$[0, -1, 0, -21, -27]$$ $$1048576/117$$ $$119808$$ $$[2]$$ $$384$$ $$-0.29253$$ $$\Gamma_0(N)$$-optimal
2496.o1 2496v2 $$[0, -1, 0, -81, 273]$$ $$3631696/507$$ $$8306688$$ $$[2]$$ $$768$$ $$0.054047$$

## Rank

sage: E.rank()

The elliptic curves in class 2496v have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2496v do not have complex multiplication.

## Modular form2496.2.a.v

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.