# Properties

 Label 2496.r Number of curves $2$ Conductor $2496$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("r1")

sage: E.isogeny_class()

## Elliptic curves in class 2496.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2496.r1 2496o2 $$[0, 1, 0, -11609, 477447]$$ $$42246001231552/14414517$$ $$59041861632$$ $$$$ $$3072$$ $$1.0384$$
2496.r2 2496o1 $$[0, 1, 0, -624, 9486]$$ $$-420526439488/390971529$$ $$-25022177856$$ $$$$ $$1536$$ $$0.69180$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 2496.r have rank $$1$$.

## Complex multiplication

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

## Modular form2496.2.a.r

sage: E.q_eigenform(10)

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