# Properties

 Label 2496.f Number of curves $2$ Conductor $2496$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 2496.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2496.f1 2496r2 $$[0, -1, 0, -393, 1449]$$ $$1643032000/767637$$ $$3144241152$$ $$$$ $$1280$$ $$0.51681$$
2496.f2 2496r1 $$[0, -1, 0, -328, 2398]$$ $$61162984000/41067$$ $$2628288$$ $$$$ $$640$$ $$0.17024$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form2496.2.a.f

sage: E.q_eigenform(10)

$$q - q^{3} - 2q^{7} + q^{9} + 4q^{11} - q^{13} - 6q^{17} + 6q^{19} + O(q^{20})$$ ## 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. 