# Properties

 Label 2576.d Number of curves $2$ Conductor $2576$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 2576.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2576.d1 2576e2 $$[0, 1, 0, -488, -4316]$$ $$12576878500/1127$$ $$1154048$$ $$$$ $$640$$ $$0.20324$$
2576.d2 2576e1 $$[0, 1, 0, -28, -84]$$ $$-9826000/3703$$ $$-947968$$ $$$$ $$320$$ $$-0.14333$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 2576.d have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2576.d do not have complex multiplication.

## Modular form2576.2.a.d

sage: E.q_eigenform(10)

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