# Properties

 Label 2760.d Number of curves $4$ Conductor $2760$ CM no Rank $0$ Graph # Related objects

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

E.isogeny_class()

## Elliptic curves in class 2760.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2760.d1 2760a3 $$[0, -1, 0, -2456, 47676]$$ $$1600610497636/9315$$ $$9538560$$ $$$$ $$1792$$ $$0.52925$$
2760.d2 2760a2 $$[0, -1, 0, -156, 756]$$ $$1650587344/119025$$ $$30470400$$ $$[2, 2]$$ $$896$$ $$0.18267$$
2760.d3 2760a1 $$[0, -1, 0, -31, -44]$$ $$212629504/43125$$ $$690000$$ $$$$ $$448$$ $$-0.16390$$ $$\Gamma_0(N)$$-optimal
2760.d4 2760a4 $$[0, -1, 0, 144, 3036]$$ $$320251964/4197615$$ $$-4298357760$$ $$$$ $$1792$$ $$0.52925$$

## Rank

sage: E.rank()

The elliptic curves in class 2760.d have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2760.d do not have complex multiplication.

## Modular form2760.2.a.d

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + 4 q^{7} + q^{9} + 4 q^{11} + 6 q^{13} + q^{15} - 2 q^{17} + 4 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 