# Properties

 Label 76440.ce Number of curves $4$ Conductor $76440$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("ce1")

sage: E.isogeny_class()

## Elliptic curves in class 76440.ce

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
76440.ce1 76440cq4 $$[0, 1, 0, -407696, -100332576]$$ $$31103978031362/195$$ $$46984304640$$ $$[2]$$ $$442368$$ $$1.6533$$
76440.ce2 76440cq3 $$[0, 1, 0, -35296, -262816]$$ $$20183398562/11567205$$ $$2787061966940160$$ $$[2]$$ $$442368$$ $$1.6533$$
76440.ce3 76440cq2 $$[0, 1, 0, -25496, -1572096]$$ $$15214885924/38025$$ $$4580969702400$$ $$[2, 2]$$ $$221184$$ $$1.3068$$
76440.ce4 76440cq1 $$[0, 1, 0, -996, -43296]$$ $$-3631696/24375$$ $$-734129760000$$ $$[2]$$ $$110592$$ $$0.96019$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 76440.ce have rank $$0$$.

## Complex multiplication

The elliptic curves in class 76440.ce do not have complex multiplication.

## Modular form 76440.2.a.ce

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.