# Properties

 Label 6762.bc Number of curves $4$ Conductor $6762$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bc1")

sage: E.isogeny_class()

## Elliptic curves in class 6762.bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6762.bc1 6762bb4 $$[1, 1, 1, -8763602, 9981900641]$$ $$632678989847546725777/80515134$$ $$9472524999966$$ $$$$ $$184320$$ $$2.3499$$
6762.bc2 6762bb3 $$[1, 1, 1, -626662, 107865953]$$ $$231331938231569617/90942310746882$$ $$10699271917059920418$$ $$$$ $$184320$$ $$2.3499$$
6762.bc3 6762bb2 $$[1, 1, 1, -547772, 155767961]$$ $$154502321244119857/55101928644$$ $$6482686803037956$$ $$[2, 2]$$ $$92160$$ $$2.0034$$
6762.bc4 6762bb1 $$[1, 1, 1, -29352, 3145113]$$ $$-23771111713777/22848457968$$ $$-2688098231477232$$ $$$$ $$46080$$ $$1.6568$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 6762.bc have rank $$0$$.

## Complex multiplication

The elliptic curves in class 6762.bc do not have complex multiplication.

## Modular form6762.2.a.bc

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} + 2 q^{5} - q^{6} + q^{8} + q^{9} + 2 q^{10} + 4 q^{11} - q^{12} - 2 q^{13} - 2 q^{15} + q^{16} - 6 q^{17} + q^{18} + O(q^{20})$$

## 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. 