# Properties

 Label 6762.m Number of curves $2$ Conductor $6762$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 6762.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6762.m1 6762t2 $$[1, 0, 1, -12262962, -16528997180]$$ $$1733490909744055732873/99355964553216$$ $$11689129873721309184$$ $$$$ $$405504$$ $$2.7224$$
6762.m2 6762t1 $$[1, 0, 1, -722482, -289233724]$$ $$-354499561600764553/101902222098432$$ $$-11988694527658426368$$ $$$$ $$202752$$ $$2.3759$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form6762.2.a.m

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - 2 q^{5} - q^{6} - q^{8} + q^{9} + 2 q^{10} - 4 q^{11} + q^{12} + 4 q^{13} - 2 q^{15} + q^{16} + 4 q^{17} - q^{18} + 2 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 