# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("o1")

sage: E.isogeny_class()

## Elliptic curves in class 6762.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6762.o1 6762k1 $$[1, 0, 1, -4681, 456236]$$ $$-1967079625/14486688$$ $$-83512873469088$$ $$$$ $$15120$$ $$1.3544$$ $$\Gamma_0(N)$$-optimal
6762.o2 6762k2 $$[1, 0, 1, 41624, -11527498]$$ $$1383521234375/10764582912$$ $$-62055678335680512$$ $$[]$$ $$45360$$ $$1.9037$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form6762.2.a.o

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 