# Properties

 Label 76664f Number of curves $2$ Conductor $76664$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 76664f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
76664.c1 76664f1 $$[0, 0, 0, -13690, 455877]$$ $$6912000/1813$$ $$74426591672272$$ $$$$ $$153216$$ $$1.3705$$ $$\Gamma_0(N)$$-optimal
76664.c2 76664f2 $$[0, 0, 0, 34225, 2937874]$$ $$6750000/9583$$ $$-6294363181426432$$ $$$$ $$306432$$ $$1.7171$$

## Rank

sage: E.rank()

The elliptic curves in class 76664f have rank $$0$$.

## Complex multiplication

The elliptic curves in class 76664f do not have complex multiplication.

## Modular form 76664.2.a.f

sage: E.q_eigenform(10)

$$q - q^{7} - 3 q^{9} + 4 q^{11} + 4 q^{17} - 2 q^{19} + O(q^{20})$$ ## 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 Cremona 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 Cremona labels. 