# Properties

 Label 768.f Number of curves $2$ Conductor $768$ CM no Rank $1$ Graph # Related objects

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

E.isogeny_class()

## Elliptic curves in class 768.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
768.f1 768g2 $$[0, 1, 0, -93, 315]$$ $$2744000/9$$ $$294912$$ $$$$ $$128$$ $$-0.085141$$
768.f2 768g1 $$[0, 1, 0, -3, 9]$$ $$-8000/81$$ $$-41472$$ $$$$ $$64$$ $$-0.43171$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 768.f have rank $$1$$.

## Complex multiplication

The elliptic curves in class 768.f do not have complex multiplication.

## Modular form768.2.a.f

sage: E.q_eigenform(10)

$$q + q^{3} - 4 q^{7} + q^{9} - 4 q^{11} - 4 q^{13} - 2 q^{17} + 4 q^{19} + O(q^{20})$$

## 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. 