# Properties

 Label 76664.k Number of curves $2$ Conductor $76664$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

## Elliptic curves in class 76664.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
76664.k1 76664k2 $$[0, -1, 0, -55216, -4915572]$$ $$3543122/49$$ $$257475776595968$$ $$$$ $$405504$$ $$1.5708$$
76664.k2 76664k1 $$[0, -1, 0, -456, -206212]$$ $$-4/7$$ $$-18391126899712$$ $$$$ $$202752$$ $$1.2242$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 76664.k have rank $$1$$.

## Complex multiplication

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

## Modular form 76664.2.a.k

sage: E.q_eigenform(10)

$$q + 2q^{3} + 4q^{5} + q^{7} + q^{9} + 8q^{15} + 2q^{17} + 2q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 