# Properties

 Label 912.k Number of curves $4$ Conductor $912$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 912.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
912.k1 912k3 $$[0, 1, 0, -1400832, 637689780]$$ $$74220219816682217473/16416$$ $$67239936$$ $$$$ $$5760$$ $$1.7946$$
912.k2 912k2 $$[0, 1, 0, -87552, 9941940]$$ $$18120364883707393/269485056$$ $$1103810789376$$ $$[2, 2]$$ $$2880$$ $$1.4480$$
912.k3 912k4 $$[0, 1, 0, -84992, 10553268]$$ $$-16576888679672833/2216253521952$$ $$-9077774425915392$$ $$$$ $$5760$$ $$1.7946$$
912.k4 912k1 $$[0, 1, 0, -5632, 144308]$$ $$4824238966273/537919488$$ $$2203318222848$$ $$$$ $$1440$$ $$1.1014$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 912.k have rank $$0$$.

## Complex multiplication

The elliptic curves in class 912.k do not have complex multiplication.

## Modular form912.2.a.k

sage: E.q_eigenform(10)

$$q + q^{3} + 2q^{5} + q^{9} + 4q^{11} + 2q^{13} + 2q^{15} - 6q^{17} + q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 