# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 912.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
912.c1 912e3 $$[0, -1, 0, -6848, 220416]$$ $$8671983378625/82308$$ $$337133568$$ $$$$ $$864$$ $$0.79865$$
912.c2 912e4 $$[0, -1, 0, -6688, 231040]$$ $$-8078253774625/846825858$$ $$-3468598714368$$ $$$$ $$1728$$ $$1.1452$$
912.c3 912e1 $$[0, -1, 0, -128, 0]$$ $$57066625/32832$$ $$134479872$$ $$$$ $$288$$ $$0.24934$$ $$\Gamma_0(N)$$-optimal
912.c4 912e2 $$[0, -1, 0, 512, -512]$$ $$3616805375/2105352$$ $$-8623521792$$ $$$$ $$576$$ $$0.59592$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form912.2.a.c

sage: E.q_eigenform(10)

$$q - q^{3} + 4 q^{7} + q^{9} - 4 q^{13} + 6 q^{17} - q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 