# Properties

 Label 154.c Number of curves $4$ Conductor $154$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 154.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
154.c1 154b3 $$[1, -1, 1, -5164, -141529]$$ $$15226621995131793/2324168$$ $$2324168$$ $$$$ $$96$$ $$0.62717$$
154.c2 154b4 $$[1, -1, 1, -604, 2343]$$ $$24331017010833/12004097336$$ $$12004097336$$ $$$$ $$96$$ $$0.62717$$
154.c3 154b2 $$[1, -1, 1, -324, -2137]$$ $$3750606459153/45914176$$ $$45914176$$ $$[2, 2]$$ $$48$$ $$0.28060$$
154.c4 154b1 $$[1, -1, 1, -4, -89]$$ $$-5545233/3469312$$ $$-3469312$$ $$$$ $$24$$ $$-0.065974$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 154.c have rank $$0$$.

## Complex multiplication

The elliptic curves in class 154.c do not have complex multiplication.

## Modular form154.2.a.c

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + 2 q^{5} - q^{7} + q^{8} - 3 q^{9} + 2 q^{10} - q^{11} + 2 q^{13} - q^{14} + q^{16} + 2 q^{17} - 3 q^{18} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 