# Properties

 Label 546c Number of curves $4$ Conductor $546$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 546c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
546.b3 546c1 $$[1, 0, 1, -57, -164]$$ $$19968681097/628992$$ $$628992$$ $$$$ $$96$$ $$-0.11250$$ $$\Gamma_0(N)$$-optimal
546.b2 546c2 $$[1, 0, 1, -137, 380]$$ $$281397674377/96589584$$ $$96589584$$ $$[2, 2]$$ $$192$$ $$0.23407$$
546.b1 546c3 $$[1, 0, 1, -1957, 33140]$$ $$828279937799497/193444524$$ $$193444524$$ $$$$ $$384$$ $$0.58064$$
546.b4 546c4 $$[1, 0, 1, 403, 2756]$$ $$7264187703863/7406095788$$ $$-7406095788$$ $$$$ $$384$$ $$0.58064$$

## Rank

sage: E.rank()

The elliptic curves in class 546c have rank $$1$$.

## Complex multiplication

The elliptic curves in class 546c do not have complex multiplication.

## Modular form546.2.a.c

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - 2q^{5} - q^{6} - q^{7} - q^{8} + q^{9} + 2q^{10} - 4q^{11} + q^{12} + q^{13} + q^{14} - 2q^{15} + q^{16} - 2q^{17} - q^{18} - 4q^{19} + O(q^{20})$$ ## 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 Cremona 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 Cremona labels. 