# Properties

 Label 316050ic Number of curves $2$ Conductor $316050$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("ic1")

sage: E.isogeny_class()

## Elliptic curves in class 316050ic

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
316050.ic2 316050ic1 $$[1, 0, 0, -45963, -2549583]$$ $$5841725401/1857600$$ $$3414762225000000$$ $$$$ $$2488320$$ $$1.6844$$ $$\Gamma_0(N)$$-optimal
316050.ic1 316050ic2 $$[1, 0, 0, -290963, 58455417]$$ $$1481933914201/53916840$$ $$99113473580625000$$ $$$$ $$4976640$$ $$2.0310$$

## Rank

sage: E.rank()

The elliptic curves in class 316050ic have rank $$1$$.

## Complex multiplication

The elliptic curves in class 316050ic do not have complex multiplication.

## Modular form 316050.2.a.ic

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} + q^{8} + q^{9} - 2q^{11} + q^{12} - 2q^{13} + q^{16} - 4q^{17} + q^{18} + 6q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 