# Properties

 Label 15210.bc Number of curves $2$ Conductor $15210$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bc1")

sage: E.isogeny_class()

## Elliptic curves in class 15210.bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15210.bc1 15210bh2 $$[1, -1, 1, -69998, 6403011]$$ $$10779215329/1232010$$ $$4335127500989610$$ $$$$ $$129024$$ $$1.7327$$
15210.bc2 15210bh1 $$[1, -1, 1, 6052, 501531]$$ $$6967871/35100$$ $$-123507906011100$$ $$$$ $$64512$$ $$1.3862$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 15210.bc have rank $$1$$.

## Complex multiplication

The elliptic curves in class 15210.bc do not have complex multiplication.

## Modular form 15210.2.a.bc

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} - 2q^{7} + q^{8} - q^{10} + 4q^{11} - 2q^{14} + q^{16} - 8q^{17} + 6q^{19} + O(q^{20})$$ ## 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 LMFDB 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 LMFDB labels. 