# Properties

 Label 59248bc Number of curves $2$ Conductor $59248$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 59248bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
59248.f2 59248bc1 $$[0, 1, 0, 291832, 285534196]$$ $$4533086375/60669952$$ $$-36787528826500415488$$ $$$$ $$1419264$$ $$2.4351$$ $$\Gamma_0(N)$$-optimal
59248.f1 59248bc2 $$[0, 1, 0, -5125128, 4179245044]$$ $$24553362849625/1755162752$$ $$1064251712847898738688$$ $$$$ $$2838528$$ $$2.7816$$

## Rank

sage: E.rank()

The elliptic curves in class 59248bc have rank $$0$$.

## Complex multiplication

The elliptic curves in class 59248bc do not have complex multiplication.

## Modular form 59248.2.a.bc

sage: E.q_eigenform(10)

$$q - 2q^{3} + q^{7} + q^{9} + 4q^{11} - 6q^{17} - 6q^{19} + O(q^{20})$$ ## 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 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. 